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英语作文有关实验的题目Title: The Importance of Experiments in Scientific Research。
Experiments play a crucial role in scientific research as they provide a way to test hypotheses, validate theories, and discover new knowledge. Without experiments, scientists would not be able to gather empirical evidence to support their claims or make advancements in their respective fields. In this essay, we will explore the significance of experiments in scientific research and why they areessential for progress and innovation.First and foremost, experiments are essential fortesting hypotheses. A hypothesis is a proposed explanation for a phenomenon based on observations and previous knowledge. Through experiments, scientists can design controlled conditions to test their hypotheses anddetermine whether they are valid or not. This processallows researchers to gather empirical evidence and drawconclusions based on objective data rather than speculation or intuition.Moreover, experiments are crucial for validating theories. Scientific theories are broad explanations that have been extensively tested and supported by numerous experiments and observations. By conducting experimentsthat support or refute a theory, scientists can strengthen the validity of the theory and build a stronger foundation for future research. This process of validation isessential for building a consensus within the scientific community and advancing our understanding of the natural world.In addition, experiments are essential for discovering new knowledge. Through experimentation, scientists can uncover unexpected results, patterns, or relationships that were previously unknown. These discoveries can lead to new insights, theories, technologies, and applications that have the potential to revolutionize our understanding of the world around us. Without experiments, many groundbreaking discoveries and innovations would not havebeen possible.Furthermore, experiments are essential for progress and innovation in science. By testing hypotheses, validating theories, and discovering new knowledge, experiments drive scientific advancements and push the boundaries of human knowledge. They provide a platform for creativity, exploration, and discovery that fuels scientific curiosity and drives researchers to explore new frontiers. Without experiments, scientific research would stagnate, and our understanding of the world would remain limited.In conclusion, experiments are essential for scientific research as they provide a way to test hypotheses, validate theories, and discover new knowledge. They play a crucial role in advancing our understanding of the natural world and driving progress and innovation in science. As we continue to conduct experiments and push the boundaries of human knowledge, we will undoubtedly uncover new insights and discoveries that will shape the future of scientific research.。
初一英语科学实验步骤单选题30题(答案解析)1.First,we need some tools for the experiment.Which one is NOT a tool?A.test tubeB.beakerC.pencilD.flask答案：C。
本题考查对实验工具的认知。
A“test tube”试管、B“beaker”烧杯、D“flask”烧瓶都是常见的实验工具，而C“pencil”铅笔不是实验工具。
2.We should prepare enough materials.What's the plural form of “leaf”?A.leavesB.leafsC.leafesD.leavs答案：A。
本题考查名词的复数形式。
“leaf”的复数是“leaves”。
3.Before starting the experiment,we need to clean the table.Which verb form is correct?A.cleanedB.cleaningC.cleansD.to clean答案：B。
本题考查动词的现在分词形式。
“need to do sth.”后面接动词原形，“clean the table”是需要做的事情，用现在分词“cleaning”表示正在进行的动作。
4.We have to put on gloves to protect our hands.What's the meaning of “put on”?A.take offB.wearC.put downD.take away答案：B。
本题考查短语“put on”的意思。
“put on”表示“穿上、戴上”，与“wear”意思相近。
A“take off”是“脱下”；C“put down”是“放下”；D“take away”是“拿走”。
5.In the experiment,we need some water.What's the correct quantifier?A.a fewB.a littleC.fewD.little答案：B。
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安庆Unit,24年小学五年级上册英语第1单元期末试卷[含答案]考试时间：90分钟（总分:140）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 填空题：I write a letter to my __________. (亲戚)2. 填空题：We have ______ (许多) activities planned for the weekend.3. 选择题：What is the scientific study of the atmosphere and weather called?A. GeologyB. MeteorologyC. AstronomyD. Biology答案:B4. 听力题：The first successful test of an atomic bomb was in _______.5. 选择题：What is the process of taking in food called?A. DigestionB. IngestionC. AbsorptionD. Elimination答案: B6. 听力题：A nonpolar molecule does not have a positive or negative ______.7. 填空题：The __________ (气体) state has no fixed shape or volume.A ______ is an elevated area of land similar to a mountain.9. 听力题：Acids can be found in many ______ substances.10. 选择题：What is the name of the famous landmark located in London?A. Eiffel TowerB. Big BenC. ColosseumD. Statue of Liberty答案：B11. 填空题：We should learn about _____ (当地) plants and their uses.12. 选择题：What do we call the written record of a person's life?A. BiographyB. AutobiographyC. NovelD. Memoir答案: A13. 填空题：My _____ (阿姨) loves to cook and bake delicious treats.我阿姨喜欢烹饪和烘焙美味的点心。
金华2024年小学6年级英语第三单元测验卷(有答案)考试时间：90分钟（总分:110）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、听力题：A __________ is a reaction that absorbs heat.2、选择题：Which holiday celebrates the birth of Jesus?A. HalloweenB. ThanksgivingC. ChristmasD. Easter3、What do we call the process of taking care of plants?A. GardeningB. CookingC. DrawingD. Writing答案:A4、听力题：The first successful test of an atomic bomb was in _______.5、What is the name of the famous mountain in Africa?A. Mount EverestB. Mount KilimanjaroC. Mount FujiD. Mount McKinley答案: B6、选择题：What do we use to protect our eyes from the sun?A. HatB. ScarfC. SunglassesD. Goggles7、填空题：The dolphin plays with _________. (水)8、听力题：The ______ helps transport nutrients in the body.9、听力题：The _____ is the distance between two points in space.10、What do you drink in the morning?A. WaterB. JuiceC. MilkD. All of the above11、填空题：The discovery of penicillin was made by ________ (弗莱明).12、 to _______ (听音乐) in the evening. 填空题：She love13、填空题：The __________ was a conflict between Britain and its American colonies. (美国独立战争)14、What do you call a vehicle that travels on tracks?A. CarB. TrainC. BusD. Bicycle答案:B15、填空题：I like to collect ______.16、Which planet is known as the Red Planet?A. MarsB. VenusC. JupiterD. Mercury答案:AA __________ is a unit of measurement for temperature.18、听力题：The stars are ___ (fading/shining) brightly.19、听力题：The _____ (computer/tablet) is useful.20、填空题：There are many ________ in the ocean.21、What do we call the process of a caterpillar becoming a butterfly?A. MetamorphosisB. GrowthC. ChangeD. Transformation答案: A22、听力题：The ________ (strategy) guides our actions.23、What is the capital of Italy?A. VeniceB. RomeC. FlorenceD. Milan答案:B24、What is the primary language spoken in the UK?A. SpanishB. FrenchC. EnglishD. German答案:C25、What is the capital of Sweden?A. OsloB. StockholmC. CopenhagenD. Helsinki答案:B26、听力题：She sings beautifully in ___. (class)A sunflower follows the _____ (太阳).28、听力题：The _______ is great for attracting bees.29、听力题：The kite is ___ (flying) high in the sky.30、听力题：The waves are ___ (crashing) on the shore.31、听力题：Meteor showers occur when Earth passes through a trail of _______.32、填空题：In _____ (日本), sushi is a popular dish.33、填空题：I can ______ (担任) a leadership role.34、听力题：The Earth's crust is affected by both human and natural ______.35、What is the capital of Belgium?A. BrusselsB. AntwerpC. GhentD. Bruges答案: A. Brussels36、What do you call the process of water turning into vapor?A. PrecipitationB. EvaporationC. CondensationD. Freezing答案:B37、听力题：A solution that cannot dissolve any more solute is called ______.38、What is the name of the famous painting by Leonardo da Vinci?A. The Starry NightB. The Last SupperC. Mona LisaD. The Scream答案:C39、Which planet is closest to the sun?a. Earthb. Venusc. Mercuryd. Mars答案:c40、Where do fish live?A. TreesB. GroundC. WaterD. Sky答案:C41、填空题：The ______ (小鸟) sings sweet songs in the morning.42、听力题：The Earth's tilt causes the changing of the ______.43、听力题：A ______ is a large area of flat land.44、听力题：The _______ is a common sight in gardens.45、What is the capital of the United States?A. New YorkB. Washington D.C.C. Los AngelesD. Chicago答案:B46、听力题：My aunt lives _____ the city. (near)47、wildlife corridor) connects habitats for animals. 填空题：The ____48、What is the name of the period before history was written?A. PrehistoryB. Ancient historyC. Medieval timesD. Modern history答案:A49、听力题：__________ are essential for maintaining healthy ecosystems.50、What do we call a scientist who studies animals?A. BotanistB. GeologistC. ZoologistD. Biologist答案:C. Zoologist51、Which animal has a pouch for carrying its young?A. DogB. CatC. KangarooD. Elephant答案: C52、听力题：In a chemical formula, the numbers that show how many atoms of each element are present are called _____.53、填空题：In _____ (印度), the Taj Mahal is a famous landmark.54、What is the main ingredient in sushi?A. RiceB. BreadC. NoodlesD. Potatoes答案:A55、听力题：The process of burning is called ______.56、填空题：The cake looks _______ (很好吃)。
初一英语科学实验设计步骤单选题40题及答案1.First,we need to prepare some tools for the experiment.Which one is NOT necessary?A.test tubeB.beakerC.scissorsD.microscope答案：C。
本题考查科学实验器材的认知。
A 选项“test tube”（试管）、B 选项“beaker”（ 烧杯）和D 选项“microscope”（ 显微镜）在很多科学实验中可能会用到，而剪刀通常不是实验必需的器材。
2.The purpose of this experiment is to observe_____.A.the growth of plantsB.the change of weatherC.the behavior of animalsD.the movement of stars答案：A。
本题考查对不同实验目的的理解。
一般初一阶段的科学实验中比较容易涉及观察植物的生长，B 选项观察天气变化、C 选项观察动物行为、D 选项观察星星的运动通常不是初一科学实验的主要目的。
3.Before starting the experiment,we should_____.A.play gamesB.read booksC.prepare materialsD.watch TV答案：C。
本题考查实验准备的常识。
在开始实验前应该准备材料，A 选项玩游戏、B 选项读书、D 选项看电视都与实验准备无关。
4.Which of the following is important for a scientific experiment?A.being lazyB.being carelessC.being carefulD.being noisy答案：C。
本题考查科学实验的态度。
在科学实验中要细心，A 选项懒惰、B 选项粗心、D 选项吵闹都是不好的态度。
2024年五年级英语科学研究方法单选题30题1. What is the first step in a scientific experiment?A. Make a hypothesis.B. Conduct the experiment.C. Observe and ask questions.D. Analyze the results.答案：C。
解析：科学研究的第一步通常是观察并提出问题。
A 选项提出假设是在观察和提问之后。
B 选项进行实验是在有了假设等步骤之后。
D 选项分析结果是实验完成后。
2. After making a hypothesis, what should you do next?A. Repeat the experiment.B. Record the data.C. Conduct the experiment.D. Draw a conclusion.答案：C。
解析：提出假设后应该进行实验来验证假设。
A 选项重复实验一般在得到初步结果后。
B 选项记录数据是在实验过程中。
D 选项得出结论是实验结束后。
3. What do you do during an experiment?A. Make a prediction.B. Analyze the data.C. Record the data.D. Form a conclusion.答案：C。
解析：在实验过程中要记录数据。
A 选项做预测一般在实验前。
B 选项分析数据是实验后。
D 选项形成结论也是实验后。
4. Before starting an experiment, you should:A. Conduct the experiment.B. Make a hypothesis.C. Analyze the results.D. Draw a conclusion.答案：B。
解析：在开始实验前应该提出假设。
中考英语科学探究方法应用单选题40题1.In a science experiment, we should first ______ the problem.A.askB.stateC.findD.solve答案：B。
本题考查科学实验步骤的表达。
首先在科学实验中，我们应该先陈述问题，“state the problem”是科学实验的第一步。
选项A“ask”通常后面接某人，表示询问某人；选项C“find”是找到，通常是在实验过程中找某些现象等；选项D“solve”是解决，在实验中是最后一步。
2.When doing an experiment, we need to ______ a hypothesis.A.makeB.doC.haveD.give答案：A。
在做实验时，我们需要提出一个假设，“make a hypothesis”是固定表达。
选项B“do”通常后面接具体的事情；选项C“have”表示有，不合适；选项D“give”后面通常接对象，如give sb sth。
3.After making a hypothesis, we should ______ an experiment to test it.A.doB.makeC.takeD.have答案：A。
提出假设后，我们应该做实验来测试它，“do an experiment”是固定搭配。
选项B“make”通常用于制造物品等；选项C“take”常见的用法有take a test 等；选项D“have”表示有，不合适。
4.During an experiment, we should carefully ______ the results.A.lookB.watchC.seeD.observe答案：D。
在实验过程中，我们应该仔细观察结果。
“observe”更强调有目的、仔细地观察。
选项A“look”通常后面接介词at 再加对象；选项B“watch”通常用于观看动态的事物；选项C“see”更侧重于看到这个动作本身。
广州2024年08版小学6年级下册英语第三单元真题考试时间：80分钟（总分:140）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、填空题：The ______ (小鸡) hatches from an egg.2、填空题：The __________ (历史的启发性探讨) foster understanding.3、听力题：My grandma loves to bake ____ (bread).4、听力题：My uncle is a ______. He takes care of animals.5、What is 10 + 5?A. 12B. 14C. 15D. 16答案: C6、填空题：The first successful test of a nuclear bomb occurred in ________ (1945).7、填空题：I like to create adventures with my toy ________ (玩具名称).8、填空题：I want to learn how to grow _____ (植物).9、填空题：The ancient Sumerians are known for creating one of the earliest forms of ________ (文字).10、填空题：The discovery of ________ has fundamentally altered our understanding of physics.11、听力题：The chemical symbol for silver is _______.12、听力题：The ____ has a thick fur coat to keep warm in winter.13、填空题：The first successful kidney transplant was performed in _______. (1954年)14、What do we call a person who helps in emergencies?A. NurseB. FirefighterC. TeacherD. Chef15、填空题：My friend has a ______ (猫咪) that likes to play with yarn.16、听力题：The ____ has a unique tail and likes to climb trees.17、填空题：A hamster loves to collect ______ (食物) for later.18、听力题：The symbol for ytterbium is _____.19、填空题：The __________ (历史学) helps us understand past events and their impacts.20、填空题：The horse eats ________________ (草).21、填空题：I like to go to the beach and collect ________ (贝壳). Each one is unique and ________ (美丽).22、填空题：The __________ (历史的支持) is essential for growth.23、What do we call the phenomenon of water droplets falling from the sky?A. RainB. SnowC. SleetD. Hail答案:A24、听力题：I want to ________ (research) a topic.25、填空题：A _____ (热带) rainforest has many types of plants.26、What is the currency used in the USA?a. Eurob. Dollarc. Poundd. Yen答案:B27、选择题：What is the capital of Sri Lanka?A. ColomboB. KandyC. GalleD. Negombo28、选择题：What do you call the act of creating a sculpture?A. CarvingB. ShapingC. MoldingD. All of the above29、听力题：The three states of matter are solid, liquid, and ______.30、填空题：The fish swims in _______ (深水) where it feels safe.31、听力题：The Cold War was a period of tension between _______ and the West.32、What do you call a person who studies the atmosphere?A. MeteorologistB. ClimatologistC. GeologistD. Oceanographer答案: A33、What is the opposite of kind?A. MeanB. NiceC. GentleD. Caring答案:A34、填空题：We have a ______ (快乐的) family outing every month.35、填空题：The _____ (花期) varies among different plants.36、填空题：The elephant is the largest _________ (动物) on land.37、What do you call a person who studies languages?A. LinguistB. TranslatorC. InterpreterD. Polyglot答案: A38、听力题：The dog is _____ under the table. (sleeping)39、填空题：The city of __________ is known as the "Big Apple." (纽约)40、听力题：The ______ is a group of animals that includes elephants and hippos.41、填空题：My friend is very ________ (善良).42、听力题：My aunt loves to cook ____ (southern cuisine).43、What is the name of the famous English playwright?A. Charles DickensB. Mark TwainC. William ShakespeareD. Ernest Hemingway44、How many days are in a year?A. 365B. 366C. 360D. 364答案:A45、填空题：My _____ (舅舅) is a pilot.46、填空题：I can assemble my ________ (玩具名称) in different ways.47、Which animal is known for its long neck?A. ElephantB. GiraffeC. KangarooD. Zebra答案:B48、听力题：The state of matter that has a definite shape and volume is a _______.49、听力题：The cat is ______ (curious) about everything.50、填空题：Every year, we celebrate my birthday with a big ________ (聚会) and lots of cake.51、What is the name of the famous landmark in Brazil?A. Christ the RedeemerB. Statues of Easter IslandC. Great WallD. Eiffel Tower答案: A52、填空题：Fungi are not _____ (植物) but they thrive in soil.53、填空题：The clock is _______ (在墙上).54、听力题：A _______ can help beautify your community.55、听力题：The ______ is a talented filmmaker.56、What is the name of the electronic device used to communicate over long distances?A. TelephoneB. ComputerC. RadioD. Television答案:A57、听力题：I like to ________ my friends on weekends.58、听力题：The chemical symbol for chlorine is __________.59、听力题：The ancient Sumerians are credited with creating the first form of _______.60、What is the boiling point of water?A. 50 degrees CelsiusB. 75 degrees CelsiusC. 100 degrees CelsiusD. 150 degrees Celsius答案: C. 100 degrees Celsius61、听力题：The _______ changes its appearance with the seasons.62、填空题：A parakeet enjoys hanging from its ______ (栖木).63、What do you call a liquid that can dissolve other substances?A. SolventB. SoluteC. MixtureD. Solution答案:A64、听力题：The capital of Bhutan is _______.65、What is the main ingredient in potato chips?A. CornB. WheatC. PotatoesD. Rice答案: C66、听力题：A ____ is a friendly animal that wags its tail.67、填空题：My brother is a big __________. (粉丝)68、听力题：My uncle is a ______. He travels a lot for work.69、填空题：My favorite sport is _______ (棒球).70、听力题：I want to _____ (visit) historical sites.71、填空题：A ____(valley) is a low area between hills or mountains.72、填空题：The invention of the light bulb changed the way people _____.73、听力题：The bird is ___ its nest. (building)74、听力题：She counts _____ (to/from) ten every day.75、填空题：My _____ (玩具赛车) is very fast.76、听力题：A ______ is a small, flying insect.77、What is the opposite of 'clean'?A. DirtyB. NeatC. TidyD. Polished答案:A78、What do you call a story that is made up?A. BiographyB. FictionC. Non-FictionD. History答案: B79、Which fruit is known for having seeds on the outside?A. StrawberryB. RaspberryC. BlackberryD. Blueberry答案：A80、填空题：I enjoy watching ______ with my family. (我喜欢和家人一起看______。
中考英语科学实验创新思考单选题40题1.The first step in a scientific experiment is to _____.A.make a hypothesisB.collect dataC.define the problemD.draw a conclusion答案：C。
本题主要考查科学实验的步骤。
选项A“make a hypothesis”是提出假设，通常在定义问题之后。
选项B“collect data”是收集数据，在定义问题和提出假设之后。
选项C“define the problem”是定义问题，是科学实验的第一步。
选项D“draw a conclusion”是得出结论，在收集数据和分析数据之后。
2.When conducting an experiment, we should _____.A.change the variables randomlyB.record the results carefullyC.guess the outcomeD.skip some steps if they seem difficult答案：B。
本题考查科学实验的正确做法。
选项A“change the variables randomly”随机改变变量是错误的，变量应控制好进行实验。
选项B“record the results carefully”认真记录结果是正确的做法。
选项C“guess the outcome”猜测结果不可取。
选项D“skip some steps if they seem difficult”跳过困难步骤是错误的。
3.In a chemistry experiment, adding a certain substance causes areaction. This is an example of _____.A.a control groupB.an independent variableC.a dependent variableD.a constant答案：B。
姆佩巴效应实验作文范文英文回答：The Mere Exposure Effect is a psychological phenomenon that states that people tend to develop a preference for things that they are familiar with or have been exposed to repeatedly. This effect was first studied by Robert Zajonc in the 1960s.In one of the classic experiments on the Mere Exposure Effect, participants were shown a series of nonsense words. Some words were repeated more often than others. Afterward, participants were asked to rate the words based on how much they liked them. The results showed that participants rated the words that were repeated more often as more likable than the words that were shown less frequently.This experiment suggests that familiarity plays a significant role in shaping our preferences. When we are exposed to something repeatedly, it becomes more familiarto us, and we tend to develop a positive attitude towards it. This effect can be observed in various aspects of our lives, including our preferences for music, art, and even people.中文回答：姆佩巴效应是一种心理现象，它表明人们倾向于对他们熟悉或重复接触过的事物产生偏好。
a rX iv:physics /98243v1[physics.bio-ph]24Feb1998First experimental tests of the Peyrard-Bishop model applied to the melting of very short DNAs Alessandro Campa ∗1Physics Laboratory,Istituto Superiore di Sanit`a and INFN Sanit`a Viale Regina Elena,299,00161Roma,Italy Andrea Giansanti 2Physics Dept.,Universit`a di Roma “La Sapienza”and INFM Unit`a Roma 1P.le Aldo Moro,2,00185Roma,Italy February 23,1998Abstract The melting curves of short heterogeneous DNA chains in solution are calculated on the basis of statistical thermodynamics and compared to experiments.The computation of the partition function is based on the Peyrard-Bishop hamiltonian,which has already been adopted in the theo-retical description of the melting of long DNA chains.In the case of short chains it is necessary to consider not only the breaking of the hydrogen bonds between single base pairs,but also the complete dissociation of the two strands forming the double helix.There is a need for a theory of the melting of short DNA chains (oligonu-cleotides).The melting is the highly cooperative thermal disruption of the hydrogen bonds between complementary bases in the double helix,as usually monitored by the UV absorption increment due to the unstacking of the sepa-rated bases [1].At the equilibrium melting temperature half of the bonds are disrupted.Synthetic oligonucleotides of a fixed length and base pairs sequence have been used for a long time as model systems for the study of the structural and thermodynamical properties of the longer and more complex natural forms of DNA [2].Many studies have shown the effects of both sequence and sol-vent composition on the melting curves of oligonucleotides in solution [3].More recently particular attention has been given to the study of sequence specific ef-fects on the thermal stability of a variety of specially designed oligonucleotides,due to their importance in the exploitation of molecular biological techniques in gene therapy [4]and genome mapping [5].Predictive information has been gained through an extensive thermodynamical investigation on the melting be-havior of oligonucleotides,based on the computation of the Gibbs free energy,at afixed solvent composition,as a sum of contributions from nearest neigh-bors in the sequences[6,7].This phenomenology and the predictive power of the thermodynamical approach should then be confronted with a microscopic theory of short,heterogeneous DNA chains.Modellization of DNA melting was initially motivated by the study of the important process of transcription,in which the double helix has to be locally opened to allow reading of the genetic code.It was based,already many years ago,on Ising-like models[8,9],and more recently on an approach based on the modified self-consistent phonon approximation[10](see also[11]and references therein).These methods allow only equilibrium estimates of the probability of bond disruption.However,it is also important to consider DNA dynamics,both at melting and pre-melting temperatures.There is an interest in relaxation and kinetic phenomena,which are relevant for the pharmacological applications[4], and in the study of nonlinear energy localization and transduction.With a particular focus on the last problem,discrete nonlinear models of DNA(see, e.g.,[12,13],and for a review[14]),have been introduced;sequence effects have been considered in[15].These models are appealing,because they are simplified microscopic models with a small number of degrees of freedom,and thus are affordable also for the simulation of very long times.The experimentally available melting curves offer a way to optimize the parameters of these models, and therefore also increase the confidence for their use in dynamical studies.With a particular interest in thermal stability,a dynamical model was intro-duced by Peyrard and Bishop in1989[16](PB model).The authors have shown, through statistical mechanics calculations and constant temperature molecular dynamics[16,17,18],applied to the case of a very long homogeneous DNA chain,that the model can give a satisfactory melting curve,especially after the improvement introduced in[18].The PB model has been successively applied to heterogeneous chains,either modelling the heterogeneity with a quenched disorder[19],or properly choosing basis sets of orthonormal functions for the kernels appearing in the expression of the partition function[20],but compar-ison with experimental data was not attempted.In all these works the fact that the DNAs considered are quite long was essential,for the following rea-son.In a solution with two types of DNA single strands,A and B,there is a thermal equilibrium between dissociated strands and associated double strands (the duplexes AB),and a thermal equilibrium,in the duplexes,between broken and unbroken interbase hydrogen bonds.The average fractionθof bonded base pairs can then be factorized asθ=θextθint[8,9].θext is the average fraction of strands forming duplexes,whileθint is the average fraction of unbroken bonds in the duplexes.The dissociation equilibrium can be neglected in the case of long chains,whereθint and thusθgo to0whenθext is still practically1.On the contrary,in the case of short chains the processes of single bond disruption and strand dissociation tend to happen in the same temperature range;therefore, the computation of bothθint andθext is essential.In Ref.[20]the factorization ofθis stated,but only the case of long chains is then considered.The aim of this work is to show,through a comparison with experimental data,that the onedimensional PB model can be used to compute the melting2curves of short DNAs.It will also be shown how to take into account the dissociation equilibrium.The potential of the PB model [16,17,18]isgivenby:U=ikN N i =1<ϑ(y 0−y i )>where ϑ(y )is the Heaviside step function and the canonical average <·>is de-fined considering only the double strand configurations.We have chosen a value of 2˚A for y 0.After a discretization of the coordinate variables and the introduc-tion of a proper cutoffon the maximum value of the y i s [10],the computations needed for the canonical averages are readily reduced to the multiplication of finite matrices,since the potential (1)couples only nearest neighbors,and are easily performed by suitable computer programs.3Let us now considerθext.At equilibrium the chemical potentials of the three species A,B and AB[22]are related by the equation:µAB−µA−µB=0. Using the definition of the chemical potentials as derivatives of the free energy, and in turn the relation of the latter to the partition functions,we obtain an equation involving appropriate partition functions.In the usual experimental conditions the solutions can be considered ideal;with the further assumption that the model takes into account effectively the presence of the solvent,we get the usual equilibrium condition:N AB Z(A)Z(B)δ2+2δwhereδis given by the following expression:δ=Z(A)Z(B)a av Z int(AB)a av Z ext(A)Z ext(B)a AT a GC to makeseparately dimensionless both fractions,that therefore can not depend on the choice of units.Without any such normalization thefirst fraction would have the dimensions of an inverse of a length,since the overall translation is not included in Z int.It is included in the external functions,that,however,have to take into account also the dynamics not described by the simple onedimensional model,and related to conformational movements(like,for example,the winding of the strands).This point has already been considered in Ising models:the influence on the dissociation process of the degrees of freedom not described by the model can not be neglected,and it must be accounted for in some way.In analogy to what has been proposed for the Ising models[8,9]on the basis of the partition functions of rigid bodies[24],we make the following choice:a av Z ext(A)Z ext(B)n0N−pθint+q(3)4where the parameters p and q can befixed by a comparison with experimental melting curves;n0is the single strand concentration N0/V,and n∗is a chosen reference concentration(we have taken1µM,a usual concentration in experi-ments).We defer further comments about this equation after the presentation of the results.We show here the comparison of our calculations with the experimental melting curves that have been obtained,in our lab,for three different oligonu-cleotides,in a10mM Na phosphate buffer,0.1mM Na2EDTA,200mM NaCl, pH6.7.One of the oligonucleotides contained27base pairs,and the other two had21base pairs.The sequences are given by:s1)5′CTTCTTATTCTTATTGTTCGTCTTCTC3′s2)5′CTCTTCTCTTCTTTCTCTCTC3′s3)5′GTGTTAACGTGAGTATAGCGT3′and by the respective complementary strands.We have considered the case s3) at two different concentrations.The single strand concentration was:s1):2.4µM,s2):1.7µM,s3):3.1µM and120µM.In Fig.1we show the experimental and computed melting curves.As it can be seen,there are sequence and concen-tration effects on the experimental melting curves,which are well reproduced by the computed curves.Note that a40fold concentration increase for s3)yields an increase of only5degrees in the melting temperature(a logarithmic depen-dence on the concentration is expected[1]).Similar differences between curves at the low concentrations should then be due to sequence and length effects.We would like to stress that in the case s3)the parameters p and q have beenfitted to the experimental curve at the lower concentration.The comparison with the experimental curve at the higher concentration has then been performed with only the change of the value of n0in Eq.(3),without changing the values of p and q;this has reproduced the difference between the melting temperatures of the two cases,that differ by about5degrees.This fact indicates that the concentration dependence of the left hand side of Eq.(3)is described by the preexponential factor,while the parameters p and q are related to the molecular conformation.In conclusion,our comparisons show that it is feasible to compute the equilib-rium melting profile of DNA oligonucleotides with the PB nonlinear model.We would also like to note that the modellization of the external partition functions ratio as in Eq.(3)is very similar to that adopted in Ising models for medium size DNAs(100-600base pairs)[8,9].This confirms that this term is related to the conformationalflexibility of the double and single strands,not described by a onedimensional model.The internal term is related to the onedimensional hamiltonian and then to nearest neighbor interactions.For long DNAs(large N),at temperatures in whichθint is already close to0,the part in Eq.(2) depending on the internal partition functions goes as e−γN for some positive γ,and thusδ≈0andθext≈1.This N dependence of the internal part can be seen,for example,in the case of homogeneous sequences with the transfer matrix method[16,17,18].It is expected to be the same for heterogeneous5sequences.References[1]C.R.Cantor and P.R.Schimmel,Biophysical Chemistry,(W.H.Freemanand Company,San Francisco,1980).Vol.III.[2]L.A.Marky,K.S.Blumenfeld,S.Kozlowski,and K.J.Breslauer,Biopoly-mers22,1247(1983).[3]K.J.Breslauer,Methods Enzymol.259,221(1995).[4]E.T.Kool,Annu.Rev.Biophys.Biomol.Struct.25,1(1996).[5]M.Doctycz et al.,J.Biol.Chem.270,8439(1995).[6]K.J.Breslauer,R.Franck,H.Bl¨o cker,and L.A.Marky,Proc.Natl.Acad.Sci.U.S.A.83,3746(1986).[7]J.SantaLucia,H.T.Allawi,and P.A.Seneviratne,Biochemistry35,3555(1996).[8]D.Poland 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