Unique Spin Dynamics and Unconventional Superconductivity in the Layered Heavy Fermion Comp

The Effects of Mutations on Motions of Side-chains in Protein L Studied by2H NMR Dynamics andScalar CouplingsOscar Millet1†,Anthony Mittermaier1†,David Baker2andLewis E.Kay1*1Protein Engineering Network Center of Excellence and Departments of Medical Genetics,Biochemistry and Chemistry,University of Toronto,1King’s College Circle Toronto,Ont.,Canada M5S1A82Department of Biochemistry University of Washington Seattle,WA98195,USA Recently developed2H spin relaxation experiments are applied to study the dynamics of methyl-containing side-chains in the B1domain of protein L and in a pair of point mutants of the domain,F22L and A20V. X-ray and NMR studies of the three variants of protein L studied here establish that their structures are very similar,despite the fact that the F22L mutant is3.2kcal/mol less stable.Measurements of methyl2H spin relaxation rates,which probe dynamics on a picosecond–nanosecond time scale,and three-bond3J C g–CO,3J C g–N and3J C a–C d scalar coupling constants,which are sensitive to motion spanning a wide range of time-scales,reveal changes in the magnitude of side-chain dynamics in response to mutation.Observed differences in the time-scale of motions between the variants have been related to changes in energetic barriers. Of interest,several of the residues with different motional properties across the variants are far from the site of mutation,suggesting the presence of long-range interactions within the protein that can be probed through studies of dynamics.q2003Elsevier Science Ltd.All rights reserved Keywords:side-chain dynamics;deuterium relaxation;protein stability; site-directed mutagenesis*Corresponding authorIntroductionThe structural and dynamic properties of pro-teins are determined by their primary amino acid sequence.Elucidation of the rules that govern this relationship is of immense practical and intellectual importance.Numerous studies have investigated the consequences of changes in protein primary sequence by characterizing the stability,structure and activity of mutant proteins.1 Far fewer have examined the changes in internal dynamics that accompany amino acid substi-tutions.Conformationalfluctuations modulate distant-dependent energetic interactions,contri-bute to the entropy of functionally relevant states and can guide enzymatic reaction pathways.2–4It is important,therefore,to develop robust methods to study these processes and to understand the relation between protein dynamics and primary sequence.NMR relaxation experiments are sensitive to protein internal dynamics spanning a wide range of time-scales(extending from seconds to pico-seconds)and can pinpoint their location with atomic resolution.5Most studies have focused on using15N spin relaxation as a probe of backbone amide motions in proteins6but recently interest has emerged in the study of side-chain dynamics as well.2Dynamic analyses of side-chains typically focus on methyl groups,monitoring the decay of 13C or2H magnetization.7Deuterium longitudinal (R1)and transverse(R1r)relaxation measurements in fractionally deuterated protein samples have been used to characterize determinants of ligand binding in SH2domains8and RNA–protein complexes,9protein stability10and hydrophobic core formation in de novo protein design.11Recently we have extended the number of experimentally accessible deuterium relaxation rates from two (R1and R1r)to a total offive observables.12 This enables the application of more complicated physical models in the interpretation of the data, allowing,for example,the detection of nanosecond (ns)time-scale motions in side-chains.13†O.M.and A.M.contributed equally to this work.E-mail address of the corresponding author:kay@pound.med.utoronto.cadoi:10.1016/S0022-2836(03)00471-6J.Mol.Biol.(2003)329,551–563We have chosen the wild-type (WT)B1immuno-globulin binding domain of peptostreptoccocal protein L and two single hydrophobic core mutants,A20V and F22L,as a model system 14to investigate how single point mutations affect protein internal dynamics with particular emphasis on changes in nanosecond time-scale motions.Examination of the five 2H relaxation rates per methyl group reveals several changes in nanosecond time-scale dynamics in response to the A20V and F22L substitutions.We have per-formed extensive simulations to better understand the sensitivity of 2H relaxation parameters to motions on multiple time-scales and present some useful guidelines for establishing whether nano-second time-scale side-chain dynamics are present.This is important,since the present study is among the first that compares side-chain dynamics in a series of mutant proteins and robust protocols for estimating the amplitudes and time-scales of dynamics are,therefore,of particular interest.In addition we report values of three-bond 3J C g –CO ,3J C g –N and 3J C a –C d scalar coupling constants,which we show can be used in conjunction with 2H relaxation data to place bounds on the time-scale of side-chain motions.We compare the dynamics of A20V ,F22L and the WT protein in relation to their molecular structures and recast differences in nanosecond time-scale motions in terms of changes in dihedral angle potential energy functions.Results and DiscussionThe global fold of protein L is unaffected by the mutations A20V,F22LEquilibrium denaturation experiments show changes in the free energy of unfolding,DD G F ;U ¼D G M F ;U 2D G WTF ;U ;of 1.23kcal/mol and 23.22kcal/mol for A20V (increased stability relative to WT)and F22L (decreased stability),respectively,at 228C.15Although differences in solvation energy can completely account for the difference in free energy,DDG F ;U ;for A20V (1.24kcal/mol for A !V)16and partially for F22L (20.12kcal/mol,F !L)16it is still necessary to ascertain to what extent the structures have been modified so that the analysis of the dynamics parameters in what follows (see below)can be interpreted in the proper framework.Crystallographic data show that the structures of A20V and the WT protein arenearly identical (backbone rmsd ¼0.5A˚,total rmsd ¼1.4A˚;K.Zhang,personal communication).Since a structure of F22L is not available,we have used NMR techniques to assess potential dif-ferences from the WT.15N–1H dipolar couplings are exquisitely sensitive to the orientations of amide bond vectors within the molecular frame,with alterations of the secondary or tertiary struc-ture of the protein reported by large changes in the couplings.Residual amide dipolar couplings measured on all three protein samples showgoodFigure parison of 15N–1H residual dipolar couplings predicted on the basis of best-fit alignment frame para-meters and the WT crystal structure (1HZ641)with experimental data obtained for the protein L B1domain (A)A20V ,(B)WT and (C)F22L.Experimental uncertainties are indicated by error bars in the bottom right-hand corners of the panels.(D)Plot of D iso versus P 2(cos u )(where u is the angle between an NH bond vector and the unique axis of the diffusion tensor,P 2(x )¼(3x 221)/2for WT (white),A20V (gray)and F22L (black).Extracted values for 1/(6D iso )are consistent with the presence of purely monomeric species in solution.agreement with those predicted from the WT crys-tal structure (Figure 1A–C ),indicating that the overall backbone structures in solution are essen-tially the same as that of the WT in a crystalline environment.In addition,the hydrodynamic properties of the three molecules were investigated by analysis of backbone 15N relaxation data.17The high degree of overlap shown in Figure 1D indi-cates that all three molecules have very similar diffusion tensors.In addition,methyl regions of 13C–1H correlation maps for WT,A20V and F22L are similar,suggesting that there are no large struc-tural changes of the hydrophobic cores of the proteins.This agrees with numerous studies showing that the average conformation of a protein is remarkably invariant to amino acid substitution,with minimal rearrangement accompanying substi-tutions of non-native side-chains at both surface and core positions.18,19The backbone 15N relaxation data were used to extract order parameters,reflecting the amplitudes of NH bond vector motions,with a value of 1(0)corresponding to complete (no)ordering.Order parameter values do not show substantial dif-ferences when data for the three molecules are compared (see below),with a large change for only a single residue,L22(0.87in WT,0.75in F22L).This result is consistent with previous dynamic studies where few significant deviations in the 15N-derived backbone order parameters were found in proteins with altered stability.20,21Side-chain 2H NMR relaxation experiments are sensitive to nanosecond motionsMethyl 2H relaxation experiments were per-formed on fractionally deuterated,uniformly 13C,15N labeled protein samples.For spin I ¼1nucleisuch as deuterium,five independent relaxation rates for three coherences and two populations can be measured by recording a series of 13C–1H correlation experiments.12We have measured these five rates for methyl deuterons in each of the three forms of protein L studied (WT,A20V ,F22L)at a single field,500MHz (1H frequency).Deuterium relaxation is dominated by the quadrupolar mechanism where only three frequen-cies (0,v D and 2v D ,with v D the deuterium reso-nance frequency)determine the rates of decay of each 2H nucleus.A measure of the “amount”of motion occurring at each frequency,v ,is given by the spectral density function,J (v ),that corresponds to the cosine Fourier transform of the autocorrela-tion function describing the time dependence of the orientation of the C–D bond.Since the five relaxation rates depend upon the spectral density function evaluated at frequencies of 0,v D and 2v D ,J (0),J (v D )and J (2v D )can be calculated without the assumption of any motional model.13It is often instructive,however,to recast the J (v )values in terms of site-specific dynamics parameters that reflect the amplitude,S 2,of the motion of the methyl 3-fold axis by fitting the relaxation rates to a model (referred to in what follows as LS-2)of the form:22,23J ðv Þ¼19S 2t R 1þv 2t 2Rþ1219S 2t1þv 2t 2t 21¼t 21e þt 21Rð1Þwhere t R is the overall tumbling time of the protein determined from 15N relaxation data and t e is the effective correlation time for rotations about and motions of the C methyl –C bond.Figure 2shows the experimental values of J (v)Figure parison of spectral density values for T5g 2(A)and I6d 1(B),obtained from five deuterium relaxation rates by singular value decomposition 13(blue circles)with theoretical curves generated assuming a global overall correlation time (black,LS-2model)and a local correlation time (red,LS-3model)for the methyl groups in each of the three proteins.(blue circles)at frequencies(Hz)of0,v D/2p and2v D/2p superimposed on the best-fit spectral density curves(black lines)predicted by the LS-2 model for a pair of methyl groups,T5g2and I6d1, from A20V,WT and F22L protein L B1domains. In the case of T5g2(Figure2A)the LS-2model is able to reproduce the experimental data for all forms of the protein.The dynamics of this methyl group can be adequately described,therefore,in terms of a model in which there is rapid pico-second time-scale rotation about the C b–C g2bond, which in turn undergoes rapid librations.In con-trast,the LS-2model cannot reproduce the spectral densities for I6d1(Figure2(B)).A slightly more complex model(LS-3),in which t R is replaced with an effective correlation time t R,eff,as an additionalfitting parameter in equation(1),repro-duces the data in this case(red curves)and in all cases for which LS-2fails.Failure of the LS-2 model can result,in part,from anisotropic overall tumbling.In the present case,however,the range of calculated t R values for the methyl groups based on diffusion parameters obtained from15N relaxation data and the X-ray structure of protein L is small(3.8–4.3ns;for23methyl groups the range is3.9–4.1ns)13and cannot account for the differences in observed and calculated J(v)values. These differences reflect the presence of slower nanosecond time-scale processes(which are not accounted for by the LS-2model),likely arising from rotameric side-chain jumps around x1and/or x2dihedral angles13in addition to the picosecond time-scale dynamics described above.In the LS-3 model,slow motions are incorporated into the effec-tive local correlation time t R,eff(if their time-scales are greater than approximately2ns)with S2and t e reflecting motions on the picosecond time-scale.13,24 In principle,more complicated models can be used which explicitly take into account the effects of motions on different time-scales.The extended model-free approach(model LS-4)has been used extensively with15N relaxation data to yield an order parameterðS2sÞand correlation time(t s)per residue describing nanosecond internal motions,in addition to the fast time-scale parameters(S2f and t f).25In this case the spectral density function is given by:JðvÞ¼19S2f S2st01þv2t0þ19S2fð12S2sÞt11þv2t1þS2s1219S2ft21þv2t2þ1219S2f£ð12S2s Þt31þv2t23;1=t0¼1=t R1=t1¼ð1=t RÞþð1=t sÞ;1=t2¼ð1=t RÞþð1=t fÞ;1=t3¼ð1=t RÞþð1=t sÞþð1=t fÞð2ÞIn a recent study of side-chain dynamics in WTprotein L we found thatfits using the LS-4modelof a comprehensive relaxation data set comprisedof rates recorded at spectrometer frequencies of400,500,600and800MHz were often unstable inthe sense that large errors in thefitting parameterswere extracted from the analysis.13Subsequentextensive simulations in our laboratory have con-firmed thatfits of either2H or13C-labeled methylside-chain relaxation parameters using the LS-4model are not nearly as stable as corresponding ana-lyses of15N relaxation data,even if extensive datasets(measured at the four spectrometerfieldsshown above)with small errors(3%)are used asinput.The difference in the robustness of backboneand side-chain data analyses arises from theadditional factor of1/9(which is absent for15Nrelaxation data),which significantly decreases thesensitivity of the relaxation data to the dynamicsparameters S2s;S2f and t s.24Moreover,simulationshave established that the x2values obtained byfitting thefive relaxation rates to an LS-4spectraldensity model(four parameters)do not follow thedistribution expected for one degree of freedom.Note that thefive rates are not independent,sincethey depend on only three spectral density values(J(0),J(v D),J(2v D))and it is therefore not possible toextract four parameters from data obtained at asingle spectrometerfield.In contrast,fits using LS-2(two parameters)or LS-3(three parameters)spectraldensity models follow the x2distributions expectedfor three and two degrees of freedom,respectively.Thus,quite independent of the(lack of)robustnessof the LS-4model forfitting methyl dynamics data,it is not valid for use in the present analysis in anyevent.In what follows,therefore,we will use theLS-3model in cases where analyses using an LS-2form of the spectral density function fail.The“relative goodness offits”of thefivemeasured relaxation rates/residue using LS-2andLS-3models have been analyzed with F-teststatistics.26Simulations of thefive2H relaxationrates that have been measured here(spectrometerfield of500MHz)using the LS-2model to generatedata free from nanosecond motions have shown,not surprisingly,that when a95%confidence limitis used to distinguish between LS-2and LS-3models,false positives(i.e.selection of the LS-3model)are obtained in approximately5%of thecases(data not shown).A related question ofinterest concerns the efficacy of the F-test approachfor identifying nanosecond dynamics in caseswhere such motions exist.To investigate this weturn to simulations again and generate2H spinrelaxation data sets(allfive rates at a single spec-trometerfield,500MHz)using the LS-4modelwith dynamics parameters in the following ranges,0.2,S f2,1.0,0,S s2,0.5,0,t f,100ps,1,t s,10ns, 3.8,t R,4.6ns(i.e.all ratesderived from a model that includes nanosecondmotions).A distribution of overall correlationtimes, 3.8,t R,4.6ns,was used in the simu-lations to reflect the range of t R values found inprotein L resulting from diffusion anisotropy, D k/D’¼1.38(see Materials and Methods). Gaussian noise was subsequently added to the rates(ranging from0.01%to10%)and they were thenfit to LS-2and LS-3models.Figure3A shows the fraction of data sets that were betterfit with the LS-3spectral density function(95%confidence limit)versus the error in thefitted relaxation rates. For very low errors the majority of residues are correctly identified as having nanosecond motions. As the error increases,however,it becomes increasingly difficult to select the more complex model(LS-3)over LS-2and many of the residues are undetected(note that all residues should be detected as they all have nanosecond motions in the simulation).Ultimately as the errors increase we expect that the acceptance level will drop to 5%(broken line in the Figure),reflecting simply the95%cutoff criteria that we use in the F-test.Table1lists the methyl groups whose relaxation data could befit using the simple LS-2model (95%confidence limit),indicating that the methyl dynamics are well described assuming only picose-cond time-scale motions,along with their dynamics parameters.Notably,this Table com-prises the majority of methyl-containing residues in each of the three variants of protein L(97%for A20V,94%for WT and83%for F22L).Similar levels of nanosecond dynamics have also been observed in2H relaxation studies of the N-terminal SH3domain from drk and the fyn SH3domain where7%and21%of the methyl-containing resi-dues,respectively,were betterfit using the LS-3 model.Of note,the values of S2and t e obtained from thefits are very well conserved across the different variants of the protein,with one excep-tion,L40d2,where different S2and t e values are obtained for the A20V mutant.This gives us aFigure3.Plot of the fraction ofsynthetic data sets derived usingthe LS-4spectral density modelwith large amplitude nanoseconddynamics(S s2,0.5)that are betterfit with the LS-3spectral densitythan the LS-2(95%confidencelimit)versus the error in thefittedrelaxation rates(see the text fordetails)(A).Histogram of t R,effvalues generated fromfits usingthe LS-3form of J(v)to datasets generated with the LS-2model and the parameters0.2,S2,1.0,0,t e,100ps and3.8,t R,4.6ns.Values of t R,eff forthose residues in protein L that arebetterfit with the LS-3model thanthe LS-2are indicated(B).Histo-gram of S s2(C)and t s(D)valueswhich give t R,eff,3ns and p values,0.05in a comparison of LS-2and LS-3models when data is gen-erated according to equation(2)with0.2,S f2,1.0,0,S s2,1.0,0,t f,100ps and1,t s,20nsandfit using LS-2and LS-3models.high degree of confidence in our data and suggests strongly that when differences do arise in relax-ation parameters they are very likely real.In addition to the2H spin relaxation data reported here,we also show the three-bond scalar couplings27,283J C a–C d,3J C g–N and3J C g–CO that have been measured for methyl-containing residues and used as a probe of x1/x2dynamics to comp-lement the relaxation measurements(see below). Notably,several methyl groups(six in F22L,two in WT and one in A20V)in protein L show strong evidence of nanosecond time-scale dynamics from 2H spin relaxation measurements.For these resi-dues the LS-2model is unable to reproduce the experimental spectral density values to within error and all residues show a statistically signifi-cant reduction in residual x2fromfits using the LS-3model relative to LS-2according to F-statistics (95%confidence limit).Table2lists the dynamics parameters,S2and t R,eff,that are extracted from fits(LS-3)of the residues that show nanosecond motions in at least one of the three forms of protein L that are studied here(highlighted in bold).In addition,the three-bond scalar couplings3J C a–C d, 3J C g–N and3J C g–CO are also listed.Of interest,the results in Figure3A suggest that with the level of errors in our experimental data sets(ranging from approximately2%for A20V and WT to4–7%for F22L)it is unlikely that all residues with nano-second time-scale dynamics will be identified, with less than50%in the case of F22L.In cases where nanosecond motions are detected,however,the simulations described below suggest that they likely arise from large amplitude dynamicsðS2s, 0:6Þ:It can be shown that t R,eff values obtained from fitting the data to the LS-3model are quite sensi-tive to the presence of nanosecond motions,13pro-vided that the magnitude of fast internal motions does not overwhelm the effect of overall tumbling. Figure3B shows the distribution of t R,eff values obtained from LS-3fits of synthetic data generated using the LS-2form of J(v)(no nanosecond time-scale dynamics)with0.2,S2,1.0, 0,t e,100ps and 3.8,t R,4.6ns,along with the t R,eff values obtained for those residues in pro-tein L identified as dynamic on the nanosecond time-scale by F-tests.The distribution is centered about t R,eff,4ns,since t R,iso¼4.05ns and97%of the values lie to the right of3ns.Note that the width of the distribution is larger than the range of t R values used in the simulation,since experi-mental errors are also included(see Materials and Methods).For residues with nanosecond dynamics it is quite clear that lower t R,eff values than would be expected(less than3ns for protein L)in the absence of nanosecond dynamics are obtained. Low values of t R,eff are very informative in terms of providing insight into the underlying dynamics. By way of example,we have simulated2H relax-ation data using the LS-4spectral density model(i.e.with nanosecond time-scale dynamics)with0.2,S f2,1.0,0,S s2,1.0,0,t f,100ps, 1,t s,20ns and 3.8,t R,4.6ns andfit theTable2.Side-chain dynamical parameters and measured3J side-chain scalar couplings for residues whose2H relaxa-tion are bestfit using the LS-3form of J(v)in at least one variant of protein L(i.e.nanosecond dynamics)Methyl group S2(LS-3)a t R,eff(ns)a Rotamer(deg.)b3J C a–C d(Hz)a3J C g–N(Hz)a3J C g–CO(Hz)a A20VI6d1c0.49(0.04) 2.95(0.16)260 1.9(0.1)––L10d10.24(0.03) 3.25(0.15)180 2.4(0.1)––L10d20.26(0.06) 3.12(0.14)180 2.0(0.1)––T19g20.52(0.08) 3.76(0.05)þ60–0.8(0.1) 2.1(0.2)T39g20.86(0.05) 4.01(0.12)þ60–0.8(0.1) 2.2(0.1)T48g20.75(0.03) 3.76(0.17)þ60–d dWTI6d1c0.49(0.03) 2.76(0.10)260 2.1(0.2)––L10d10.21(0.04) 3.38(0.20)180 2.3(0.1)––L10d20.26(0.02) 2.83(0.22)180 1.8(0.1)––T19g2c0.82(0.04) 2.71(0.18)160–0.9(0.1) 2.0(0.2)T39g20.87(0.03) 3.56(0.12)þ60–0.8(0.1) 2.2(0.2)T48g20.75(0.03) 3.73(0.15)þ60– 1.1(0.1) 3.1(0.2)F22LI6d1c0.47(0.07) 2.47(0.17)260 1.9(0.2)––L10d1c0.17(0.03) 2.45(0.13)180 1.7(0.1)––L10d2c0.29(0.04) 2.88(0.09)180 2.0(0.1)––T19g20.57(0.03) 3.22(0.07)þ60–0.7(0.1) 2.2(0.1)L22d1c0.50(0.06) 2.91(0.18)– 2.2(0.2)––L22d20.69(0.07) 2.17(0.12)– 2.0(0.1)––T39g2c0.95(0.08) 2.79(0.10)160– 1.1(0.1) 2.1(0.1)T48g2c0.72(0.03) 2.76(0.14)160–0.9(0.1) 1.9(0.1)a Errors in experimental data in parentheses.b Rotamers obtained from the crystal structures:1HZ5and1HZ6.41c Residues identified as dynamic using F-test statistics(see the text).d Data not available due to signal overlap.rates to both LS-2and LS-3spectral density models.The input values of S 2s and t s for those cases where the LS-3model is preferred (F -test,95%confidence)and where t R,eff ,3ns are plotted in Figure 3C and D ,respectively.For t R,eff ,3ns the distribution of t s lies predominantly in the range of 1–10ns (75%).Moreover,the values of S 2s are clustered from 0to 0.6(92%)and show no correlation with the input values of t s .Note that the definition of “low values of t R,eff ”(in what follows we use less than 3ns for protein L)will vary depending on the protein,but can be easily calculated on a case-by-case basis using simu-lations of the type described here.The methyl-containing residues identified as dynamic on a nanosecond time-scale in Table 2are superimposed on the structure of protein L in Figure 4.In addition,the amplitudes of backbone motions,established from 15N spin relaxation measurements,are color coded on the ribbon dia-grams of each structure.It is clear that there are essentially no differences in backbone order.In contrast,however,differences in the numbers of residues showing side-chain nanosecond dynamics are observed.Of note,the I6d 1methyl is the only one that displays nanosecond motions in all three forms of the protein.L10d 1,d 2are selected as dynamic on a nanosecond time-scale in the case of F22L but not WT or A20V (see Table 2).In the case of L10d 1the probability of a chance improvement in fit using the LS-3versus LS-2form of J (v )is 83%(p ¼0.83)for WT and 90%(p ¼0.90)for A20Vand the separation between “nanosecond dynamics”and “no nanosecond dynamics”is rela-tively clear.Such a separation is much less clear for L10d 2,where p values of 0.17and 0.25are obtained for WT and A20V ,respectively.Values of p from fits of T19,T39and T48for (F22L,WT,A20V)are (0.69,0.02,0.75),(0.03,0.87,0.90)and (0.04,0.75,0.85)respectively,and we can be reason-ably confident here that residues not selected by the LS-3model are unlikely to be dynamic on a nanosecond time-scale.It is important to empha-size the distinction on the one hand between establishing the presence of nanosecond motions (for example,using the F -test criterion described above)and establishing the absence of nanosecond dynamics for those residues that do not pass the F -test criterion.Correlation with scalar coupling dataIn addition to measuring deuterium spin relaxa-tion parameters,three-bond 13C a –13C d ,13C g –13CO and 13C g –15N scalar coupling constants 27,28were obtained for all three variants of protein L and are reported in Tables 1and 2.These values depend directly on the dihedral angles x 2(3J C a –C d )and x 1(3J C g –CO ,3J C g –N )and can be used to detect rotameric averaging on time-scales ranging from a few hundredths of a second to picoseconds.29Also included in Table 1are the expected scalar coupl-ings for dihedral angles of ^60and 1808.30With the exception of V20,the measured scalarcouplingFigure 4.Structure of the B1domain of protein L (PDB accession code 1HZ641)with the locations of methyl groups undergoing nanosecond motions indicated by gray beads.The backbone ribbon is colored according to 15N order parameter where yellow and red correspond to regions of higher and lower flexibility,respectively.Black arrows indicate the sites of mutation.values reported in Table1are consistent with a single predominant x1/x2rotamer in all three variants of protein L examined.For these residues the2H relaxation data are wellfit using the LS-2 spectral density model(i.e.absence of nanosecond time-scale dynamics)and the x1/x2angles obtained on the basis of the scalar coupling data are in agreement with those from the X-ray structures of the protein.For V20the3J C g–CO couplings,in par-ticular,indicate averaging.Of interest,the order parameters for the g1and g2positions are very different;since motions that involve only rotations about x1would lead to equal order parameters, the dynamics are more complex at this site.All residues with detected nanosecond motions (highlighted in red in Table2)give values of scalar couplings that are consistent with either extensive averaging about the relevant dihedral angles(x1 or x2)or,much less likely,non-staggered dihedral angle values.The complementarity between scalar coupling and deuterium relaxation measurements is well illustrated by the data for T48(see Table2). In the WT protein,3J C g–CO and3J C g–N coupling con-stants are equal to3.1Hz and1.1Hz,respectively, corresponding to theþ60rotamer.A previous analysis of dipolar couplings showed a small degree of x1averaging for this residue with the 260rotamer populated to approximately15%.31 The experimental3J C g–N coupling constant in the WT protein is consistent with some exchange between theþ60and260rotamers,however,in F22L,values of1.9Hz and0.9Hz for3J C g–CO and 3J C g–N,respectively,are diagnostic of more exten-sive dynamics.Moreover,the2H data strongly support the fact that only in the case of F22L are large amplitude nanosecond time-scale dynamics present for this residue.The source of these dynamics is almost certainly rotation about x1and it seems likely,therefore,that the motion that con-tributes to the additional averaging of the scalar couplings in T48,F22L is in the nanosecond regime. Many of the residues for which averaged scalar coupling values are measured also display nano-second time-scale dynamics from analysis of2H spin relaxation rates.Conspicuous exceptions from Table2include T39in A20V,WT and T19in A20V,F22L.In the case of T39,scalar coupling values indicate significant averaging in all forms of the protein.However,only in the case of the F22L variant does the LS-2model fail in the analysis of the relaxation data for this residue. Similarly for T19only the WT protein shows nano-second dynamics using the criteria outlined above, yet the values of the scalar couplings indicate aver-aging in all variants.It is important to note,how-ever,that there need not be a correlation between the presence of nanosecond time-scale dynamics (as monitored by spin relaxation measurements) and averaging as reported by scalar couplings.For example,the simulations described above show that the“window”in which2H relaxation experi-ments can detect slow motions according to F-test statistics and t R,eff values below3ns is quite sensi-tive to the motional time-scale.In the present case, values of t R,eff below3ns,extracted for all of the residues selected as dynamic on the nanosecond time-scale(Table2),indicate that the underlying dynamics likely involve large amplitudes and time-scales between approximately1ns and10ns (see Figure3C and D).In contrast,averaged scalar couplings can reflect motions over a much wider time-scale.In this way torsion angle dynamics with time constants that lie outside the1–10ns window(Figure3D)would escape detection by 2H spin relaxation(sensitive only to picosecond to nanosecond motions)and yet would efficiently average scalar coupling constants.Thus,the presence of dynamics that average scalar couplings but not relaxation parameters can be used to set boundaries regarding the time-scale of averaging.In the case of T39the extensive averaging detected by scalar couplings in A20V and WT likely is the result of motions on time-scales greater than10ns so that the dynamics are invisible to2H spin relaxation,yet they must be fast enough to avoid spectral broadening(milli-second time-scale).The nanosecond motions reported for T39by the2H data in the case of F22L but not for A20V or WT may reflect additional intra-rotameric dynamics superimposed on the slower torsion angle jumps that the averaged scalar coupling data report.Alternatively,the effect of the F22L mutation may be to increase the rate of the rotameric jumps in thefirst place so that they are shifted into the nanosecond regime.Since the evidence from NMR experiments and molecular dynamics simulations is that librations within a rotameric well occur on the picosecond time-scale32we tend to favor the second scenario listed above.Of note,values of S2are similar for all three variants,suggesting that the amplitudes of fast(ps)dynamics are similar in the three cases. The measured scalar couplings for T19,like for T39,are consistent with extensive x1averaging.In this case,however,the relaxation data are only conclusive about nanosecond dynamics at this pos-ition in the WT protein(see Table2).Notably,the S2value(reporting on picosecond dynamics)is high for the WT(0.82)and significantly lower for both mutants(0.52and0.57for A20V and F22L), possibly resulting from a shift in averaging for T19from the nanosecond regime for WT to the picosecond time frame for the mutants.Comparison with molecular structuresAnalysis of the X-ray structures of A20V and WT establishes that the residues that show differential picosecond and nanosecond time-scale motions in the three proteins(L10,T19,T39,L40,T48)do not make direct contacts with the mutated residues.It is therefore of interest to try to understand the structural features that might be responsible for the changes in dynamics associated with amino acid substitutions.For example,T39is far from the site of mutation in F22L(.10A˚)and yet。

TAUP2334-96 ACTION AND PASSION AT A DISTANCEAn Essay in Honor of Professor Abner Shimony∗Sandu PopescuDepartment of Physics,Boston University,Boston,MA02215,U.S.A.Daniel RohrlichSchool of Physics and Astronomy,Tel-Aviv University,Ramat-Aviv69978Tel-Aviv,Israel(May7,1996)AbstractQuantum mechanics permits nonlocality—both nonlocal correlations andnonlocal equations of motion—while respecting relativistic causality.Is quan-tum mechanics the unique theory that reconciles nonlocality and causality?We consider two models,going beyond quantum mechanics,of nonlocality—“superquantum”correlations,and nonlocal“jamming”of correlations—andderive new results for the jamming model.In one space dimension,jammingallows reversal of the sequence of cause and effect;in higher dimensions,how-ever,effect never precedes cause.∗To appear in Quantum Potentiality,Entanglement,and Passion-at-a-Distance:Essays for Ab-ner Shimony,R.S.Cohen,M.A.Horne and J.Stachel,eds.(Dordrecht,Netherlands:Kluwer Academic Publishers),in press.1I.INTRODUCTIONWhy is quantum mechanics what it is?Many a student has asked this question.Some physicists have continued to ask it.Few have done so with the passion of Abner Shimony.“Why is quantum mechanics what it is?”we,too,ask ourselves,and of course we haven’t got an answer.But we are working on an answer,and we are honored to dedicate this work to you,Abner,on your birthday.What is the problem?Quantum mechanics has an axiomatic structure,exposed by von Neumann,Dirac and others.The axioms of quantum mechanics tell us that every state of a system corresponds to a vector in a complex Hilbert space,every physical observable corre-sponds to a linear hermitian operator acting on that Hilbert space,etc.We see the problem in comparison with the special theory of relativity.Special relativity can be deduced in its entirety from two axioms:the equivalence of inertial reference frames,and the constancy of the speed of light.Both axioms have clear physical meaning.By contrast,the numerous axioms of quantum mechanics have no clear physical meaning.Despite many attempts, starting with von Neumann,to derive the Hilbert space structure of quantum mechanics from a“quantum logic”,the new axioms are hardly more natural than the old.Abner Shimony offers hope,and a different approach.His point of departure is a remark-able property of quantum mechanics:nonlocality.Quantum correlations display a subtle nonlocality.On the one hand,as Bell[1]showed,quantum correlations could not arise in any theory in which all variables obey relativistic causality[2].On the other hand,quantum correlations themselves obey relativistic causality—we cannot exploit quantum correlations to transmit signals at superluminal speeds[3](or at any speed).That quantum mechanics combines nonlocality and causality is wondrous.Nonlocality and causality seem prima facie incompatible.Einstein’s causality contradicts Newton’s action at a distance.Yet quan-tum correlations do not permit action at a distance,and Shimony[4]has aptly called the nonlocality manifest in quantum correlations“passion at a distance”.Shimony has raised the question whether nonlocality and causality can peacefully coexist in any other theory2besides quantum mechanics[4,5].Quantum mechanics also implies nonlocal equations of motion,as Yakir Aharonov[6,7] has pointed out.In one version of the Aharonov-Bohm effect[8],a solenoid carrying an isolated magneticflux,inserted between two slits,shifts the interference pattern of electrons passing through the slits.The electrons therefore obey a nonlocal equation of motion:they never pass through theflux yet theflux affects their positions when they reach the screen[9]. Aharonov has shown that the solenoid and the electrons exchange a physical quantity,the modular momentum,nonlocally.In general,modular momentum is measurable and obeys a nonlocal equation of motion.But when theflux is constrained to lie between the slits, its modular momentum is completely uncertain,and this uncertainty is just sufficient to keep us from seeing a violation of causality.Nonlocal equations of motion imply action at a distance,but quantum mechanics manages to respect relativistic causality.Still,nonlocal equations of motion seem so contrary to relativistic causality that Aharonov[7]has asked whether quantum mechanics is the unique theory combining them.The parallel questions raised by Shimony and Aharonov lead us to consider models for theories,going beyond quantum mechanics,that reconcile nonlocality and causality. Is quantum mechanics the only such theory?If so,nonlocality and relativistic causality together imply quantum theory,just as the special theory of relativity can be deduced in its entirety from two axioms[7].In this paper,we will discuss model theories[10–12] manifesting nonlocality while respecting causality.Thefirst model manifests nonlocality in the sense of Shimony:nonlocal correlations.The second model manifests nonlocality in the sense of Aharonov:nonlocal dynamics.Wefind that quantum mechanics is not the only theory that reconciles nonlocality and relativistic causality.These models raise new theoretical and experimental possibilities.They imply that quantum mechanics is only one of a class of theories combining nonlocality and causality;in some sense,it is not even the most nonlocal of such theories.Our models raise a question:What is the minimal set of physical principles—“nonlocality plus no signalling plus something else simple and fundamental”as Shimony put it[13]—from which we may derive quantum mechanics?3II.NONLOCALITY I:NONLOCAL CORRELATIONSThe Clauser,Horne,Shimony,and Holt [14]form of Bell’s inequality holds in any classical theory (that is,any theory of local hidden variables).It states that a certain combination of correlations lies between -2and 2:−2≤E (A,B )+E (A,B )+E (A ,B )−E (A ,B )≤2.(1)Besides 2,two other numbers,2√2and 4,are important bounds on the CHSH sum ofcorrelations.If the four correlations in Eq.(1)were independent,the absolute value of the sum could be as much as 4.For quantum correlations,however,the CHSH sum ofcorrelations is bounded [15]in absolute value by 2√2.Where does this bound come from?Rather than asking why quantum correlations violate the CHSH inequality,we might ask why they do not violate it more .Suppose that quantum nonlocality implies that quantum correlations violate the CHSH inequality at least sometimes.We might then guess that relativistic causality is the reason that quantum correlations do not violate it maximally.Could relativistic causality restrict the violation to 2√2instead of 4?If so,then nonlocalityand causality would together determine the quantum violation of the CHSH inequality,and we would be closer to a proof that they determine all of quantum mechanics.If not,then quantum mechanics cannot be the unique theory combining nonlocality and causality.To answer the question,we ask what restrictions relativistic causality imposes on joint probabilities.Relativistic causality forbids sending messages faster than light.Thus,if one observer measures the observable A ,the probabilities for the outcomes A =1and A =−1must be independent of whether the other observer chooses to measure B or B .However,it can be shown [10,16]that this constraint does not limit the CHSH sum ofquantum correlations to 2√2.For example,imagine a “superquantum”correlation functionE for spin measurements along given axes.Assume E depends only on the relative angle θbetween axes.For any pair of axes,the outcomes |↑↑ and |↓↓ are equally likely,and similarly for |↑↓ and |↓↑ .These four probabilities sum to 1,so the probabilities for |↑↓4and|↓↓ sum to1/2.In any direction,the probability of|↑ or|↓ is1/2irrespective of a measurement on the other particle.Measurements on one particle yield no information about measurements on the other,so relativistic causality holds.The correlation function then satisfies E(π−θ)=−E(θ).Now let E(θ)have the form(i)E(θ)=1for0≤θ≤π/4;(ii)E(θ)decreases monotonically and smoothly from1to-1asθincreases fromπ/4to 3π/4;(iii)E(θ)=−1for3π/4≤θ≤π.Consider four measurements along axes defined by unit vectorsˆa ,ˆb,ˆa,andˆb separated by successive angles ofπ/4and lying in a plane.If we now apply the CHSH inequality Eq.(1)to these directions,wefind that the sum of correlationsE(ˆa,ˆb)+E(ˆa ,ˆb)+E(ˆa,ˆb )−E(ˆa ,ˆb )=3E(π/4)−E(3π/4)=4(2)violates the CHSH inequality with the maximal value4.Thus,a correlation function could satisfy relativistic causality and still violate the CHSH inequality with the maximal value4.III.NONLOCALITY II:NONLOCAL EQUATIONS OF MOTIONAlthough quantum mechanics is not the unique theory combining causality and nonlocal correlations,could it be the unique theory combining causality and nonlocal equations of motion?Perhaps the nonlocality in quantum dynamics has deeper physical signficance.Here we consider a model that in a sense combines the two forms of nonlocality:nonlocal equations of motion where one of the physical variables is a nonlocal correlation.Jamming,discussed by Grunhaus,Popescu and Rohrlich[11]is such a model.The jamming paradigm involves three experimenters.Two experimenters,call them Alice and Bob,make measurements on systems that have locally interacted in the past.Alice’s measurements are spacelike separated from Bob’s.A third experimenter,Jim(the jammer),presses a button on a black box.This event is spacelike separated from Alice’s measurements and from Bob’s.The5black box acts at a distance on the correlations between the two sets of systems.For the sake of definiteness,let us assume that the systems are pairs of spin-1/2particles entangled in a singlet state,and that the measurements of Alice and Bob yield violations of the CHSH inequality,in the absence of jamming;but when there is jamming,their measurements yield classical correlations(no violations of the CHSH inequality).Indeed,Shimony[4]considered such a paradigm in the context of the experiment of Aspect,Dalibard,and Roger[17].To probe the implications of certain hidden-variable the-ories[18],he wrote,“Suppose that in the interval after the commutators of that experiment have been actuated,but before the polarization analysis of the photons has been completed, a strong burst of laser light is propagated transverse to but intersecting the paths of the propagating photons....Because of the nonlinearity of the fundamental material medium which has been postulated[in these models],this burst would be expected to generate exci-tations,which could conceivably interfere with the nonlocal propagation that is responsible for polarization correlations.”Thus,Shimony asked whether certain hidden-variable theories would predict classical correlations after such a burst.(Quantum mechanics,of course,does not.)Here,our concern is not with hidden-variable theories or with a mechanism for jamming; rather,we ask whether such a nonlocal equation of motion(or one,say,allowing the third experimenter nonlocally to create,rather than jam,nonlocal correlations)could respect causality.The jamming model[11]addresses this question.In general,jamming would allow Jim to send superluminal signals.But remarkably,some forms of jamming would not; Jim could tamper with nonlocal correlations without violating causality.Jamming preserves causality if it satisfies two constraints,the unary condition and the binary condition.The unary condition states that Jim cannot use jamming to send a superluminal signal that Alice (or Bob),by examining her(or his)results alone,could read.To satisfy this condition,let us assume that Alice and Bob each measure zero average spin along any axis,with or without jamming.In order to preserve causality,jamming must affect correlations only,not average measured values for one spin component.The binary condition states that Jim cannot use6jamming to send a signal that Alice and Bob together could read by comparing their results, if they could do so in less time than would be required for a light signal to reach the place where they meet and compare results.This condition restricts spacetime configurations for jamming.Let a,b and j denote the three events generated by Alice,Bob,and Jim, respectively:a denotes Alice’s measurements,b denotes Bob’s,and j denotes Jim’s pressing of the button.To satisfy the binary condition,the overlap of the forward light cones of a and b must lie entirely within the forward light cone of j.The reason is that Alice and Bob can compare their results only in the overlap of their forward light cones.If this overlap is entirely contained in the forward light cone of j,then a light signal from j can reach any point in spacetime where Alice and Bob can compare their results.This restriction on jamming configurations also rules out another violation of the unary condition.If Jim could obtain the results of Alice’s measurements prior to deciding whether to press the button,he could send a superluminal signal to Bob by selectively jamming[11].IV.AN EFFECT CAN PRECEDE ITS CAUSE!If jamming satisfies the unary and binary conditions,it preserves causality.These con-ditions restrict but do not preclude jamming.There are configurations with spacelike sep-arated a,b and j that satisfy the unary and binary conditions.We conclude that quantum mechanics is not the only theory combining nonlocal equations of motion with causality.In this section we consider another remarkable aspect of jamming,which concerns the time sequence of the events a,b and j defined above.The unary and binary conditions are man-ifestly Lorentz invariant,but the time sequence of the events a,b and j is not.A time sequence a,j,b in one Lorentz frame may transform into b,j,a in another Lorentz frame. Furthermore,the jamming model presents us with reversals of the sequence of cause and effect:while j may precede both a and b in one Lorentz frame,in another frame both a and b may precede j.To see how jamming can reverse the sequence of cause and effect,we specialize to the7case of one space dimension.Since a and b are spacelike separated,there is a Lorentz frame in which they are simultaneous.Choosing this frame and the pair(x,t)as coordinates for space and time,respectively,we assign a to the point(-1,0)and b to the point(1,0). What are possible points at which j can cause jamming?The answer is given by the binary condition.It is particularly easy to apply the binary condition in1+1dimensions,since in 1+1dimensions the overlap of two light cones is itself a light cone.The overlap of the two forward light cones of a and b is the forward light cone issuing from(0,1),so the jammer, Jim,may act as late as∆t=1after Alice and Bob have completed their measurements and still jam their results.More generally,the binary condition allows us to place j anywhere in the backward light cone of(0,1)that is also in the forward light cone of(0,-1),but not on the boundaries of this region,since we assume that a,b and j are mutually spacelike separated.(In particular,j cannot be at(0,1)itself.)Such reversals may boggle the mind,but they do not lead to any inconsistency as long as they do not generate self-contradictory causal loops[19,20].Consistency and causality are intimately related.We have used the term relativistic causality for the constraint that others call no signalling.What is causal about this constraint?Suppose that an event(a“cause”) could influence another event(an“effect”)at a spacelike separation.In one Lorentz frame the cause precedes the effect,but in some other Lorentz frame the effect precedes the cause; and if an effect can precede its cause,the effect could react back on the cause,at a still earlier time,in such a way as to prevent it.A self-contradictory causal loop could arise.A man could kill his parents before they met.Relativistic causality prevents such causal contradictions[19].Jamming allows an event to precede its cause,but does not allow self-contradictory causal loops.It is not hard to show[11]that if jamming satisfies the unary and binary conditions,it does not lead to self-contradictory causal loops,regardless of the number of jammers.Thus,the reversal of the sequence of cause and effect in jamming is consistent.It is,however,sufficiently remarkable to warrant further comment below,and we also show that the sequence of cause and effect in jamming depends on the space dimension in a surprising way.8The unary and binary conditions restrict the possible jamming configurations;however, they do not require that jamming be allowed for all configurations satisfying the two con-ditions.Nevertheless,we have made the natural assumption that jamming is allowed for all such configurations.This assumption is manifestly Lorentz invariant.It allows a and b to both precede j.In a sense,it means that Jim acts along the backward light cone of j; whenever a and b are outside the backward light cone of j and fulfill the unary and binary conditions,jamming occurs.V.AN EFFECT CAN PRECEDE ITS CAUSE??That Jim may act after Alice and Bob have completed their measurements(in the given Lorentz frame)is what may boggle the mind.How can Jim change his own past?We may also put the question in a different way.Once Alice and Bob have completed their measurements,there can after all be no doubt about whether or not their correlations have been jammed;Alice and Bob cannot compare their results andfind out until after Jim has already acted,but whether or not jamming has taken place is already an immutable fact. This fact apparently contradicts the assumption that Jim is a free agent,i.e.that he can freely choose whether or not to jam.If Alice and Bob have completed their measurements, Jim is not a free agent:he must push the button,or not push it,in accordance with the results of Alice and Bob’s measurements.We may be uncomfortable even if Jim acts before Alice and Bob have both completed their measurements,because the time sequence of the events a,b and j is not Lorentz invariant;a,j,b in one Lorentz frame may transform to b,j,a in another.The reversal in the time sequences does not lead to a contradiction because the effect cannot be isolated to a single spacetime event:there is no observable effect at either a or b,only correlations between a and b are changed.All the same,if we assume that Jim acts on either Alice or Bob—whoever measures later—we conclude he could not have acted on either of them, because both come earlier in some Lorentz frame.9What,then,do we make of cause and effect in the jamming model?We offer two points of view on this question.One point of view is that we don’t have to worry;jamming does not lead to any causal paradoxes,and that is all that matters.Of course,experience teaches that causes precede their effects.Yet experience also teaches that causes and effects are locally related.In jamming,causes and effects are nonlocally related.So we cannot assume that causes must precede their effects;it is contrary to the spirit of special relativity to impose such a demand.Indeed,it is contrary to the spirit of general relativity to assign absolute meaning to any sequence of three mutually spacelike separated events,even when such a sequence has a Lorentz-invariant meaning in special relativity[20].We only demand that no sequence of causes and effects close upon itself,for a closed causal loop—a time-travel paradox—would be self-contradictory.If an effect can precede its cause and both are spacetime events,then a closed causal loop can arise.But in jamming,the cause is a spacetime event and the effect involves two spacelike separated events;no closed causal loop can arise[11].This point of view interprets cause and effect in jamming as Lorentz invariant;observers in all Lorentz frames agree that jamming is the effect and Jim’s action is the cause.A second point of view asks whether the jamming model could have any other interpretation. In a world with jamming,might observers in different Lorentz frames give different accounts of jamming?Could a sequence a,j,b have a covariant interpretation,with two observers coming to different conclusions about which measurements were affected by Jim?(No ex-periment could ever prove one of them wrong and the other right[21].)Likewise,perhaps observers in a Lorentz frame where both a and b precede j would interpret jamming as a form of telesthesia:Jim knows whether the correlations measured by Alice and Bob are nonlocal before he could have received both sets of results.We must assume,however,that observers in such a world would notice that jamming always turns out to benefit Jim;they would not interpret jamming as mere telesthesia,so the jamming model could not have this covariant interpretation.Finally,we note that a question of interpreting cause and effect arises in quantum me-10chanics,as well.Consider the measurements of Alice and Bob in the absence of jamming. Their measured results do not indicate any relation of cause and effect between Alice and Bob;Alice can do nothing to affect Bob’s results,and vice versa.According to the con-ventional interpretation of quantum mechanics,however,thefirst measurement on a pair of particles entangled in a singlet state causes collapse of the state.The question whether Alice or Bob caused the collapse of the singlet state has no Lorentz-invariant answer[11,22].VI.JAMMING IN MORE THAN ONE SPACE DIMENSIONAfter arguing that jamming is consistent even if it allows reversals of the sequence of cause and effect,we open this section with a surprise:such reversals arise only in one space dimension!In higher dimensions,the binary condition itself eliminates such configurations; jamming is not possible if both a and b precede j.To prove this result,wefirst consider the case of2+1dimensions.We choose coordinates(x,y,t)and,as before,place a and b on the x-axis,at(-1,0,0)and(1,0,0),respectively.Let A,B and J denote the forward light cones of a,b and j,respectively.The surfaces of A and B intersect in a hyperbola in the yt-plane.To satisfy the binary condition,the intersection of A and B must lie entirely within J.Suppose that this condition is fulfilled,and now we move j so that the intersection of A and B ceases to lie within J.The intersection of A and B ceases to lie within J when its surface touches the surface of J.Either a point on the hyperbola,or a point on the surface of either A of B alone,may touch the surface of J.However,the surfaces of A and J can touch only along a null line(and likewise for B and J);that is,only if j is not spacelike separated from either a or b,contrary to our assumption.Therefore the only new constraint on j is that the hyperbola formed by the intersection of the surfaces of A and B not touch the surface of J.If we place j on the t-axis,at(0,0,t),the latest time t for which this condition is fulfilled is when the asymptotes of the hyperbola lie along the surface of J.They lie along the surface of J when j is the point(0,0,0).If j is the point(0,0,0),moving j in either the x-or y-direction will cause the hyperbola to intersect the surface of J.We conclude that11there is no point j,consistent with the binary condition,with t-coordinate greater than0. Thus,j cannot succeed both a and b in any Lorentz frame(although it could succeed one of them).For n>2space dimensions,the proof is similar.The only constraint on j arises from the intersection of the surfaces of A and B.At a given time t,the surfaces of A and B are (n−1)-spheres of radius t centered,respectively,at x=−1and x=1on the x-axis;these (n−1)-spheres intersect in an(n−2)-sphere of radius(t2−1)1/2centered at the origin. This(n−2)sphere lies entirely within an(n−1)-sphere of radius t centered at the origin, and approaches it asymptotically for t→∞.The(n−1)-spheres centered at the origin are sections of the forward light cone of the origin.Thus,j cannot occur later than a and b.Wefind this result both amusing and odd.We argued above that allowing j to succeed both a and b does not entail any inconsistency and that it is contrary to the spirit of the general theory of relativity to exclude such configurations for jamming.Nonetheless,wefind that they are automatically excluded for n≥2.VII.CONCLUSIONSTwo related questions of Shimony[4,5]and Aharonov[7]inspire this essay.Nonlocality and relativistic causality seem almost irreconcilable.The emphasis is on almost,because quantum mechanics does reconcile them,and does so in two different ways.But is quantum mechanics the unique theory that does so?Our answer is that it is not:model theories going beyond quantum mechanics,but respecting causality,allow nonlocality both ways.We qualify our answer by noting that nonlocality is not completely defined.Relativistic causality is well defined,but nonlocality in quantum mechanics includes both nonlocal correlations and nonlocal equations of motion,and we do not know exactly what kind of nonlocality we are seeking.Alternatively,we may ask what additional physical principles can we impose that will single out quantum mechanics as the unique theory.Our“superquantum”and “jamming”models open new experimental and theoretical possibilities.The superquantum12model predicts violations of the CHSH inequality exceeding quantum violations,consistent with causality.The jamming model predicts new effects on quantum correlations from some mechanism such as the burst of laser light suggested by Shimony[4].Most interesting are the theoretical possibilities.They offer hope that we may rediscover quantum mechanics as the unique theory satisfying a small number of fundamental principles:causality plus nonlocality“plus something else simple and fundamental”[13].ACKNOWLEDGMENTSD.R.acknowledges support from the State of Israel,Ministry of Immigrant Absorption, Center for Absorption in Science.13REFERENCES[1]J.S.Bell,Physics1,195(1964).[2]The term relativistic causality denotes the constraint that information cannot be trans-ferred at speeds exceeding the speed of light.This constraint is also called no signalling.[3]G.C.Ghirardi,A.Rimini and T.Weber,Lett.Nuovo Cim.27(1980)263.[4]A.Shimony,in Foundations of Quantum Mechanics in Light of the New Technology,S.Kamefuchi et al.,eds.(Tokyo,Japan Physical Society,1983),p.225.[5]A.Shimony,in Quantum Concepts in Space and Time,R.Penrose and C.Isham,eds.(Oxford,Claredon Press,1986),p.182.[6]Y.Aharonov,H.Pendleton,and A.Petersen,Int.J.Theo.Phys.2(1969)213;3(1970)443;Y.Aharonov,in Proc.Int.Symp.Foundations of Quantum Mechanics,Tokyo, 1983,p.10.[7]Y.Aharonov,unpublished lecture notes.[8]Y.Aharonov and D.Bohm,Phys.Rev.115(1959)485,reprinted in F.Wilczek(ed.)Fractional Statistics and Anyon Superconductivity,Singapore:World-Scientific,1990;[9]It is true that the electron interacts locally with a vector potential.However,the vectorpotential is not a physical quantity;all physical quantities are gauge invariant.[10]S.Popescu and D.Rohrlich,Found.Phys.24,379(1994).[11]J.Grunhaus,S.Popescu and D.Rohrlich,Tel Aviv University preprint TAUP-2263-95(1995),to appear in Phys.Rev.A.[12]D.Rohrlich and S.Popescu,to appear in the Proceedings of60Years of E.P.R.(Work-shop on the Foundations of Quantum Mechanics,in honor of Nathan Rosen),Technion, Israel,1995.14[13]A.Shimony,private communication.[14]J.F.Clauser,M.A.Horne,A.Shimony and R.A.Holt,Phys.Rev.Lett.23,880(1969).[15]B.S.Tsirelson(Cirel’son),Lett.Math.Phys.4(1980)93;ndau,Phys.Lett.A120(1987)52.[16]For the maximal violation of the CHSH inequality consistent with relativity see also L.Khalfin and B.Tsirelson,in Symposium on the Foundations of Modern Physics’85,P.Lahti et al.,eds.(World-Scientific,Singapore,1985),p.441;P.Rastall,Found.Phys.15,963(1985);S.Summers and R.Werner,J.Math.Phys.28,2440(1987);G.Krenn and K.Svozil,preprint(1994)quant-ph/9503010.[17]A.Aspect,J.Dalibard and G.Roger,Phys.Rev.Lett.49,1804(1982).[18]D.Bohm,Wholeness and the Implicate Order(Routledge and Kegan Paul,London,1980);D.Bohm and B.Hiley,Found.Phys.5,93(1975);J.-P.Vigier,Astr.Nachr.303,55(1982);N.Cufaro-Petroni and J.-P.Vigier,Phys.Lett.A81,12(1981);P.Droz-Vincent,Phys.Rev.D19,702(1979);A.Garuccio,V.A.Rapisarda and J.-P.Vigier,Lett.Nuovo Cim.32,451(1981).[19]See e.g.D.Bohm,The Special Theory of Relativity,W.A.Benjamin Inc.,New York(1965)156-158.[20]We thank Y.Aharonov for a discussion on this point.[21]They need not be incompatible.An event in one Lorentz frame often is another eventin another frame.For example,absorption of a virtual photon in one Lorentz frame corresponds to emission of a virtual photon in another.In jamming,Jim might not only send instructions but also receive information,in both cases unconsciously.(Jim is conscious only of whether or not he jams.)Suppose that the time reverse of“sending instructions”corresponds to“receiving information”.Then each observer interprets the sequence of events correctly for his Lorentz frame.15。

Understanding the Unique Mechanism of L -FMAU (Clevudine)against Hepatitis B Virus:Molecular Dynamics Stud iesYouhoon Chong and Chung K.Chu*Department of Pharmaceutical and Biomedical Sciences,College of Pharmacy,The University of Georgia,Athens,GA 30602,USAReceived 8May 2002;accepted 13August 2002Abstract—The molecular dynamics simulation of HBV-polymerase .DNA .l -FMAU-TP complex demonstrated that l -FMAU-TP may not serve as a substrate for HBV polymerase because the appropriate binding of l -FMAU-TP to the active site of HBV polymerase may not take place without the unfavorable conformational adjustment,which prevents l -FMAU-TP from being incorporated into the growing viralDNA chain.#2002Elsevier Science Ltd.All rights reserved.In the last several years,active pursuit of effective anti-hepatitis B virus (HBV)agents has resulted in the iden-tification of a number of potentially useful nucleoside analogues.Treatment with nucleosides has shown immediate clinical benefits such as reduced viral load,suppression of progression of liver disease,and induc-tion of immunological clearance or seroconversion.l -FMAU (clevudine)was reported by Chu et al.1as a potent antiviralagent against H BV (EC 500.1m M in HepG2 2.2.15cells)as well as EBV,which has low cytotoxicities in a variety of cell lines including MT2,CEM,H1and HepG22.2.15and bone marrow pro-genitor cells.l -FMAU is metabolized in cells by the cellular thymidine kinase as well as deoxycytidine kinase to its monophosphate,and subsequently to the di-and triphosphate.2l -FMAU is currently undergoing phase II clinical trials in patients who are chronically infected with HBV.Hepadnaviruses replicate by a multistep mechanism that begins with reverse transcription of pregenomic RNA.The DNA synthesis is initiated by a primer which directly binds the first nucleotide (dGTP)of the DNA minus strand.3The DNA plus strand is then synthesized with the minus strand as a template to yield the mature,partially double-stranded DNA virus.Therefore,understanding how and which of these three distinct phases of hepadnaviralrepl ication (priming,reverse transcription and DNA-dependent DNA synth-esis)can be blocked by nucleoside analogues,can pro-vide valuable information for the discovery of more potent and safe anti-HBV drugs.Even though l -FMAU is known to act specifically on viral DNA synthesis,and its triphosphate inhibits the HBV DNA synthesis in a dose-dependent manner 4without being incorporated into the DNA or chain termina-tion,5the precise understanding of the mechanism of action of l -FMAU at the polymerase level has not been realized.It is known that nucleoside inhibitors,in general,interfere with the viral polymerase activ-ities by both competitive inhibition and incorpora-tion to the viralDNA strands.6Most of the antiviral nucleoside analogues studied thus far,with the exception of ribavirin,7exerted their antiviral action through the inhibition of viralpol ymerase and their incorporation into the viralDNA.By using replicating cores extracted from congenitally infected ducks,the anti-HBV mechanism of 3TC-TP was determined to be the inhibition of virus replica-tion by acting as a chain terminator of both the RT and DNA polymerase activities of the enzyme.8Also,even though entecavir and lobucavir are not obligate chain terminators of DNA synthesis by vir-tue of the OH group content of their sugar moieties,endogenous sequencing reactions conducted in repli-cative HBV nucleocapsids suggested that they may act as chain terminators by introducing enough structuraldistortion to precl ude the enzyme from optimalinteraction with the 30end of the growing DNA chain.9It was found that l -FMAU-TP is not a substrate of EBV DNA polymerase,which sug-gests that the anti-EBV activity of l -FMAU may0960-894X/02/$-see front matter #2002Elsevier Science Ltd.All rights reserved.P I I :S 0960-894X(02)00747-3Bioorganic &MedicinalChemistry Letters 12(2002)3459–3462*Corresponding author.Tel.:+1-706-542-5379;fax:+1-706-542-5381;e-mail:************not be due to its incorporation into EBV DNA.10 Therefore,of considerable mechanistic interest is how l-FMAU-TP can competitively inhibit the HBV polymerase,4without being incorporated into the growing HBV-DNA chain.For this purpose,l-FMAU-TP/HBV polymerase complex was con-structed and simulated by molecular dynamics to obtain the structuralas wel las mechanistic informa-tion of l-FMAU-TP in a molecular level.MethodsThe three-dimensionalstructuralinformation of H BV polymerase is still not available.However,the recently published homology model of HBV polymerase using HIV-1reverse transcriptase as a template11could be used for the construction of HBV polymerase. l-FMAU-TP complex.Therefore,the HBV polymerase domain was modeled by the composer module in Sybyl, version6.7(Tripos,Inc.)using the crystalstructure of HIV-1RT(PDB code1RTD).12The two Mg2+ions, thymidine triphosphate and template-primer duplex were located at the same position as the HIV-1RT. DNA.dNTP complex structure(1RTD).The stability of the modeled HBV polymerase.DNA.thymidine tri-phosphate complex was confirmed by performing mole-cular mechanics energy minimization and molecular dynamics simulation by using the molecular graphics and simulation program MacroModel,version7.0 (Schro dinger,Inc.).The complex was minimized until there was no significant movement in atomic coordi-nates using MMFF94s forcefield in the presence of GB/ SA continuum water model before performing molecular dynamics simulations.A conjugate gradient,Polak-Ribiere1st derivative method was used for energy mini-mization.Molecular dynamics simulations on HBV polymerase.DNA.l-FMAU-TP was performed with MMFF94s in the presence of GB/SA continuum water modelon a Sil icon Graphics Octane2workstation run-ning the IRIX6.5operating system by heating from0to 300K over5ps and equilibrating at300K for an addi-tional10ps.Production dynamics simul ations were carried out for500ps with a step size of1.5fs at300K.A shake algorithm was used to constrain covalent bonds to hydrogen atoms.For simulation of the HBV poly-merase.l-FMAU-TP complex,the residues further away than15A from the active site were not considered and the residues from6to15A were constrained by harmonic constraints.Only residues inside6A sphere from the l-FMAU-TP were allowed to move freely. The Monte Carlo conformational search of l-FMAU was performed in5000steps,in the presence of GB/SA water modelusing MM3forcefiel d.Results and DiscussionAs was pointed out by Das et al.,11there were several interesting structuraldifferences at the active sites between the template enzyme,HIV-1reverse tran-scriptase(RT)and thefinalmodelof H BV pol ymerase.Among those differences,the most outstanding one on which we focused was Met519in HBV polymerase which corresponds to Gln151in RT(Fig.1).In RT, Gln151is tightly bound to the neighboring residues such as Arg72and Lys73by hydrogen bonding and participates in the formation of the‘30-OH pocket’. Since this residue is directly involved in the stabilization of the bound nucleoside triphosphate,Q151M mutation causes multidrug resistance in RT.13Therefore,of great structuralinterest was the rol e of Met519at the active site of HBV polymerase(Fig.1).The crystalstructure of l-FMAU was obtained from the Cambridge StructuralDatabase(Fig.2a).In con-formationalpoint of view,l-FMAU is very character-istic since the gauche effects caused by the two electron withdrawing groups at the20(F)and30(OH)positions (Fig.2b)shift the equilibrium to the south(20-endo) conformation(Fig.2c).On the other hand,the ternary complex of RT,which was used as a template for the construction of the homology model of HBV polymerase,showed that although the DNA appears to be predominantly in the B-form,the base pairs close to the polymerase active site have an A-like conformation with a widened minor groove.12It is important that in B-DNA the20-deoxy-sugars prefer a distinct south conformation,whereas in A-DNA the20-deoxysugars require puckering in the antipodalnorth conformation,14which disfavors the location of20-endo l-nucleoside at the active site ofthe parison of the active site residues between the template (HIV-1RT)and the modeled HBVpolymerase.Figure2.Structure of l-FMAU:(a)X-ray structure of l-FMAU;(b) l-FMAU has two electron withdrawing groups at the20and30posi-tions;(c)Gauche effect favors20-endo(south)conformation.3460Y.Chong,C.K.Chu/Bioorg.Med.Chem.Lett.12(2002)3459–3462polymerase.Docking the l-FMAU-TP at the active site of HBV polymerase was challenging because of the steric hindrance of the sugar moiety of l-FMAU with the30-end of the primer strand.Additionally,the30-OH group of l-FMAU was found to be in too close contact to the aromatic ring of Phe436(Fig.3a).Therefore,the RT-like active site conformation may not be able to accommodate l-FMAU-TP.As the HBV polymerase has Met519,which is not involved in the specific interaction with the active site residues,the active site of HBV polymerase is not as tight as that of RT.Therefore,the conformationalflexibil ity of H BV polymerase provided by Met519might generate a favorable conformation to accommodate l-FMAU-TP (Fig.3b).The conformationalspace of the active site of HBV polymerase was investigated by simulating the complex by molecular dynamics to give a stable ternary complex which was free of steric hindrance among the 30-end of the primer strand,l-FMAU-TP and the aro-matic ring of Phe436(Fig.3).The conformational adjustment initiated at Met519propagated to the nearby Phe436to give enough space for l-FMAU-TP (Fig.3b)to undergo the conformationalchange from 20-endo to30-endo(Fig.4).As a result,the sugar moi-eties of l-FMAU-TP and30-terminalnucl eoside of the primer strand could acquire enough space between each other(Figs.4and5).Even though theflexibility of the HBV polymerase gave a different active site conformation which could accommodate l-FMAU-TP,its binding should take place through a conformational change in its own sugar ring.Since the20-endo conformation of FMAU is found in its X-ray structure and believed to be the most stable, the conformationalchange in l-FMAU-TP can be an unfavorable process with a loss of binding energy.The relative stabilities of20-endo and30-endo conformations of l-FMAU were compared by a Monte Carlo con-formationalsearch,which found the20-endo conforma-tion as a global minimum(À120.93kcal/mol)with45 hits.However,the30-endo conformer was found as stable as the global minimum conformer(À120.86kcal/mol)of 20-endo with37hits,which suggests that l-FMAU-TP can adjust its conformation to bind to the active site of HBV polymerase without significant loss of energy.On the other hand,the conformationalchange in l-FMAU-TP resulted in an interesting change in the polymerization geometry of the growing viral DNA chain(Fig.6).Since this polymerization should take place by the S N2-type attack of the30-OH group at the 30-end of the primer strand on the a-phosphorous atom of the nucleoside triphosphate,the distance andrelative Figure3.Before(right)and after(left)molecular dynamics simulationof HBV polymerase l-FMAU-TP complex:(a)the steric hindranceamong thefinalprimer residue,l-FMAU-TP and Phe436is relievedafter simulation;(b)the conformational change in Phe436induced byMet519provides enough space for l-FMAU-TP to adjust its con-formation.Figure5.The monitored interatomic distances(H–H00,H–H0and H0–F)shows that the conformationalchange in l-FMAU-TP providedenough space between thefinalprimer residue and l-FMAU-TP.Among the triphosphate part of l-FMAU-TP,only a-phosphorousatom is shown forclarity.Figure4.Conformationalchange of l-FMAU-TP from20-endo(right)to30-endo(left)after molecular dynamics simulation.Y.Chong,C.K.Chu/Bioorg.Med.Chem.Lett.12(2002)3459–34623461orientation between the two atoms are critical.As can be found in many X-ray structures of the protein including the DNA duplex and the nucleoside triphos-phate substrate,the optimum distance between the nucleophile (30-OH at the primer end)and the reaction center (a -phosphorous of the nucleoside triphosphate)isaround 3.5A.12In l -FMAU-TP binding to the active site of HBV polymerase,however,as the sugar moiety of l -FMAU-TP separates from the 30-end of the primer strand by the conformationalchange,its a -phosphate atom also moves out from the 30-OH group of the pri-mer end by more than 2A(5.7A )(Fig.6).Therefore,the incorporation of l -FMAU-TP to the growing viral DNA chain to act as a chain terminator would not take place easily because of this deformed polymerization geometry,which may be the reason that l -FMAU is not incorporated to the HBV DNA.In summary,because of the unique conformation of l -FMAU,the binding of its triphosphate to the active site of HBV polymerase should take place with conforma-tionalchanges at the enzyme active site as wel las the l -FMAU-TP itself.During this conformational change,however,the nucleophile and the reaction center for the S N 2-type DNA chain elongation separate from each other to give a deformed polymerization geometry.Taken together,by the molecular dynamics simulation study of HBV-polymerase .DNA .l -FMAU-TP com-plex,we have demonstrated that l -FMAU-TP can act as a competitive inhibitor by binding to the active site of HBV polymerase,but not act as a substrate because thebinding of l -FMAU-TP to the active site of HBV polymerase cannot take place without the conforma-tionaladjustment,which prevents l -FMAU-TP from being incorporated into the growing viralDNA chain.This result may suggest that l -FMAU-TP occupies the catalytic site of the polymerase,thereby inhibits the priming of the HBV DNA chain elongation.AcknowledgementsThis research was supported by the U.S.Public Health Service Grant (AI32351)from the NationalInstitutes of Health and the Department of Veterans Affairs.References and Notes1.Chu,C.K.;Ma,T.-W.;Shanmuganathan,K.;Wang,C.-G.;Xiang,Y.-J.;Pai,S.B.;Yao,G.-Q.;Sommadossi,J.-P.;Cheng,Y.C.Antimicrob.Agents Chemother.1995,39,979.2.Chu,C.K.;Boudinot,F.D.;Peek,S.F.;Hong,J.H.;Choi,Y.;Korba,B.E.;Gerin,J.L.;Cote,P.J.;Tennant,B.C.;Cheng,Y.-C.Antiviral Therapy 1998,3(Suppl.3),113.3.Wang,G.-H.;Seeger,C.Cell 1992,71,663.4.Pai,S.B.;Liu,S.-H.;Zhu,Y.-L.;Chu,C.K.;Cheng,Y.-C.Antimicrob.Agents Chemother.1996,40,380.5.Cheng,Y.-C.Personalcommunication.6.(a)Hart,G.J.;Orr,D.C.;Penn,C.R.;Figueiredo,H.T.;Boehme,N.M.;Cameron,J.M.Antimicrob.Agents Che-mother.1992,36,1688.(b)St.Clair,M.H.;Richards,C.A.;Spector,T.;Weinhold,K.J.;Miller,W.H.;Langlois,A.J.;Furman,P.A.Antimicrob.Agents Chemother.1987,31,1972.7.Crotty,S.;Cameron,C.;Andino,R.J.Mol.Med.2002,80,86.8.Severini,A.;Liu,X.-Y.;Wilson,J.S.;Tyrrell,D.L.J.Antimicrob.Agents Chemother.1995,39,1430.9.Seifer,M.;Hamatake,R.K.;Colonno,R.J.;Standring,D.N.Antimicrob.Agents Chemother.1998,42,3200.10.Yao,G.-Q.;Liu,S.-H.;Chou,E.;Kukhanova,M.;Chu,C.K.;Cheng,Y.-C.Biochem.Pharmacol.1996,51,941.11.Das,K.;Xiong,X.;Yang,H.;Westland,C.E.;Gibbs,C.;Sarafianos,S.G.;Arnold,E.J.Virol.2001,75,4771.12.Huang,H.;Chopra,R.;Verdine,G.L.;Harrison,S.C.Science 1998,282,1669.13.(a)Iversen,A.F.N.;Shafer,R.W.;Wehrly,K.;Winters,M.A.;Mullins,J.I.;Chesebro,B.;Merigan,T.C.J.Virol.1996,70,1086.(b)Shirasaka,T.;Kavlick,M.F.;Ueno,T.;Gao,W.-Y.;Kojima,E.;Alcaide,M.L.;Chokekijchai,S.;Roy,B.M.;Arnold,E.;Yarchoan,R.;Mitsuya,H.Proc.Natl.Acad.Sci.U.S.A.1995,92,2398.14.For a comprehensive review of these concepts see Saenger,W.In Principles of Nucleic Acid Structure ;Springer:NewYork.Figure 6.The conformationalchange in l -FMAU-TP separates its a -phosphorous atom from the 30-OH group in the finalprimer residue(dGMP),which deforms the normalpol ymerization geometry (3.5A)for the viralchain el ongation.Among the triphosphate part of l -FMAU-TP,only a -phosphorous atom was shown for clarity.3462Y.Chong,C.K.Chu /Bioorg.Med.Chem.Lett.12(2002)3459–3462。

a r X i v :c o n d -m a t /0508281v 3 [c o n d -m a t .o t h e r ] 23 S e p 2005Dynamic nuclear polarization of a single charge-tunable InAs/GaAs quantum dotB.Eble,1O.Krebs,1,∗A.Lema ˆitre,1K.Kowalik,1,2A.Kudelski,1P.Voisin,1B.Urbaszek,3X.Marie,3and T.Amand 31CNRS-Laboratoire de Photonique et Nanostructures,Route de Nozay,91460Marcoussis,France2Institute of Experimental Physics,Warsaw University,Ho˙z a 69,00-681Warsaw,Poland3Laboratoire de Nanophysique Magn´e tisme et Opto´e lectronique,INSA,31077Toulouse Cedex 4,France(Dated:July 12,2005)We report on the dynamic nuclear polarization of a single charge-tunable self-assembled InAs/GaAs quantum dot in a longitudinal magnetic field of ∼0.2T.The hyperfine interaction be-tween the optically oriented electron and nuclei spins leads to the polarization of the quantum dot nuclei measured by the Overhauser-shift of the singly-charged excitons (X +and X −).When going from X +to X −,we observe a reversal of this shift which reflects the average electron spin optically written down in the quantum dot either in the X +state or in the final state of X −recombination.We discuss a theoretical model which indicates an efficient depolarization mechanism for the nuclei limiting their polarization to ∼10%.PACS numbers:71.35.Pq,72.25.Fe,72.25.Rb,78.67.HcSpin dynamics of an electron confined in a self-assembled semiconductor quantum dot (QD)is currently the subject of an intense research [1,2,3,4,5,6,7].It indeed represents a promising direction for implement-ing quantum computation algorithms in solid state,be-cause once the electron is confined in a quantum dot,its spin dynamics at low temperature is almost no longer subjected to the random perturbations which lead to re-laxation and decoherence in bulk or quantum wells.For example the usual spin relaxation due to spin-orbit in-teraction turns out to be quite negligible [1,8].The sub-sisting sources of relaxation which have been identified in real QDs are (i)the exchange interaction with additional hole(s)or electron(s)[6]and (ii)the hyperfine interaction with the QD nuclei spins [3,4].In order to address this issue with optical techniques,field-effect structures em-bedding charge-tunable QDs [9]offer an amazing poten-tial :the exchange-induced spin relaxation can be kept under control e.g.by extracting the hole from a photo-excited electron-hole pair (named further exciton)[1]or by adding a charge preventing the exchange to operate [6,10],while the effective role of the hyperfine interaction which only affects the conduction band electrons can be investigated by controlling the nature (electron or hole)of the spin-polarized carrier.In this Letter we address the issue of hyperfine in-teraction in a self-assembled charge-tunable InAs/GaAs quantum dot submitted to an external magnetic field of ∼0.2T.Optical excitation with circularly polarized light is used for writing down the electron and/or hole spins,whereas an external bias applied to the n-Schottky-type sample controls the electronic charge [6,9,11,12].The same single QD has been studied in three differentregimes:when the electron spin ˆSe interacting with the nuclear spins ˆIj (i)forms with two photo-excited holes a positive trion X +,(ii)forms a neutral exciton X 0,and (iii)results from the radiative recombination of a nega-tive trion X −made of two electrons and one hole.Bymeasuring the Overhauser shift of the X +or X −Zee-man splitting [13,14,15],we show that the small applied magnetic field leads to the optically-induced polarization of the QD nuclei,with a non-linear dependence on theaverage electron spin ˆS e zdeduced from the photolumi-nescence (PL)circular polarization.Remarkably,this shift changes sign with the crossing from X +to X −.We present a theoretical description of the nuclear polariza-tion dynamics in InAs/GaAs QDs explaining most of our results.The sample which has already been used in Ref.[6]was grown by molecular beam epitaxy on a [001]-oriented semi-insulating GaAs substrate.The InAs QDs are grown in the Stranski-Krastanov mode 25nm above a 200nm-thick n +-GaAs layer and capped by an intrin-sic GaAs (25nm)/Al 0.3Ga 0.7As (120nm)/GaAs (5nm)multilayer.The QD charge is controlled by an electrical bias applied between a top Schottky contact and a back ohmic contact.We used a metallic mask evaporated on the Schottky gate with 1µm-diameter optical apertures to spatially select single QDs.FIG.1:Gray-scale contour plot of the PL intensity from a single InAs QD at T=5K versus the detection energy and applied bias under intra-dot excitation at 1.31eV.2Figure 1shows the T=5K PL intensity contour plot against bias and detectionenergyofthe singleQDthathas been extensively studied in this work.The identifi-cation of the different spectral lines and of the associated QD charge relies on several robust observations :(i)Be-tween 0V and ∼0.15V we only observe the PL emission from the ground state exciton X 0clearly identified by its fine structure [Fig.2(b)][16]and by the biexciton (hardly perceptible in Fig.1)appearing under stronger excita-tion at lower energy.(ii)Above 0.15V the X −trion red-shifted by ∼6meV shows up indicating the charging of the QD with an electron [6,17,18].Both lines (X 0and X −)still coexist because under non strictly-resonant excitation (here 1.31eV)a single photo-hole can be cre-ated in the QD giving rise to optical recombination with the resident electron.(iii)Above 0.35V,the neutral ex-citon line definitely disappears indicating the occupation with 2electrons.(iv)For negative bias a symmetrical charging effect occurs for holes.The neutral exciton line which disappears as a result of the electron tunnelling out of the QD,is replaced by a 3meV blue-shifted line assigned to the trion X +[12,19].Although the applied bias only controls the conduction band chemical poten-tial and thus cannot itself generates the QD charging with holes,this effect is achieved under strong intra-dot exci-tation.It directly creates a hole within the QD,which does not escape as the electron thanks to its larger effec-tive mass.To study the influence of hyperfine interaction on spin dynamics,optical orientation experiments have been per-formed in presence of a small longitudinal magnetic field parallel to the QD growth axis z [2,13,20].The lat-ter was provided by a permanent magnet simply put below the sample within the cryostat cold finger.Its amplitude B ext at the sample position was estimated to ≈0.2T.We used a standard micro-PL setup based on a ×50microscope objective,a double spectrometer of 0.6m-focal length and a Nitrogen-cooled CCD array detector,providing a spectral resolution of 30µeV and a precision on line position of about 1µeV after de-convolution by a Lorentzian fit.The optical excitation and detection were both performed along the z axis.Thus the degree of PL circular polarization defined by ρc =(I σ+−I σ−)/(I σ++I σ−),where I σ+(−)denotes the PL intensity measured in σ+(−)polarization,traces theaverage spin S ez =−ρc /2of the electron participating in the PL signal [20].This results from the usually accepted assumption of pure heavy-hole ground state with angular momentum projection m z =±32,±3δ21+δ2Z.Figure 2(c)shows the PL spectra resolved in circular po-larization.Under linearly polarized excitation we find for the three lines a Zeeman splitting δZ ≈28µeV in agree-ment with an exciton g -factor of ∼3[16].Under circularly polarized excitation a significant deviation from the sole Zeeman interaction is now observed :the X +splitting gets larger in σ+excitation by +10µeV and smaller in σ−by -15µeV.This so-called Overhauser shift (OHS)denoted δn indicates the polarization of the QD nuclear3 spins which progressively builds up through the hyper-fine interaction with the optically oriented electrons in the QD.Remarkably a symmetrical but reversed effect occurs for X−with a shiftδn=+15µeV inσ−andδn=-25µeV inσ+,whereas the PL from X−and X+shows the same helicity.This OHS reversal demonstrates that in the case of a spin-polarized X−for which the total electron spin is zero,the mechanism leading to nuclear polarization doesn’t operate during X−lifetime but takes place due to the interaction with the single electron left in the QD after the optical recombination.This con-trasts with the results reported for GaAs QDs[15].For X0which still shows a weak polarization at0.2T,we observed no significative OHS except when there is an overlapp with X+(situation of Fig.2(c)because of exci-tation at higher energy),in which case it only acts as a probe of OHS produced by X+.An other feature of these results is the pronounced OHS asymmetry when chang-ing the excitation fromσ+toσ−.This clearly appears in Fig.3which reports the bias dependence of circular po-larization and of the trion spin splitting.This asymmetry means that polarizing the nuclear spins in the direction which produces a larger effectivefield for the electron is more difficult than in the opposite direction.The total electron spin splitting represents indeed the main energy cost of the electron-nucleiflip-flop process(the Zeeman splitting of nuclei being much smaller),which thus pro-duces a negative feedback on the nuclear polarization as we show in the following.FIG.3:(Color online)(a)circular polarization and(b)spin splitting of X+and X−PL lines against applied bias at B ext=0.2T,underσ+(red)andσ−(blue)polarized excita-tion at1.31eV.The gray-shaded area represents the region of X0stability and the solid lines are a guide for the eye.(c) Overhauser shift versus circular polarization for X−(+0.4V) and X+(-0.2V)measured for excitation polarizations vary-ing fromσ+toσ−.Solid lines are theoreticalfits according to Eq.4obtained with g e2ˆσe confined in a QD with N nuclear spins is given by[13,20]:ˆHhf=ν02 (1) whereν0is the two-atom unit cell volume,r j is the position of the nuclei j with spinˆI j,A j is the con-stant of hyperfine interaction with the electron and ψ(r)is the electron envelope function.The sum goes over the nuclei interacting significantly with the electron (i.e.essentially in the effective QD volume defined by V=( |ψ(r)|4d r)−1=ν0N/2).This interaction has two important effects on the electron-nuclei spin sys-tem.(i)It acts as an effective magneticfield B n≈ j A j I j/(Ng eµB)on the electron spin of g-factor g e. In absence of nuclear polarization,this random nuclear field averages to zero but showsfluctuations∝A/√2/Nν0over the involved nuclei.This also amounts to consider a uni-form nuclear polarizationρα= Iαz /Iαfor each isotopic specieαof the QD.The theory of time-dependent per-turbation up to the second order applied to theflip-flop interaction characterized by a correlation timeτc yields the following equation rate[24]:d IαzTα( Iαz −Qα S e z )(2) where Qα=Iα(Iα+1)Tα=2f eτcg XδZ+δn)τc/¯h 2Aα4 spins byδn=−2 αxα Iαz Aαwhere xαis the fractionof specieα.Note Eq.(2)is only valid under the conditionof weak nuclear polarization[20,24].This is experimen-tally verified here with a maximum polarizationρα≈0.1deduced from the measured OHS(≈25µeV)divided byits maximum theoretical value(≈250µeV for a realisticInGaAs QD).The stationary solution of Eq.(2)driven bythe electron polarization S e z /S close to unity is there-fore far from being reached which means that nucleardepolarization must be taken into account.The physicalorigin of this mechanism likely relies on the dipolar(orquadrupolar)coupling between nuclei,that in spite ofthe screening by the applied magneticfield opens a wayfor nuclear spin diffusion due to the time-dependent hy-perfine interaction with electron spin[13].However,sincewe could not investigate further this effect by varying thefield,we simply describe it by adding to Eq.(2)the term−f e Iαz /T d where T d is a depolarization time constantindependent onα.The OHS reached at equilibrium isthen given by the implicit equation:δn=−∆∗ S e zδZ+δn)2 (4)g Xwhere∆∗=2˜A αxαQα,κ=τc/T d(N/˜A)2and wehave used˜A(≈50µeV)instead of Aαwhich indeedweakly depends onα.Here we treat∆∗,τc andκasfitting parameters,whileδn,δZ, S e z can be determinedfrom the experiments.Note yet that∆∗amounts to≈1.3meV for a realistic In(Ga)As QD(with x In=0.3,x Ga=0.2,x As=0.5).Equation(4)clearly shows the negative feedback ofthe OHS on its equilibrium value through the electronspin splitting(g e5[11]J.J.Finley et al.,Phys.Rev.B63,73307(2001).[12]M.Ediger et al.,Appl.Phys.Lett.86,211909(2005).[13]D.Gammon et al.,Phys.Rev.Lett.86,5176(2001).[14]T.Yokoi et al.,Phys.Rev.B71,41307(R)(2005).[15]A.S.Bracker et al.,Phys.Rev.Lett.94,47402(2005).[16]M.Bayer et al.,Phys.Rev.B65,195315(2002).[17]B.Urbaszek et al.,Phys.Rev.Lett.90,247403(2003).[18]J.J.Finley et al.,Phys.Rev.B63,161305(R)(2001).[19]The weaker line denoted X+⋆is assigned to a hot trionbecause of its broad Lorentzian lineshape and its5meVredshift resulting of triplet configuration.[20]F.Meier and B.Zakharchenya,Optical Orientation,vol.8of Modern Problem in Condensed Matter Sciences (North-Holland,Amsterdam,1984).[21]G.Bester et al.,Phys.Rev.B67,161306(R)(2003).[22]L.Besombes et al.,Phys.Rev.Lett.85,425(2000).[23]I.A.Akimov et al.,Appl.Phys.Lett.81,4730(2002).[24]A.Abragam,Principles of Nuclear Magnetism(OxfordUniversity Press,1961),chap.8.。

a r X i v :c o n d -m a t /0301403v 2 [c o n d -m a t .d i s -n n ] 27 M a y 2003Ordering and Broken Symmetry in Short-Ranged Spin Glasses C.M.Newman ∗newman @ Courant Institute of Mathematical Sciences New York University New York,NY 10012,USA D.L.Stein †dls @ Depts.of Physics and Mathematics University of Arizona Tucson,AZ 85721,USA Abstract In this topical review we discuss the nature of the low-temperature phase in both infinite-ranged and short-ranged spin glasses.We analyze the meaning of pure states in spin glasses,and distinguish between physical,or “observable”,states and (probably)unphysical,“invisi-ble”states.We review replica symmetry breaking,and describe what it would mean in short-ranged spin glasses.We introduce the notion of thermodynamic chaos,which leads to the metastate construct.We apply these tools to short-ranged spin glasses,and conclude that replica symmetry breaking,in any form,cannot describe the low-temperature spin glass phase in any finite dimension.We then discuss the remaining possible scenarios that could describe the low-temperature phase,and the differences they exhibit in some of their physical prop-erties —in particular,the interfaces that separate them.We also present rigorous results on metastable states and discuss their connection to thermodynamic states.Finally,we discuss some of the differences between the statistical mechanics of homogeneous systems and those with quenched disorder and frustration.KEY WORDS:spin glass;Edwards-Anderson model;Sherrington-Kirkpatrick model;replica symmetry breaking;mean-field theory;pure states;ground states;metastates;domain walls;inter-faces;metastable statesContents1Introduction42A Brief History of Early Theoretical Developments72.1The Edwards-Anderson Hamiltonian (7)2.1.1Frustration (8)2.2Mean Field Theory,the Sherrington-Kirkpatrick Model,and the Parisi Solution..9 3Open Problems114Nature of Ordering in the Infinite-Ranged Spin Glass144.1Thermodynamic Pure States (14)4.2Overlap Functions and Distributions (16)4.3Non-Self-Averaging (17)4.4Ultrametricity (20)5Detection of Many States in Spin Glasses215.1Chaotic Size Dependence in the SK model (22)5.1.1States (22)5.1.2Overlaps (23)5.2Chaotic Size Dependence in the EA model (24)5.2.1“Observability”of States (24)5.2.2Sensitivity to Boundary Conditions and“Windows” (26)5.2.3Domain Walls and Free Energies (26)5.2.4Many States and Chaotic Size Dependence (28)6Metastates306.1Motivation and Mathematical Construction (30)6.2Physical Meaning and Significance (31)6.2.1Observable States and Thermodynamic Chaos (31)6.2.2Finite vs.Infinite V olumes (31)7Can a Mean-Field Scenario Hold in Short-Ranged Models?327.1Translation-Ergodicity (32)7.2The Standard SK Picture (34)7.3The Nonstandard SK Picture (36)7.4What Non-Self-Averaging Really Means (38)7.5Differences Between the Standard and Nonstandard Pictures (39)7.6Invariance of the Metastate (39)8Structure of the Low-T Spin Glass Phase428.1Remaining Possibilities (42)8.2The Problem with P(q) (43)9Interfaces459.1Space-Filling Interfaces and Observable States (45)9.2Invisible States (46)9.3Relation Between Interfaces and Pure States (47)9.4Low-Lying Excited States (47)10Summary and Discussion4910.1Summary (49)10.1.1Are the Pure States We Discuss the‘Usual’Ones? (50)10.1.2Is the P J(q)Used to Rule Out the Standard SK Picture the‘Correct’One?5010.2Comparison to Other Work (51)10.2.1Numerical Studies (51)10.2.2Analytical Studies (52)10.2.3Renormalization Group Studies and Types of Chaoticity (52)10.3Effects of a Magnetic Field (54)11Other Topics5511.1Metastable States (55)11.1.1A New Dynamical Method (55)11.1.2Results (57)11.2The Statistical Mechanics of Homogeneous vs.Disordered Systems (58)(a)(b)(c)(d)Figure1:A rough sketch of the classical ground states of:(a)a crystal;(b)a glass;(c)a ferro-magnet;(d)an Ising spin glass.In(a)and(b)the dots represent atoms;in(c)and(d)the arrows represent localized magnetic moments.(In the case of(b),it is more accurate to describe the configuration as a frozen metastable state.)1IntroductionDespite decades of intensive investigation,the statistical mechanics of systems with both quenched disorder and frustration remains an open problem.Among such systems,the spin glass is arguably the prototype,and inarguably the most studied.Spin glasses are systems in which competition between ferromagnetic and antiferromagnetic interactions among localized magnetic moments(or more colloquially,“spins”)leads to a magneti-cally disordered state(Fig.1).The prime example of a metallic spin glass is a dilute magnetic alloy, in which a magnetic impurity(typically Fe or Mn)is randomly diluted within a nonmagnetic metal-lic host,typically a noble metal.The competition between ferromagnetic and antiferromagnetic interactions arises in these systems from the RKKY interactions[1,2,3]between the localized spins,mediated by the conduction electrons.But many other types of spin glass,with different microscopic mechanisms for their“spin glass-like”behavior,exist.Certain insulators,in which low concentrations of magnetic impuri-ties are randomly substituted for nonmagnetic atoms,also display spin glass behavior.A well-known example[4]is Eu x Sr1−x S,with x roughly between.1and.5,where the competition arises largely from nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interac-Figure2:Low-field magnetic susceptibilityχ(T)in Au Fe alloys at varying concentrations of iron impurity.From Cannella and Mydosh[6].tions.There are many other materials that exhibit spin glass behavior,both metallic and insulating, crystalline and amorphous.They can display Ising,planar,or Heisenberg behavior,and come in both classical and quantum varieties.In this review we consider only classical spin glasses[5].What are the main experimental features of spin glasses?One is the presence of a cusp in the low-field ac susceptibility(Fig.2),asfirst observed in Au Fe alloys by Cannella and Mydosh [6].This cusp becomes progressively rounded as the external magneticfield increases[7].The specific heat,however,rather than showing a similar singularity,typically displays a broad maxi-mum(Fig.3)at temperatures somewhat higher than the“freezing temperature”T f defined via the susceptibility peak(see,e.g.,[8]).Probes of the low-temperature magnetic structure using neutron scattering,M¨o ssbauer studies, NMR and other techniques confirm the absence of long-range spatial order coupled with the pres-ence of temporal order insofar as the spin orientations appear to be frozen on the timescale of the experiment.An extensive description of these and related experiments are presented in the review article by Binder and Young[9].Spin glasses are also characterized by a host of irreversible and non-equilibrium behaviors, including remanence,hysteresis,anomalously slow relaxation,aging and related phenomena.Be-cause this review will focus on static equilibrium behavior,these topics will not be treated here,butit is important to note that explaining these phenomena are essential to any deeper understandingFigure3:Magnetic specific heat of C m of Cu Mn at1.2%manganese impurity.The arrow indicates the freezing temperature T f as discussed in the text.From Wenger and Keesom[8].of spin glasses.For reviews,see[9,10,11,12].The quest to attain a theoretical understanding of spin glasses has followed a tortuous path, and to this day many of the most basic and fundamental issues remain unresolved.An extensive discussion of theoretical ideas can be found in a number of reviews[9,10,11,13,14,15,16]. The good news is that research into spin glasses has uncovered a variety of novel and sometimes stunning concepts;the bad news is that it is not clear how many of these apply to real spin glasses themselves.In this review we will explore some of these issues,in particular the nature of ordering and broken symmetry in the putative spin glass phase.As afirst step,one needs to capture mathematically the absence of orientational spin ordering in space with the presence of frozenness,or order in time.This was achieved early on by Edwards and Anderson(EA)[17],who noted that a low temperature pure phase of spin glasses should be characterized by a vanishing magnetization per spinM=limL→∞1|ΛL|x∈ΛLσx 2(2)whereσx is the spin at site x,ΛL is a cube of side L centered at the origin,and · denotes a thermalaverage.However,it was later discovered that,while the EA order parameter q EA plays a central role in describing the spin glass phase,it is insufficient to describe the low temperature ordering—at least in a mean-field version of the problem.In the following sections we will explain this statement, explore the relationship between the mean-field spin glass problem and its short-ranged version, and discuss some new and general insights and tools that may turn out to be useful in unraveling the complexities of the statistical mechanics of inhomogeneous systems.2A Brief History of Early Theoretical DevelopmentsQuestions regarding spin glass behavior fall naturally into two classes:thefirst pertains to proper-ties of a system in thermal equilibrium,and the second to those related to nonequilibrium dynam-ics.It is still not certain whether spin glasses possess nontrivial equilibrium properties,but their nonequilibrium ones surely are.As already noted,throughout this review we will focus primarily on spin glasses in thermal equilibrium.Perhaps the most fundamental question that can be asked is whether there exists such a thing as a true,thermodynamic spin glass phase;that is,is there a sharp phase transition from the high-temperature paramagnetic state to a low-temperature spin glass state in zero external magnetic field?Of course,this is presumably the simplest transition that could in principle occur;one could also ask aboutfield-induced transitions,ferromagnetic to spin glass transitions,and others. But given that all of these questions remain open,we’ll confine our attention here to the simplest of these.And even here,although experimental and numerical studies have tended to favor an affirmative answer,the issue is by no means resolved.2.1The Edwards-Anderson HamiltonianIn order to proceed,we need a specific model to study.The majority of theoretical investigations begin with a Hamiltonian proposed by Edwards and Anderson[17]:H=− <x,y>J xyσxσy−h xσx,(3) where(to keep things as general as possible)x is a site in a d-dimensional cubic lattice,σx is the spin at site x,the spin couplings J xy are independent,identically distributed random variables,h is an external magneticfield,and thefirst sum is over nearest neighbor sites only.We will usually take the spins to be Ising variables,i.e.,σx=±1.Throughout most of the paper we will chooseh=0and the spin couplings J xy to be symmetrically distributed about zero;as a result,the EA Hamiltonian in Eq.(3)has global spin inversion symmetry.Popular choices for the distribution of the couplings J xy are bimodal and Gaussian.Most of what we discuss below will be independent of which of these is chosen,but for specificity(and to avoid accidental degeneracies when discussing ground states)we will choose the couplings from a Gaussian distribution with mean zero and variance one.It is important to note the the disorder is quenched:once chosen,the couplings arefixed for all time.We denote by J a particular realization of the couplings,corresponding physically to a specific spin glass sample.Proper averaging over quenched disorder is done on extensive quantities only[18],i.e.,at the level of log Z rather than Z,where Z is the partition function.Of course,the EA Hamiltonian looks nothing like a faithful microscopic description of spin interactions in a dilute magnetic alloy,or an insulator like Eu x Sr1−x S—and because the statistical mechanics of the EA Hamiltonian remain to be worked out,a direct comparison with experiment remains elusive.However,a central assertion of[17]is that the essential physics of spin glasses is the competition between quenched ferromagnetic and antiferromagnetic interactions,regardless of microscopic details;and so the EA Hamiltonian remains the usual launching point for theoretical analyses of real spin glasses.2.1.1FrustrationA striking feature of random-bond models like the EA spin glass is the presence of frustration,in this case meaning the inability of any spin configuration to simultaneously satisfy all couplings.It is easily verified that,in any dimension larger than one,all of the spins along any closed circuit C in the edge lattice cannot be simultaneously satisfied ifJ xy<0.(4)<x,y>∈CThe definition of frustration given above wasfirst suggested by Toulouse[19].A different for-mulation due to Anderson[20]received less notice when it wasfirst proposed,but its underlying ideas may prove useful in more recent spin glass research.The basic notion is that frustration man-ifests itself as free energyfluctuations(e.g.,with a change in boundary conditions from periodic to antiperiodic)that scale as the square root of the surface area of a typical sample.Hence the spin glass is characterized by both quenched disorder and frustration.The presence of frustration,leading to a complicated geometry of entangled frustration contours,suggests the possibility that spin glasses,in at least some dimensions,may possess multiple infinite-volumeground or pure states unrelated by any simple symmetry transformation.We will return to this question later.We note here,though,that there exists at least one(unrealistic)spin glass model where the number of ground states can be computed in allfinite dimensions.This is the highly disordered model of the authors[21,22](see also[23])in which the coupling magnitudes scale nonlinearly with the volume(and so are no longer distributed independently of the volume,al-though they remain independent and identically distributed for each volume).It can be shown [21,22]that there exists a transition in ground state multiplicity in this model:below eight dimen-sions,it has only a single(globally spin reversed)pair of ground states,while above eight it has uncountably many ground state pairs.Interestingly,the high-dimensional ground state multiplicity can be shown to be unaffected by the presence of frustration,although frustration still plays an interesting role:it leads to the appearance of chaotic size dependence,to be discussed in Sec.5.2.2Mean Field Theory,the Sherrington-Kirkpatrick Model,and the ParisiSolutionMeanfield models often provide a usefulfirst step towards understanding the low-temperature phase of a condensed matter system;in the case of spin glasses,the usual procedure seems to have taken a particularly interesting twist.The meanfield theory of spin glasses turns out to be far more intricate than those of most homogeneous systems,and as a result several different approaches have been tried.Also noteworthy are even simpler,soluble spin glass-like models,in particular the random energy model of Derrida[24].However,here we will confine ourselves to a discussion of the Sherrington-Kirkpatrick(SK)model[25],an infinite-ranged version of the EA model in which meanfield theory is presumably exact.The SK Hamiltonian for a system of N spins is(as usual,we take externalfield to be zero):H N=−(1/√found to become negative at sufficiently low temperature.The following four years saw intensive efforts to solve for the low-temperature phase of the SK model.Of particular note is the direct meanfield approach of Thouless,Anderson,and Palmer [26],who pointed out the necessity of including the Onsager reactionfield term,and the paper by deAlmeida and Thouless[27],who studied the stability of the SK solution in the T-h plane and calculated the boundary between the regions where a single(i.e.,paramagnetic)phase is stable and the region where the low-temperature phase resides.One important question that remains open to this day is whether such an“AT line”exists for more realistic models(see Sec.10.3for further discussion).We will mainly focus,however,on what is today believed to be the correct solution for the low-temperature phase of the SK model.In a series of papers,Parisi and collaborators[28,29,30,31] proposed,and worked out the consequences of,an extraordinary ansatz for the nature of this phase. Following the mathematical procedures underlying the solution,it came to be known as replica symmetry breaking(RSB).We will not review those mathematical procedures here;they are worked out in detail in sev-eral review articles and books(see,e.g.,[9,10,11,13,14,16]).We will also omit discussion of important related developments,such as the dynamical interpretation of Sompolinsky and Zip-pelius[32,33,34].We will concern ourselves instead with both the physical and mathematical interpretations of the Parisi solution,and the type of ordering that it implies.These interpretations took several years to work out,culminating in the work of Mezard et al. [30,31]that introduced the ideas of overlaps,non-self-averaging,and ultrametricity as a means of understanding the type of order implied by the Parisi solution.These terms,and their relevance for the Parisi solution,will be described in Sec.4.For now,we simply note that the solution of the infinite-ranged SK model generated tremendous excitement;as described by Rammal et al.[35], it displayed a new type of broken symmetry“radically different from all previously known”.This is not an overstatement.The starting point is the observation that the low-temperature phase consists not of a single spin-reversed pair of states,but rather“infinitely many pure thermodynamic states”[29],not re-lated by any simple symmetry transformations.This possibility had already been foreshadowed by the Thouless-Anderson-Palmer approach[26],whose mean-field equations were known to have many solutions(not necessarily all free energy minima,except at zero temperature[36]).The ex-istence of many states meant that the correct order parameter needed to reflect their presence,and to describe the relations among them.The single EA order parameter was therefore insufficient to describe the low-temperature phase(although it retained an important role,as we’ll see);insteadone needed an order parameter function.Before we describe these ideas in more detail,we willfirst step back and consider the basic outline of the problem that interests us.In particular,we need to ask:what is it that we want to know?What are the fundamental open questions?And how do they tie in with the broader areas of condensed matter physics and statistical mechanics?These questions will be considered in the following section.3Open ProblemsIn this review we concern ourselves with perhaps the most basic questions that can be asked:is there a true spin glass phase,and if so,what is its nature?For the infinite-ranged SK model,these questions appear largely resolved,though some open questions remain.For the EA model(as a representative of more general“realistic”models,i.e.,finite-dimensional and non-infinite-ranged),the primary question of whether a thermodynamic phase transition exists remains open.There is suggestive analytical[37,38]and numerical[9, 39,40,41]evidence that a phase transition to a broken spin-flip symmetric phase is present in three-dimensional and,even more likely,in four-dimensional Ising spin glasses.However,no one has yet been able to prove or disprove the existence of a phase transition,and the issue remains unsettled[42].Of course,existence of a phase transition does not necessarily imply more than a single low-temperature phase;one could,for example,have a transition above which correlations decay ex-ponentially and below which they decay as a power law,with q EA=0at all nonzero temperatures. However,most numerical simulations and theoretical pictures that point to a low-temperature spin glass phase suggest broken spin-flip symmetry.We are therefore led to:Open Question1.Does the EA Ising model have an equilibrium phase transition above some lower critical dimension d c;and if so,does the low-temperature phase have broken spin-flip sym-metry?If the answer to this question turns out to be no,then subsequent research will need to focus on dynamical behavior,which—as in ordinary glasses—presents a range of difficult and important problems.However,given the reasonable possibility that there is indeed a sharp phase transition, it is worthwhile to ask:If there is a phase transition for the EA Ising model at some d>d c,what is the nature of the ordering of the low-temperature phase?Because of the open-ended nature of this question,it won’t be assigned a number;instead, we’ll break it down into several parts.The remaining questions assume that there is an equilibrium phase transition critical temperature T c>0,below which there is broken spin-flip symmetry (equivalently,a phase with q EA>0),but we make no assumptions as to whether d c is less than or equal to three.Open Question2.What is the number of equilibrium pure state pairs(at nonzero temperature) and ground state pairs(at zero temperature)in the spin glass phase?We have seen that the mean-field RSB picture assumes infinitely many such pairs.A competing picture,known as the droplet/scaling picture,due to Macmillan,Bray and Moore,Fisher and Huse, and others[43,44,45,46,47,48,49],asserts that there is only a single pair of pure/ground states in the spin glass phase in anyfinite dimension.Because of the importance of this picture,we discuss it briefly here.“Domain wall renormal-ization group”studies[43,44]led to a scaling ansatz[43,44,46]that in turn led to the development of a corresponding physical droplet picture[46,47,48,49]for spin glasses.In this picture,ther-modynamic and dynamic properties at low temperature are dominated by low-lying excitations corresponding to clusters of coherentlyflipped spins.The density of states of these clusters at zero energy falls off as a power law in lengthscale L,with exponent bounded from above by(d−1)/2. At low temperatures and on large lengthscales the thermally activated clusters form a dilute gas and can be considered as non-interacting two-level systems.The resulting two-state picture(in which there is no nontrivial replica symmetry breaking)is therefore significantly different from the mean-field picture arising from the SK model.So do spin glasses infinite dimensions have many equilibrium states or a single pair?Except in the highly disordered model[21,22],the answer is not known.In one dimension(where there is no internal frustration),there is only a single pair of ground states,and a single paramagnetic phase at all nonzero temperatures.In an infinite number of dimensions,there presumably would be an infinite number of pure state pairs for T<T c.Recent numerical experiments[50,51,52] seem to indicate a single pair of ground states in two dimensions(where it is believed that T c=0), but given that lattice sizes studied are still not very large,the question is not completely settled. Recent rigorous work by the authors[53,54]has led to a partial result that supports the notion that only a single pair of ground states occurs in two dimensions.In three dimensions numerical simulations give conflicting results[55,56].While the mean-field-like RSB many-state picture and the two-state droplet/scaling picture have historically been the main competing pictures,there are others as well.At least one of these will be discussed later.One often sees in the literature an unspoken assumption that the presenceof many states is synonymous with RSB,and similarly that the presence of only a single pair is equivalent to droplet/scaling.We emphasize,however,that while these are necessary requirements for each picture,respectively,they are not sufficient:each has considerable additional structure (which,in the mean-field RSB case,will be discussed in the next section).This then leads to our next question:Question3.If there do exist infinitely many equilibrium states in some dimensions and at some temperatures,are they organized according to the mean-field RSB picture?Treatment of this question is the main theme of the remainder of this review.A series of both rigorous and heuristic results,due to the authors,has largely answered this question in the negative, and it is therefore not listed as open.(A complete discussion is given in Sec.7.)However,there are remaining questions,such as:(Semi-)Open Question4.What are the remaining possibilities for the number and organiza-tion of equilibrium states in the low-temperature spin glass phase?This question is examined in Sec.8.1.In discussing this,we will not consider every logical alternative to the mean-field picture,but rather what we consider to be the most likely remaining scenarios for the low-temperature phase offinite-dimensional spin glasses.The discussion so far has considered only equilibrium pure or ground states,with a view to-wards determining the nature of broken symmetry in realistic spin glasses.However,a more gen-eral discussion of thermodynamics and dynamics,particularly with a view towards explaining experimental observations,needs to include questions about other types of states,such as: Question5.How are energetically low-lying excitations above the ground state(s)character-ized?(Sec.9.4.)Question6.What can be proven about numbers and overlaps of metastable states?Do they have any connection(s)to thermodynamic pure states?(Sec.11.1.)Although many other important questions remain open,we close here with a question of more general interest than for spin glass physics alone:Question7.In what ways do we now understand how the statistical mechanical treatment of frustrated,disordered systems differs in fundamental ways from that of homogeneous systems? (Sec.11.2.)4Nature of Ordering in the Infinite-Ranged Spin GlassWe now return to a more detailed discussion of the nature of ordering implied by Parisi’s solution of the SK model.As noted in Sec.2.2,the RSB scheme introduced by Parisi assumes the existence of many equilibrium pure states.Because the notion of pure states has generated some confusion in the literature,we detour to clarify exactly what is meant by this and related terms.The discussion here closely follows Appendix A of[57].4.1Thermodynamic Pure StatesThe notion of pure states is well-defined for short-ranged,finite-dimensional systems,but is less clear for infinite-ranged ones like the SK model.We therefore begin with a discussion of the EA model(in arbitrary d<∞),and then briefly discuss application of these ideas to the SK model.Considerfirst H J,L,the EA Hamiltonian(3)restricted to afinite volume of linear extent L.We will always take such a volume,hereafter denoted asΛL,to be an L d cube centered at the origin. In addition,we need to impose boundary conditions,which we will often take to be periodic;other possibilities include antiperiodic,free,fixed(e.g.,all spins on the boundary set equal to+1),and so on.Given a specified boundary condition,thefinite-volume Gibbs stateρ(L)J,T onΛL at temperature T is defined by:ρ(L)J,T(σ)=Z−1L,T exp{−H J,L(σ)/k B T},(6)where the partition function Z L,T is such that the sum ofρ(L)J,T over all spin configurations inΛL yields one.All equilibrium quantities of interest can be computed fromρ(L)J,T(σ),which is simply a prob-ability measure:it describes atfixed T the probability of a given spin configuration obeying the specified boundary condition appearing withinΛL.Such a(well-behaved)probability distribution is completely specified by its moments,which in this case is the set of all correlation functions withinΛL: σx1···σx m for arbitrary m and arbitrary x1,...,x m∈ΛL.Consider next the L→∞limit of a sequence of suchfinite-volume Gibbs statesρ(L)J,T(σ), each with a specified boundary condition(which may remain the same or may change with L).Of course,such a sequence may or may not have a limit;existence of a limit would require that every m-spin correlation function,for m=1,2,...,itself possesses a limit[58].A thermodynamic state ρJ,T is therefore an infinite-volume Gibbs measure,providing information such as the probability of anyfinite subset of spins taking on specified values;and of course it determines global properties such as magnetization per spin,energy per spin,and so on.。

第一章绪论一简答题1. 21世纪是生命科学的世纪。

20世纪后叶分子生物学的突破性成就，使生命科学在自然科学中的位置起了革命性的变化。

试阐述分子生物学研究领域的三大基本原则，三大支撑学科和研究的三大主要领域？答案：（1）研究领域的三大基本原则：构成生物大分子的单体是相同的；生物遗传信息表达的中心法则相同；生物大分子单体的排列（核苷酸，氨基酸）导致了生物的特异性。

（2）三大支撑学科：细胞学，遗传学和生物化学。

（3）研究的三大主要领域：主要研究生物大分子结构与功能的相互关系，其中包括DNA和蛋白质之间的相互作用；激素和受体之间的相互作用；酶和底物之间的相互作用。

2. 分子生物学的概念是什么？答案：有人把它定义得很广：从分子的形式来研究生物现象的学科。

但是这个定义使分子生物学难以和生物化学区分开来。

另一个定义要严格一些，因此更加有用：从分子水平来研究基因结构和功能。

从分子角度来解释基因的结构和活性是本书的主要内容。

3 二十一世纪生物学的新热点及领域是什么？答案：结构生物学是当前分子生物学中的一个重要前沿学科，它是在分子层次上从结构角度特别是从三维结构的角度来研究和阐明当前生物学中各个前沿领域的重要学科问题，是一个包括生物学、物理学、化学和计算数学等多学科交叉的，以结构（特别是三维结构）测定为手段，以结构与功能关系研究为内容，以阐明生物学功能机制为目的的前沿学科。

这门学科的核心内容是蛋白质及其复合物、组装体和由此形成的细胞各类组分的三维结构、运动和相互作用，以及它们与正常生物学功能和异常病理现象的关系。

分子发育生物学也是当前分子生物学中的一个重要前沿学科。

人类基因组计划，被称为“21世纪生命科学的敲门砖”。

“人类基因组计划”以及“后基因组计划”的全面展开将进入从分子水平阐明生命活动本质的辉煌时代。

目前正迅速发展的生物信息学，被称为“21世纪生命科学迅速发展的推动力”。

尤应指出，建立在生物信息基础上的生物工程制药产业，在21世纪将逐步成为最为重要的新兴产业；从单基因病和多基因病研究现状可以看出，这两种疾病的诊断和治疗在21世纪将取得不同程度的重大进展；遗传信息的进化将成为分子生物学的中心内容”的观点认为，随着人类基因组和许多模式生物基因组序列的测定，通过比较研究，人类将在基因组上读到生物进化的历史，使人类对生物进化的认识从表面深入到本质；研究发育生物学的时机已经成熟。