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等温滴定微量热仪(ITC)简介等温滴定量热法在生命科学研究中应用申明：本资料来源于网络，版权归原作者所有！等温滴定量热法(Isothermal Titration Calorimetry, ITC)是近年来发展起来的一种研究生物热力学与生物动力学的重要方法，它通过高灵敏度、高自动化的微量量热仪连续、准确地监测和记录一个变化过程的量热曲线，原位、在线和无损伤地同时提供热力学和动力学信息。
微量热法具有许多独特之处。
它对被研究体系的溶剂性质、光谱性质和电学性质等没有任何限制条件，即具有非特异性的独最小可检测热效应0.125uJ，生物样品最小用量0.4ug，温度范围2 0C - 80 0C，滴定池体积1.43 ml)。
实验时间较短(典型的ITC实验只需30-60分钟，并加上几分钟的响应时间)，操作简单(整个实验由计算机控制，使用者只需输入实验的参数，如温度、注射次数、注射量等，计算机就可以完成整个实验，再由Origin 软件分析ITC得到的数据)。
测量时不需要制成透明清澈的溶液, 而且量热实验完毕的样品未遭破坏，还可以进行后续生化分析。
尽管微量热法缺乏特异性但由于生物体系本身具有特异性，因此这种非特异性方法有时可以得到用特异方法得不到的结果，这有助于发现新现象和新规律，特别适应于研究生物体系中的各种特异过程。
ITC的用途获得生物分子相互作用的完整热力学参数，包括结合常数、结合位点数、摩尔结合焓、摩尔结合熵、摩尔恒压热容，和动力学参数(如酶活力、酶促反应米氏常数和酶转换数)。
ITC的应用范围蛋白质-蛋白质相互作用(包括抗原-抗体相互作用和分子伴侣-底物相互作用)；蛋白质折叠/去折叠；蛋白质-小分子相互作用以及酶-抑制剂相互作用；酶促反应动力学；药物-DNA/RNA相互作用；RNA折叠；蛋白质-核酸相互作用；核酸-小分子相互作用；核酸-核酸相互作用；生物分子-细胞相互作用；……加样体积：（实际体积）cell：1.43 ml，syringe：300 μl准备样品体积（最少量）cell：2 ml，syringe：500 μl样品浓度cell：几十μM到几mMsyringe：几百μM到几十mM测量Kb范围102-1012 M-1滴定实验前恒温30-60 min等温滴定量热实验所需时间，一般1.5-4 hrSample Preparation Guidelines (ITC).Proper sample preparation is essential for successful ITC testing. In particular, the minimal guidelines below must be strictly followed to insure an accurate estimate of stoichiometry (n), heat of binding (H), and binding constant (Kb) (or dissociation constant Kd = 1/Kb).1.) The macromolecule solution (the sample to be placed in the reaction cell) must have a volume of at least2.1 ml. The lowest concentration which can be studied is 3 M and this is adequate only for tight binding where Kd is smaller than 1 M. For weaker interactions, the macromolecule concentration should be 5 times Kd, or higher if possible. Preferably, the macromolecule solution should be dialyzed exhaustively against buffer for final equilibration.2.) The ligand solution (the sample to be placed in the injection syringe) must have a volume of at least 0.7 ml. Its concentration should be at least 10 times higher than the concentration of macromolecule (if the macromolecule has multiple binding sites for ligand, then the ligand concentration must be increased accordingly). The buffer solution in which the ligand is dissolved should be exactly the same buffer against which the macromolecule has been equilibrated.3.) After both solutions have been prepared, the pH of each should be checked carefully. If they are different by more that 0.05 pH units, then one of the solutions must be back-titrated so they are within the limit of 0.05 pH units. If any particles are visible in either solution, they should be filtered out.4.) If possible, the concentrations of both solutions should be accurately determined after final preparation. Accurate determination of binding parameters is only possible if concentrations of binding components are known precisely.5.) At least 20 ml of buffer must be sent along with the two samples, since this is used for rinsing the cell and for dilution if necessary.6.) If possible, DTT should be avoided as a disulfide reagent and replaced by -mercaptoethanol or TCEP.等温滴定微量热仪（ITC）基本介绍等温滴定微量热仪（ITC）基本介绍（美国MicroCal ，美国微量热公司）仪器设备名称：等温滴定微量热仪制造国别：美国制造厂商：美国微量热公司规格型号：VP-ITC品牌：MicroCal总代理商：华嘉（香港）有限公司技术指标：短期噪音水平：0.5纳卡/秒(2 纳瓦)。
等温滴定量热法(I T C)的简易操作流程：①样品的准备，包括滴定物与被滴定物(如DNA滴定蛋白质)。
a.实验前的蛋白质样品需用缓冲溶液透析(注意透析袋的正确使用)，透析时间一般为24小时，buffer体积为1L，且中途注意更换buffer，其目的是为了减少由于溶液组成不同而产生的滴定误差；b.样品的浓度要求，一般要求的浓度为微摩尔级，且滴定物(DNA)的浓度是被滴定物(蛋白质)的十倍左右为宜，且实验前需要再次确认所配样品的浓度是否符合要求；c.在进行滴定实验前，用于空白对照的缓冲液，蛋白样品以及DNA均需抽真空除气泡(15Mins左右为宜)。
②仪器的清洗。
a.在进行真空除气泡前，除气泡用容器均需用超纯水清洗三次左右，且清洗完毕后擦干内壁，防止由于残留缓冲液的稀释而导致样品浓度的改变；b.样品池(sample cell)的清洗，用超纯水清洗15次左右(每次2ml左右)，清洗完毕后，一定要将残留的超纯水吸干净；c.注射器(syringe)的清洗，用超纯水清洗3次以上(专用注射器清洗,此时无需点击open,close和purge选项)，清洗完毕后将注射器的头部擦干，之后清洗装DNA 的小试管，步骤同注射器的清洗。
③设置空白对照试验（DNA滴定缓冲液），将缓冲液置于小试管中(为了防止空气的进入，一般添加样品的量大于其实际所需的量)，打开控制界面，点击open之后，用手动注射器缓慢拉动活塞，此时注射器管中的液面上升，然后点击close, 注射器会自动将小试管中的缓冲液吸入注射器中，当缓冲液完全吸入注射器之后点击pump键，除去气泡；在清洗样品池的同时就设置所需的实验温度（套管温度，一般较反应温度稍低），并输入样品的实际浓度以及实验数据文件名和储存路径等一系列参数（如注射时间，注射次数，注射间隔时间）。
④设置滴定实验，步骤同空白试验，只需将样品池中用于空白对照的缓冲液换成蛋白样品同时修改文件名(先准备样品池中的样品，后准备注射器中的样品)。
马尔文等温滴定微量热仪
马尔文等温滴定微量热仪（Malvern Isothermal Titration Calorimetry，简
称ITC）是一种高灵敏度、高自动化的微量量热仪，用于研究生物热力学和生物动力学。
该仪器能够连续、准确地监测和记录一个变化过程的量热曲线，原位、在线和无损伤地同时提供热力学和动力学信息。
马尔文帕纳科微量热等温滴定量热仪（MicroCal iTC200）是一种已下架的生物分子相互作用无标记溶液内研究的高灵敏度低容量等温滴定量热仪。
该仪器支持在一次实验内直接测量所有结合参数，仅用10 g样品就可分析从弱到强的各种亲和结合体。
半自动维护减少了操作人员的干预，系统可升级至全自动的MicroCal Auto-iTC200，使其非常
适合那些将来对速度、灵敏度和较高强度工作的适应能力要求极高的实验室。
MicroCal iTC200的设计特点是易于使用和极其灵敏。
其亲和范围大，让亲和力从弱
到强的亲和体分析极具重现性。
自动清洗和注射器加载功能减少了操作人员的参与，同时用户友好的软件会引导所有操作实现快速、准确的分析。
通过MicroCal iTC200，可以研究大量的应用，包括表征小分子、蛋白质、抗体、核酸、脂类和其他生物分子的分子间相互作用。
它也可用于测量酶动力学。
所有结合参数（亲和力、化学计量、焓和熵）只需一次实验。
无需分析开发过程即可快速获得初步结果，无标签、无固定化且无分子量限制。
总之，马尔文等温滴定微量热仪是一种强大的实验工具，能够为生物科学研究提供热力学和动力学信息，具有广泛的应用价值。
等温滴定量热技术摘要：生物大分子可以和很多配体特异性结合，当物质结合时，热量要么产生，要么吸收。
生物大分子与配体相互作用的定量描述需要确定反应过程中热力学参数的变化。
相互作用过程中产生的热量变化可以用量热计定量监测。
等温滴定量热技术（Isothermal Titration Calorimetry, ITC）是一种监测由结合成分的添加而起始的任何化学反应的热力学技术，它已经成为鉴定生物分子间相互作用的首选方法。
它通过高灵敏度、高自动化的微量量热仪连续、准确地监测和记录一个变化过程的量热曲线，原位、在线和无损伤地同时提供热力学和动力学信息，如结合常数（Ka）、结合位点数（n），结合焓（△H）、熵（△S）、恒压热容（△Cp）和动力学数据（如酶促反应的Km和kcat ）。
这些信息提供了生物分子相互作用的真实写照。
由于几乎所有的生化反应过程都有热量变化，所以ITC具有很广泛的应用，它可以应用于蛋白质-蛋白质相互作用、蛋白质折叠/去折叠、蛋白质-小分子相互作用、酶-抑制剂相互作用、酶促反应动力学、药物-DNA/RNA相互作用、RNA折叠、蛋白质-核酸相互作用、核酸-小分子相互作用、核酸-核酸相互作用、生物分子-细胞相互作用等方面。
关键字：等温滴定量热技术、相互作用、热力学商业化的测量生物分子相互作用热量的灵敏的量热计出现在上世纪80年代后期[1]。
从此这种技术被广泛应用。
在过去的20年中，等温滴定量热技术（ITC）成为研究相互作用的常用方法。
随着现代ITC仪器的发展，ITC更加灵敏、快速、易用。
分子识别是一个复杂的过程，是生命活动的基础。
生物分子识别过程需要结合反应的热力学参数来阐明。
等温滴定微量量热法可以直接定量检测滴定反应过程中的热量变化，确定反应的结合常数K B 、结合计量比（n）、反应焓变（∆H）、熵变（∆S）、恒压热容（△Cp）和动力学数据（如酶促反应的Km和kcat ）等热力学参数，用来表征生物分子间的相互作用。
等温滴定量热仪（TA NANO ITC）操作规程
1、准备样品
该仪器滴定handle不耐有机溶剂、强酸、强碱等，将样品根据实验需要配置成适宜浓度的澄清水溶液（溶液体系需要稳定，不能在试验过程中析出固体物质）；如果试验涉及到金属离子，切忌金属离子在试验过程中与滴定池发生金属置换反应。
2、清洗仪器
用去离子水清洗仪器至少3次，每次1000mL（使用前、后各清洗3次）
3、样品脱气
对样品进行脱气处理，一般样品脱气时间≥10min
4、注入样品
参比池中加入300μL去离子水作为参比（至少每周更换一次），反应池中加入300μL被滴定液，滴定针中吸入50μL滴定液（注：溶液均已进行脱气处理）
5、仪器校准home resetting
试验首次滴定前需要对仪器进行校准，通过home resetting校准30s，校准后，装滴定针，设置参数（包括：转速，温度，单次滴定量等）
6、运行与保存
点运行按钮（蓝色三角），之后保存按钮（绿色三角），该仪器将按照设定的程序自行运行，并保存原始记录。
其他注意事项：
1、滴定针和清洗针属于易损配件，使用过程中需小心。
2、切忌样品中有机溶剂挥发对handle的腐蚀，当然其他酸碱性溶剂需要慎用！
3、试验操作前后，一定要用大量去离子水清洗，避免滴定池污染。
4、如仪器长时间不用，需要将参比池和滴定池的溶液清洗干净，避免滋生微生物。
5、试验过程中，如果仪器handle紧涩，需要适当润滑维护后方可使用。
6、在试验过程中，切忌强行将handle拔出。
7、定期保养维护，避免灰尘污染脱气设备和滴定装置。
8、该设备应置于平稳台面，周边不能剧烈震动或强烈噪音。
等温滴定量热仪原理
等温滴定量热仪是一种测量化学反应热效应的仪器，其原理主要基于热力学第一定律即能量守恒定律。
该仪器通过在反应体系中等温滴加试剂，测量反应体系的温度变化，从而计算出反应热。
具体原理如下：
1. 热力学第一定律：热量是一种能量形式，能量守恒定律表明
在一个孤立系统中，能量的总量是不变的，能量只能从一个形式转化为另一个形式。
2. 反应热的定义：反应热是在常压下，单位物质在一定温度下
发生化学反应所吸收或放出的热量。
3. 等温滴定量热仪的原理：该仪器利用绝热量热器，将反应体
系与热库隔绝，通过等温滴加试剂，使反应体系温度发生变化，测量温度变化，从而计算出反应热。
4. 计算方法：根据热力学第一定律，反应热等于热库的热量减
去绝热量热器吸收或放出的热量；根据热力学第二定律，热量的转化不是完全有效的，因此需要进行修正计算。
等温滴定量热仪在化学热力学、化学工程等领域中有广泛的应用，可以用于测定各种化学反应的热效应，评估反应的热稳定性和热动力学参数，对化学反应的设计和优化具有重要的意义。
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Calibration of nanowatt isothermal titration calorimeters with overflow reaction vesselsNeil A.Demarse a ,⇑,Colette F.Quinn a ,Dennis L.Eggett b ,Donald J.Russell a ,Lee D.Hansen caTA Instruments,Lindon,UT 84042,USAbDepartment of Statistics,Brigham Young University,Provo,UT 84602,USA cDepartment of Chemistry and Biochemistry,Brigham Young University,Provo,UT 84602,USAa r t i c l e i n f o Article history:Received 4May 2011Accepted 7June 2011Available online 16June 2011Keywords:Titration calorimetry ITCStandards Accuracy Precisiona b s t r a c tObtaining accurate results with nanowatt titration calorimeters with overflow cells requires mass calibration of the buret injection volume,chemical calibration of the reaction vessel effective volume,and chemical calibration of the calorimetric factor used to convert the measured electrical signal to heat rate.Potential errors in electrical calibration of power compensation calorimeters require validation of the calorimetric factor with chemical reactions with accurately known stoichiometries and enthalpy changes.The effective volume of the reaction vessel can be determined from the endpoint of a quantita-tive reaction with known stoichiometries.Methods for calibration and potential calibration errors to be avoided are described.Publication of results obtained must include data on calibrations and sufficient raw data to assess precision and accuracy of the results.Ó2011Elsevier Inc.All rights reserved.Nanowatt isothermal titration calorimetry (ITC)1can provide accurate measurements of the enthalpy changes of reactions,and for favorable cases can be used to obtain accurate values of equilib-rium constants,but only if the calorimeter is properly calibrated.The absence of systematic errors in procedures,injection volume,reac-tion vessel effective volume,and the calorimetric factor used to con-vert the measured electrical signal to heat rate all must be demonstrated with standard reactions.Demonstration that accurate results can be obtained for a standard reaction has historically been a requirement for acceptance of any calorimetric measurement,and the very small volumes and heat effects currently used in most ITC measurements require extraordinary care and attention to detail.Four different nanowatt isothermal titration calorimeters that operate with overflow cells are currently commercially available:the VP-ITC and ITC 200from GE Healthcare (MicroCal)and the Nano ITC Standard Volume (SV)and Nano ITC Low Volume (LV)from TA Instruments.All four calorimeters are differential power compensa-tion calorimeters,and the primary measurement is heat rate,which is derived from the power supplied by a control heater that is used to maintain a steady-state,approximately zero temperature differ-ence between the sample and reference cells,but cooling for power compensation is done differently in the GE Healthcare calorimeters than in the TA Instruments calorimeters.The power from the con-trol heater is compensated by a constant cooling mechanism that is passive in the GE Healthcare calorimeters and actively controlled in the TA Instruments calorimeters.The Nano ITC-SV and VP-ITC have approximately 1-ml reaction vessels,and the Nano ITC-LV and ITC 200have approximately 0.2-ml reaction vessels.The Nano ITC-SV is available with either gold or hastelloy reaction vessels.The Nano ITC-LV has a gold reaction vessel.Both GE Healthcare cal-orimeters have hastelloy reaction vessels.The different materials used to construct the reaction vessels have significantly different thermal conductivities that lead to differences in time constants and control software.Titrations are typically incremental,with 20–30injections of 1–10l l from a motor-driven syringe with a stainless steel needle that also serves as a stirrer.Reaction vessels in the GE Healthcare calorimeters are flat horizontal cylinders with rounded edges.The TA Instruments calorimeters are upright cylin-ders with conical ends.This difference in vessel shape creates dif-ferences in mixing properties.An ideal power compensation calorimeter would always main-tain the system in an exact isothermal condition;therefore,changes in the control power to maintain that isothermal condition would accurately measure heat from reactions.This is impossible in real systems for two reasons.The first reason involves sudden changes in heat input such as those that occur during an injection of titrant that cannot be exactly compensated by the control cir-cuit.Furthermore,these transient nonisothermal conditions cause transfer of heat between the sample cell and surroundings,includ-ing the reference cell,and this may alter the supposedly constant cooling power.The second problem arises from inevitable differences in heat distribution in the system from heat effects from reaction and from the control heater.These differences cause0003-2697/$-see front matter Ó2011Elsevier Inc.All rights reserved.doi:10.1016/j.ab.2011.06.014⇑Corresponding author.Fax:+18017631414.E-mail address:ndemarse@ (N.A.Demarse).1Abbreviations used:ITC,isothermal titration calorimetry;CBS,p -carboxy benzene sulfonamide;CAII,carbonic anhydrase II.heat exchange with the surroundings and reference cell to differ between the heat effects from a chemical reaction and the heat ef-fects from the control heater.In addition to the control heater with which measurements are made,an electrical calibration heater is included in these calorimeters.Electrical calibration of calorime-ters,however,can be subject to significant error because of failure to transfer all heat to the calorimeter vessel,because of heat gen-eration in lead wires,and because of a different distribution of heat from the calibration heater than from a chemical process[1].Be-cause there is potential for systematic errors in calibration with the electrical calibration heater,a multiplicative calorimetric factor determined with a standard chemical reaction should be used to make measured changes in control power equal to the heat effects from a reaction.Even if the calorimetric factor is believed to be unity,this must be demonstrated with a standard reaction.The effective volume of the reaction vessel in overflow vessels is not identical to the physical volume of the reaction vessel as sup-plied by the manufacturer and,therefore,must also be calibrated chemically[2].The effective volume depends on how much vol-ume is displaced by the stirrer and how much of the overflow tube is accessed by the reactant in the vessel during a reaction.Although suppliers typically warranty the syringes used to man-ufacture burets to1%linearity,the entire buret with drive system requires calibration to ensure accuracy of delivered volume.Buret calibration for total delivery volume can be conveniently done by mass,but because of their small size,individual injection volumes are difficult to measure and are best tested by chemical reaction.A test to determine the variability of the calorimetric factor, injection volume,and effective reaction vessel volume among cal-orimeters that were not chemically calibrated was done with com-mon reagents in seven Nano ITC-LVs infive laboratories and six Nano ITC-SVs with gold cells in four laboratories.Results of the mean of39experiments with the Nano ITC-LVs gave a relative standard deviation of3.6%in the endpoint and7.6%in the enthalpy change.The results from the41experiments done in Nano ITC-SVs gave a relative standard deviation of2.1%in the endpoint and4.1% in the enthalpy change.These errors indicate the magnitude of er-rors from lack of chemical calibration and not the precision ob-tained from a given calorimeter.Literature surveys[3,4]show that nanowatt titration calorime-ters with overflow cells have not been accurately calibrated;thus, previously published data are open to question.Results presented in the literature often suggest that solution concentrations,injec-tion volumes,and/or cell volumes were inaccurate;time intervals between injections were too short or incomplete mixing occurred; and poor conditions were chosen for equilibrium constant deter-minations.Publications typically include only a reference to the calorimeter model and manufacturer,a sample of raw data,a titra-tion curve with data points,and afitted curve.Rarely is any infor-mation on calibration given.For example,Baranuskiene˙and coworkers[5]attempted to apply known reactions for comparison of the accuracy of electrically calibrated calorimeters but did not describe how electrical calibrations were done,did not calibrate the effective volume of the reaction vessel,and did not test the accuracy of assumed titrant injection volumes.The stoichiometries reported are inaccurate,and this could be caused by inaccurate solution concentrations,a wrong reaction vessel effective volume, inaccurate titrant injection volumes,and/or incorrect analysis of the data.Thus,their conclusions about the accuracy of different calorimeters are not supported by their data.Currently,the most common use of calorimeters is for simulta-neous determination of equilibrium constants and enthalpy changes.The only reactions previously recommended[6,7]as test reactions for this method are the reaction of aqueous BaCl2with 18-crown-6with log K f=3.771±0.015and D R H=À31.4±0.2kJ/ mol and the reaction of p-carboxy benzene sulfonamide(CBS)with carbonic anhydrase II(CAII)with K f=1Â106MÀ1and D R H=À44kJ/mol.The usefulness of the BaCl2/18-crown-6reaction de-pends on the dynamic range of the calorimeter.The equilibrium constant is relatively small;so,to obtain50<C R K f<500(C R is the reactant concentration)and thus obtain a titration curve with the optimal shape[8],the18-crown-6concentration must be between 8.5and85mM and the BaCl2concentration must be greater than 150mM.At these concentrations,a5-l l injection produces more than2mJ,which is outside the linear dynamic range of most calo-rimeters.In addition,the reagents are not readily available as di-rectly weighable materials.As shown by the large errors(i.e., standard deviations of±15%in stoichiometry,±22%in K f,and ±25%in D R H)from a round-robin test in14laboratories[7],the CBS/CAII reaction is not a suitable standard.The reactions of Ag+ with halides as proposed by Baranuskiene˙and coworkers[5]are not recommended because of possible precipitation and plugging of the buret needle,difficulties with removal of the precipitates from the reaction vessel,and potential for reactions of the ions with the materials of construction.Others have suggested the use of a protein inhibitor reaction such as reaction of RNase A with20-CMP.This possibility is now moot because20-CMP is no longer read-ily available.Furthermore,no protein is likely to meet the challenge of being readily available in high purity,stable,easy to use,and not sensitive to small errors in preparations.We note the0.9±0.1stoi-chiometry of carbonic anhydrase reactions in Fig.4of Baranuskiene˙and coworkers’[5]article,which they(along with others[9])con-sider to be‘‘good’’for proteins.In the round-robin test involving 14laboratories,the enthalpy of binding of CBS to bovine CAII varied by±25%[5,7],and although it is not clear whether this was due to variability of materials,procedures,or calorimeters,it is clear that this reaction is not a suitable standard.Even though the reaction of Ca2+with ethylenediaminetetraacetic acid(EDTA)was recently introduced by GE Healthcare as a test kit,irreproducibility by other preparations as a result of sensitivity to ionic strength and pH makes the reaction unsuitable as a calibration reaction.To determine the likely systematic errors from lack of chemical calibration in simultaneous determinations of equilibrium con-stants,enthalpy changes,and stoichiometry,a round-robin test was run with the reaction of bicarbonate and HCl(p K a=6.35, D R H=À9.15kJ/mol)with common reagents supplied to the partic-ipants.Results from calorimeters that were not chemically cali-brated after manufacture gave p K a=6.01±0.12(5.4%low), D R H=–9.26±0.70kJ/mol(1.2%high),and n=0.993±0.036(0.7% low)for39observations in a Nano ITC-LV calorimeter;p K a= 6.22±0.06(2.0%low),D R H=–8.53±0.35kJ/mol(6.7%low),and n=1.026±0.022(2.6%high)for41observations in a gold cell Nano ITC-SV calorimeter;and p K a=6.22±0.09(2.0%low),D R H=–8.54±0.37kJ/mol(6.7%low),and n=1.042±0.027(4.2%high)for24 observations in a hastelloy cell Nano ITC-SV calorimeter.These re-sults are given only to indicate the clear need for chemical calibra-tion to obtain accurate values and not as a comparison among different calorimeters.The purposes of this article are,first,to propose methods for testing calorimeter performance;second,to propose methods and reactions for calibration of injection volume,reaction vessel effective volume,and calorimetric factor;third,to propose reac-tions for testing overall performance of experiments and proce-dures for determination and analysis of data;and lastly,to reiterate requirements to ensure the accuracy of published data. These issues have not been adequately addressed previously. Calibration proceduresTable1is a list of symbols,the calibration parameters to be determined,and the methods for doing so.Note that determination248Calibration of isothermal titration calorimeters/N.A.Demarse et al./Anal.Biochem.417(2011)247–255of the injection volume by mass is the only calibration that can be done independent of the other calibrations.Performance tests:detection limit and titrant equilibration The detection limit of a calorimeter is best determined by titra-tion of water into water(or solvent into solvent).The slope of a plot of these data(i.e.,heat per injection versus injection number,as illustrated in Fig.1)will be near zero if the buret is operating prop-erly.The detection limit(D B)is equal to twice the standard devia-tion of the average heat per injection in such a blank titration. Excessive variation(i.e.,D B>2l J/injection)may indicate a buret or temperature control problem.A test of this at25°C in seven Nano ITC-LVs infive different laboratories gave2.9±0.7l J/injec-tion for the average of18titrations with2.5-l l injections.A test in six Nano ITCs with gold cells in four laboratories gave 3.4±1.7l J/injection for the average of18titrations with5-l l injec-tions.Uncertainties are given as twice the standard deviation of the mean(D B).The syringe buret in these calorimeters is not thermostatted at the calorimeter temperature;instead,thermal equilibration of the titrant is done during passage of titrant through the syringe nee-dle/stirrer.Two effects–(i)a temperature difference between the titrant and titrate and(ii)viscousflow–cause the heat per injection to differ from zero.The heat per injection from viscous flow can be calculated from the dimensions of the injection needle, the injection rate,and the titrant viscosity[10]and is usually neg-ligible compared with the effect from the temperature difference. The blank heat is typically exothermic when the calorimeter is operated at temperatures near room temperature and below and endothermic when the calorimeter is operated above room tem-perature.Near ambient temperature,a blank heat effect larger than approximately1l J/l l usually indicates an inadequately cleaned buret or reaction vessel or that the stirrer shaft is rubbing on the entry tube.The collars on the stirrer shafts are commonly misinter-preted as bearings,but the purpose of these is to limit mixing be-tween the liquid in the tube above the collar with liquid in the reaction vessel.If these collars touch the walls of thefill tube be-cause of misalignment of the buret with thefill tube or because the stirrer shaft is bent,rubbing of these collars on thefill tube will cause frictional heating of the titrant.Buret calibrationThe best way to calibrate the buret is by weighing the amount of water delivered by a known number of steps of the stepper mo-tor.If the syringe can be removed from the drive mechanism,this can be done by overfilling the syringe,attaching the syringe to the fully open drive mechanism to remove the overfill,removing and weighing thefilled syringe,reattaching the syringe to the drive, delivering a known number of steps,and weighing the syringe and remaining water.The difference in mass and the density of water at the delivery temperature can then be used to determine the volume delivered.If the syringe cannot be removed from the drive mechanism,a similar procedure can be used,but the entire drive mechanism must be weighed.The buret injection volume(V inj)can also be calculated from the heat per injection with a quantitative reaction with a known en-thalpy change,D R H,but the result depends on prior knowledge of the calorimetric factor:V inj¼ðQ RÀQ BÞ=ðC TÞðÀD R HÞ:ð1ÞIn Eq.(1),C T is the titrant concentration,D R H is the enthalpy change for the reaction,Q R is the measured heat per injection that depends on the calorimetric factor(f),and Q B is the blank correction.D R H must be corrected to experimental conditions.The consistency of individual injection volumes is calculated as twice the standard deviation of the mean heat per injection.The total volume delivered by the buret,and thus V inj,can also be calculated from the endpoint of a titration with a quantitative reaction,but the result depends on prior knowledge of the effective reaction vessel volume,as shown in Eq.(2):V ep¼ðV RVÞðC RÞ=ðC TþC RÞ;ð2Þwhere V ep is the titrant volume at the endpoint,V RV is the effective volume of the reaction vessel,C R is the reactant concentration,and C T is the titrant concentration.Eq.(2)is derived assuming a single injection,but it correctly identifies the dependence of V ep on other variables.The equation for multiple injections is not simply written and adds unnecessary complexity to this discussion.The endpoint is typically identified as the inflection point in a curvefitted to a sig-moidal plot of the heat per injection versus injection number,but the endpoint volume may be more accurately located as the intersection of the two straight lines in a plot of total heat versusTable1Parameters to be calibrated,procedures,and interdependence of parameters.Parameter Procedure Dependence EquationDetection limit(D B)Titrate water into water Depends on precision of injection volume andtemperature control D B=2(standard deviation of mean heat per injection)Blank heat(Q B)Titrate water into water ortitrant into blank solvent Depends on D T between titrant and titrate Q B=D T(V inj)(heat capacity of water)orQ B=D T(V inj)(heat capacity of titrant)+(heat ofdilution of titrant)Injection volume (V inj)Determine mass of waterdeliveredIndependent of other parameters Mass/density of water Determine heat per injection(Q R)with quantitativereactionDepends on titrant concentration(C T)and calorimetricfactor(f)V inj=(Q RÀQ B)/(C T)(ÀD r H)Eq.(1)Determine reaction endpoint Depends on titrant concentration(C T),reactantconcentration(C R),and reaction vessel volume(V RV)V ep=(V RV)(C R)/(C T+C R)Eq.(2)Calorimetric factor(f)Determine heat per injection(Q R)with quantitativereactionDepends on injection volume(V inj),titrant concentration(C T),and blank heat(Q B)f=(V inj)(C T)(ÀD R H)/(Q RÀQ B)Eq.(3)Determine total heat(Q R)from catalyzed reactionDepends on reactant concentration(C R),reaction vesselvolume(V RV),injection volume(V inj),and blank heat(Q B)f=(C R)(V RVÀV inj)(ÀD R H)/(Q RÀQ B)Eq.(5)Effective volume of reaction vessel(V RV)Determine reaction endpoint Depends on titrant concentration(C T),reactantconcentration(C R),and injection volume(V inj)V RV=(V ep)(C T+C R)/(C R)Eq.(7)Determine total heat(Q R)from catalyzed reactionDepends on blank heat(Q B),injection volume(V inj),andreactant concentration(C R)V RV=[(Q RÀQ B)/(C R)(ÀD R H)]+(V inj)Eq.(8)Calibration of isothermal titration calorimeters/N.A.Demarse et al./Anal.Biochem.417(2011)247–255249injection number.Any reaction from diffusion from the buret nee-dle prior to thefirst injection affects only the vertical axis on such a plot and,thus,has no effect on the determined endpoint volume. The sigmoidal plot is less accurate for reactions that are quantita-tively complete at the endpoint because only one or two data points occur near the endpoint,and afitted sigmoidal curve often overes-timates the titrant volume at the endpoint.Determination of calorimetric factorThe calorimetric factor(f)can be determined from the heat per injection with a quantitative reaction,but the measured value for f depends on prior knowledge of the injection volume.The calori-metric factor is calculated asf¼ðV injÞðC TÞð¼D R HÞ=ðQ RÀQ BÞ;ð3Þwhere V inj is the volume of titrant injected,C T is the concentration of titrant,D R H is the enthalpy change for the reaction,Q R is the heat per injection during the reaction,and Q B is the heat per injection during a blank titration.The injection volume should be chosen to optimize the total heat per injection.The results should be tested for consistency by plotting the corrected heat per injection versus injection number.The slope of this plot should be near zero.Results may be averaged over several injections,and individual injections may be deleted from consideration because of mixing in the buret needle or injection of a bubble.Twice the standard deviation of the mean value for several injections is equal to the detection limit (D R)for determination of a heat of reaction.The relative uncertainty in f(d f/f)includes the uncertainty in all of the variables and is cal-culated by Eq.(4):d f=f¼½ðd V T=V TÞ2þðd C T=C TÞ2þðd D R H=D R HÞ2þðd Q R=Q RÞ2þðd Q B=Q BÞ2 0:5;ð4Þwhere d indicates the uncertainty in each of the variables.The calorimetric factor can also be determined from the total heat produced on injection of a catalyst into a known amount of substrate for a reaction with a known enthalpy change.The mea-sured value of f in this case depends on prior knowledge of the effective volume of the reaction vessel and the injection volume as shown in Eq.(5):f¼ðC RÞðV RVÀV injÞðÀD R HÞ=ðQ RÀQ BÞ:ð5ÞThe enthalpy change must be corrected to the experimental condi-tions.The relative uncertainty in f in this case is given byd f=f¼½ðd C R=C RÞ2þðd V RV=V RVÞ2þðd D R H=D R HÞ2þðd Q R=Q RÞ2þðd Q B=Q BÞ2 0:5:ð6ÞDetermination of effective volume of reaction vesselThe only way to determine the effective cell volume in overflow cells is by determining the amount of a reaction that actually oc-curs in the cell when it is overfilled with a reactant of a known con-centration.This can be done by determining the endpoint of a titration with a quantitative reaction or by determination of the heat produced when a catalyst is injected into the reaction vessel with a known concentration of substrate.The effective volume, V RV,in thefirst case is given byV RV¼V epðC TþC RÞ=C Rð7Þand in the second case is given byV RV¼ðQ RÀQ BÀV inj C R D R HÞ=ðC RÞðÀD R HÞ;ð8Þwhere Q R is the total heat measured.Eq.(7)is derived assuming a single injection but correctly identifies the dependence of V RV on other variables.The equation for multiple injections is not simply written and adds unnecessary complexity to this discussion.Interdependence of calibrated parametersThe discussion above and the equations in Table1clearly show that determination of the buret injection volume by mass is the only calibration that can be done independent of the other two cal-ibration parameters.Accurate determination of the calorimetric factor(f)and effective reaction vessel volume(V RV)from heat per injection and reaction endpoint,respectively,depend on having250Calibration of isothermal titration calorimeters/N.A.Demarse et al./Anal.Biochem.417(2011)247–255an accurate V inj.V RV and f are interdependent when determinedwith a catalyzed reaction,and so one of the other methods must also be used.Therefore,achieving independent calibration of all three parameters requiresfirst calibration of V inj by mass,followed by calibration of f from heat per injection and then calibration of V RV from endpoint determination.Alternatively,f or V RV may be determined from the total heat from a catalyzed reaction if one of the other methods determines the other parameter.The meth-ods chosen for calibration should be those that most resemble the experiments to be done after calibration.Quantitative reactions for buret calibration,determination of the chemical calorimetric factor,and effective volume of the reaction vesselReaction of strong acid with excess strong base or basic buffer for calibration of injection volume and calorimetric factorTitration of a well-defined solution of a strong acid into a solu-tion of a strong base,or of a basic buffer solution containing a large excess of base,is suitable for determination of the buret injection volume(V inj)and chemical calibration factor(f).Solutions of sulfa-mic acid,HCl,HClO4,and HNO3are suitable titrants,but HCl cor-rodes stainless steel at concentrations greater than1mM and, even in dilute solution,HCl and HNO3are sufficiently volatile to cause problems by eventual corrosion of electrical components. Sulfamic acid(p K a=1,D diss H=+0.41kJ/mol[11])may be consid-ered as a strong acid at concentrations below1mM where less than1%is undissociated,and as a solid sulfamic acid is a weighable acidimetric standard,but because of slow hydrolysis,solutions must be freshly prepared.Sulfuric acid is not suitable because the second proton ionization is incomplete(p K a2=2)and has a rel-atively large D R H.NaOH and2-amino-2-hydroxymethyl-propane-1,3-diol with p K a=8.06(also known as Tris,tris(hydroxy-methyl)aminomethane,and THAM)are the best characterized bases for this purpose,with enthalpy changes of reaction with strong acid ofÀ55.8andÀ47.4kJ/mol,respectively,at infinite dilu-tion at25°C[6,11,12].Because the base is present in large excess, the concentration does not need to be known accurately.Obtaining accurate results with these reactions requires special care to eliminate the effects of CO2.CO2cannot be entirely elimi-nated from water without extraordinary effort;neither boiling nor vacuum reduces the CO2concentration below approximately 0.01mM[13],a concentration that is significant compared with the concentrations of reagents typically used for ITC.Carbonic acid has an effective p K a2=10.33and p K a1=6.35,with enthalpy changes for protonation equal toÀ15andÀ9.15kJ/mol,respec-tively[11–13].Because these enthalpy changes are less negative than those for protonation of hydroxide ion or Tris,if carbonate or bicarbonate reacts,less heat will be produced than expected. Therefore,experimental conditions must be adjusted to prevent reaction of carbonate.Hydroxide ion is more basic than CO2À3;therefore,any CO2À3in the solution will not react as long as hydrox-ide ion is present in large excess(at least10Âany CO2À3present).Tris is less basic than CO2À3but more basic than HCOÀ3,and anyCO2in the solution will be converted into HCOÀ3in a Tris buffer.Therefore,if Tris is present in large excess(at least10ÂanyHCOÀ3present)in a Tris/HTris+buffer,the bicarbonate will not re-act with injected strong acid.Suggested conditions are titration of 40mM base with1mM acid.In the case of Tris,early injectionsshould be deleted because of possible reaction with CO2À3.Fig.2shows sample data for titration of1mM HCl into40mM Tris.Data can be analyzed byfitting the heat per injection to afirst-order linear equation.The slope should be negligibly small.The heat per injection can be calculated from the average or from the intercept,which gives the least squares value for the heat per injection.The uncertainty,as twice the standard deviation of the mean for205-l l injections,is typically±14l J/injection(n=5rep-licate titrations)as determined in a Nano ITC-SV with a gold reac-tion vessel.Calibration of isothermal titration calorimeters/N.A.Demarse et al./Anal.Biochem.417(2011)247–255251。
