Molecular Dynamics for Everyone: An Introduction to the Molecular
Contents
1. test for example The authoring system along with the model builders has allowed us to create a myriad of models and activities that can be found in the material repository within MW the internal MW page when you press the Home Button on the tool bar of MW Some of these activities have become reasonably sophisticated and self contained enough in content to be qualified as interactive textbooks For those who are interested in learning how to create models and activities a comprehensive online User s Manual which is written using the same authoring system provides numerous working examples Simulations should be easy to share A pedagogy made possible by the easy to use model builders is to involve students in creating simulations a process that can be devised to embed instructional steps that lead to progressive conceptual understanding This route of learning different from inquiry using interactive media based on existing simulations created by experts seems to be practical at college level where students have obtained adequate prior knowledge needed to understand the basics about simulations to get started and interpret the results From the point of view of social constructivism the creation process and the end product must be shared with others in order for the full effect of learning to take root It is through the creation of a molecular model that is shared and becomes what Papert calls a public entity that learning is strong2. A Pallant amp R Tinker Reasoning with Atomic Scale Molecular Dynamic Models Journal of Science Education and Technology 13 51 66 2004 9 Q Xie and R Tinker Molecular Dynamics Simulations of Chemical Reactions for Use in Educa tion Journal of Chemical Education 83 77 83 2006 10 H Jang C K Hall and Y Zhou Assembly and kinetic folding pathways of a tetrameric beta sheet complex Molecular dynamics simulations of simplified off lattice protein models Bio physical Journal 86 31 49 2004 11 S Papert Situating Constructionism in I Harel and S Papert Eds Constructionism Ablex Publishing Corporation Norwood NJ 1991
3. activity as described in the previous section The second is a data collector that gathers and stores a student s inputs from questions The third is a snapshot facility that allows students to take a snapshot image of a simulation or a graph A snapshot image captures what a student sees happen ing on the screen which are sometimes difficult to describe merely with words or numbers There is also a set of tools for annotating a snapshot image which students can use to highlight and explain certain parts of the image The fourth is a report generator that automatically converts student data into a readable page that can be printed saved or submitted The fifth is the MW Space that registers students and teachers receives and stores reports in a database and provides feedback to teachers Fig 5 shows a schematic illustration of the workflow of the Report System Pagel _ Page 2 _ Page 3 iy A 1 I Questions Questions Questions 77777 Report Generator The MW Space TeacherAccount Figure 5 The flow of collecting student work during a learning activity supported by the Report System With the Report System and its future improvements on critical issues such as data mining and data analysis MW can be a very useful tool for conducting educational research particularly for studying the effectiveness of using computational models in education While few disagree upon the extensive use of interactive media
4. in teaching many including us are still searching for the best design strategy of these media and the best pedagogy of using them The research on this avenue may provide insights that would develop the next generation of educational media Acknowledgements The author thanks B Berenfeld D Damelin D Markman A Pallant E Rosenbaum B Tinker and R Tinker for their encouragement and numerous suggestions for developing and improving the Molecular Workbench System This article is based upon work supported by funding from the National Science Foundation References 1 World Index of Molecular Visualization Resources http www molvisindex org 2 R Tinker and Q Xie Applying Computational Science to Education The Molecular Workbench Paradigm Computing in Science and Engineering in press 2008 3 Molecular Literacy http molit concord org 4 D Hestenes Notes for a Modeling Theory of Science Cognition and Instruction paper presented at The 2006 GIREP conference Modeling in Physics and Physics Education Amsterdam 2006 5 H D H ltje W Sippl D Rognan and G Folkers Molecular Modeling Basic Principles and Applications 3 4 Edition Wiley VCH 2008 6 A R Leach Molecular Modeling Principles and Applications 2 4 Edition Pearson Education 2001 7 D Hestenes Modeling Theory for Math and Science Education paper presented at the Mathe matical Modeling ICTMA 13 Education and Design Sciences 2007 8
5. similar pages in MW without a problem A model container within which a simulation runs is a core component that can be inserted into a page With a rich set of pluggable components that can communicate with a model container through command and data channels a custom user interface can be built for each simulation The user interface can comprise controls of the simulation buttons and sliders for changing the parameters and graphs for displaying the outputs Customized user interfaces are important because they establish a learning space that is constrained only within the topics covered in the activity For example Fig 4 shows a customized user interface for showing the Brownian motion Although standing behind the scene is the entire engine that is capable of doing numerous other kinds of simulations the end user of the activity needs not be concerned about anything beyond what is presented on this succinct page in order to learn the intended subject Another kind of components that can be inserted into a page is questions There are three types of questions that the author can set up multiple choice question free response question and image question An image question is a type of question invented in MW which requires the student to take a snapshot image of a simulation as an answer to the question These questions can be used to test the student s prior knowledge pre test and measure the gains after learning through an activity post
6. Molecular Dynamics for Everyone An Introduction to the Molecular Workbench Software Charles Xie Ph D The Concord Consortium qxie concord org The world moves because molecules move Studying the motion of molecules is important to the understanding of many critically important concepts in physics chemistry and biology A fundamen tal goal of scientific research is to learn how things work which at the microscopic level primarily means how atoms and molecules move to perform certain functions such as chemical reactions molecular recognition and protein synthesis Since the invention of molecular graphics a subject that focuses on visualizing molecules using 3D computer graphics chemists have embraced tools capable of rapidly displaying molecular structures and viewing them from different perspectives Because of the appealing effect of 3D graphics commercial computer aided design packages often feature molecular visualization tools to promote the products Since the advent of the Internet Era several free tools have been developed for showing molecules on the Web These tools are widely used by educators to teach molecules 1 Most molecular viewers however are mainly designed to show static structures The user can rotate and translate the entire rigid structure or change the view angle dynamically to create a motion effect but the atoms do not move relatively to each other Some viewers can sequentially display a series of static fram
7. aders can consult with Ref 6 or read the online User s Manual within MW The MD method is very useful in scientific research because it satisfies the following fundamental physical laws e The First Law of Thermodynamics The Law of Conservation of Energy automatically emerges in an MD simulation If there is no energy input output through external forces or dissipation through friction the total energy which is the summation of the potential energy and the kinetic energy for all the atoms in the system remains constant within the tolerance of numerical errors This can be used as a criterion to check if a simulation runs properly 3 The bond stretching potential given by Hooke s Law does not permit a bond to break The more a bond is stretched the greater is the force to pull the atoms back As a result the above force fields cannot be used to simulate chemical reactions which involve making and breaking bonds We have proposed a method that allows bonds to make and break and thus makes it possible to simulate some simple reactions 9 4 Some molecules such as benzene have delocalized bonds that involve more than four atoms However no higher terms of energy decomposition seem to be necessary in this treatment e The Second Law of Thermodynamics Although the Reversibility Paradox suggests that classical dynamics might be at odds with the Second Law of Thermodynamics MD simula tions of basic processes such as diffusion heat tra
8. become disadvantages when novice users in schools try to use them without the aid of an expert The overarching goal of a learner friendly MD program is that average students can use it to learn science The intermingled complexity of learning and science requires a highly integrated system that is capable of supporting both Technologically this corresponds to the encapsulation of the entire process of building models setting up conditions running and controlling simulations visualizing results recording observations testing monitoring learning progress and feedback into a single program with a unified graphical user interface In the following subsections we will discuss the important facets of such a system in details Simulations must be interactive When a scientist performs an MD simulation the goal is not to watch how it unfolds on a computer screen There is seldom a need to spend precious computing resources on visualizing the intermedi 5 Consider an impact process in an isolated system a high speed atom bombards and breaks a microcrystal If we stop the simulation after the crystal has been broken reverse the velocities of every single atom in the system and then continue to run it we can reverse the process the at oms re assemble into the original crystal The entropy decreases in this spontaneous process in the simulation without work and or cooling from the outside world This paradoxical result seems to be a violati
9. e third section we introduce our ideas to evaluate student learning based on MW materials The results of our educational research are not covered in this technical article Please see a paper by Pallant and Tinker 8 if you are interested in them How to simulate the motion of atoms and molecules Everything moves because of forces which result from the interactions among atoms and molecules We will begin with how theoretical chemists model interatomic and intermolecular interactions There are two levels of modeling for molecular interactions One is based on quantum mechanics which is beyond the scope of this article The other is based on classical mechanics which will be introduced in the following Molecular mechanics force fields Atoms basically interact with each other through van der Waals forces and electrostatic forces When they are covalently bonded to others strong forces hold them together as stable chemical groups A widely used mathematical model for the potential energy of a molecular system consists of six types of interactions U V Ver Veg Vag Vpr Viz The first type Vy is the Lennard Jones potential that has an attractive part representing the van der Waals energy and a repulsive part representing the Pauli repulsion 12 6 1 O O Mi eae 6 g i ji j ij ij where R is the distance between the i th and j th atom gij is called the van der Waals dissociation energy and oj is called the collision diam
10. es which can be different data sets of the same structure to create animations Few allow the user to simulate molecules in motion based on calculations using interatomic and intermolecular forces Funded by the National Science Foundation a team of the Concord Consortium has been developing a free open source program called the Molecular Workbench MW http mw concord org modeler which brings a dynamic molecular world to the computer screen and allows students to interact with it based on real time molecular dynamics MD calcula tions and visualizations 2 MD modeling provides a powerful means to foster the Molecular Literacy 3 because it complements and enhances traditional instructional approaches including formal mathematics Cognition can be viewed as a process of making and manipulating mental models of imaginary objects and events 4 A scientific model that comprises basic units of coherently structured knowledge in a tested and integrated framework if presented appropriately with effective pedagogy can be enormously useful in helping students develop correct mental models from which they can make logical inferences such as explanations predictions and designs Molecular modeling which is an important part of contemporary chemistry research 5 6 constitutes the theoretical foundation for creating objective conceptual models 7 that can be used by students to explain and investigate many natural phenomena at the molecu
11. eter The dissociation energy is equal to the amount of energy needed to pull a pair of atoms in the strongest van der Waals binding state apart The collision diameter is approximately the distance at which a pair of atoms bounces off from each other in a normal non reacting condensed state 2 The power of the negative term which is sometimes also called the London dispersion force has a root in the quantum mechanical calculation of the binding energy of the hydrogen molecule but the power of the positive term has no apparent theoretical basis sometimes it is set to be 9 to soften the repulsion core for condensed phases Vex is the electrostatic potential energy according to Coulomb s Law 1 9 9 Mn 9 R i j i j ij where q is the charge of the i th atom Compared with the van der Waals potential the electrostatic potential is a stronger more long range interaction A pair of charged atoms in vacuum will be able to feel each other from quite a distance away whereas a pair of neutral atoms will feel each other s existence only when they are close Ves is the bond stretching energy standing for the elastic interaction between a pair of atoms connected by a covalent bond Vaz the angle bending energy standing for the interaction among three covalently bonded atoms that form a stable angle and Vpr and Vir the proper and improper torsional energies standing for the interactions among four covalently bonded atoms that form a s
12. ftware tools But the optimal way of using simulations is to embed them in a learning environment that provides all the essential elements needed for a learning process We call such a complete package a learning activity A good learning activity motivates scaffolds and supports student exploration of models and simulations It also provides background information opportunities for reflection and methods of monitoring student progress in a context and evaluating learning MW is a versatile learning environment that offers this kind of classroom ready learning activities Moreover it provides an authoring system for epe Zoomit Up and Down the Scale Molecular Workbench V2 0 creating them oS e S oren H sare FANS 2 seso EA Commer A Ey oy awspace A learning activity in MW usually consists of multiple pages A page is a screen space in which text can be typed and styled like in a word processor and many kinds of compo nents can be inserted and customized The fact that these elements can be T D EnD END placed anywhere on a page and mixed with characters images and links allows the author to design high se quality visually appealing and self P i ore explanatory pages Authors who have Figure 4 This screenshot shows that an MD model for the experience in creating simple HTML Brownian motion is customized and contextualized in an activity that teaches the concept of scale web pages should be able to author
13. gged and dropped and edited through the supporting pop up menus and property editors User actions are undoable and redoable Annotations can be added to make a model easier to understand For a coarse grained particle model custom images can be attached to decorate the particles so that the model will bear a resemblance to illustrations commonly seen in textbooks particularly for molecular biology see the simplified graphical representation of lipid molecules that form the micelle in Fig 2 In MW there is no border between construction and run The user can at any time run the model while constructing it This characteristic feature stemming from the dynamic nature of MD models is a major difference between building a static model and a building a dynamic one In he fact test running a model c under construction is an important part of the constructing process as it allows the user to build through trail and error cycles Unstable constructs can be automatically removed or spotted when a model runs or a procedure of energy minimization is called File Edit view Template Options For users who are not satisfied with the abstraction of 2D dips models a rudimentar WYSIWYG 3D model builder CE Ww is available for creating 3D models Fig 3 It allows the user to build molecules from scratch by laying down atoms Figure 3 A screenshot of the 3D Model Builder in action It can be used to build models as comp
14. lar scale and thereby develop concrete mental models about them It is important to emphasize the educational significance of computational models based on science for example rigorous numeric methods such as MD as opposed to movies composed of frames of 1 You can watch a movie about MW at http mw concord org modeler small small html images and animations based on simple timeline rules In a computational model critical behaviors emerge from algorithms derived from first principles which give it the explanatory power that can be used to manifest existing knowledge and the predictive power that can be used to explore unknown domains A computational model can accurately simulate a large number of different phenomena by varying parameters configurations initial conditions and boundary conditions A movie or an animation in contrast can only illustrate a handful of situations that are recorded or preprogrammed Because a computational model provides a much larger intellectual space and more freedom for learners to explore create and invent effective profound learning is more likely to occur This article presents the scientific methods the educational background and the technical ideas behind the software In the first section we review the basic procedures of classical MD simulations In the second section we discuss the requirements of educational simulations and the technical work needed to be done to meet these requirements In th
15. lex as this nano car which has four short car bon nano tubes as the tires and wheels in the 3D space with the assistance of movable helper planes and joining them by radial angular and torsional bonds More complex chemical systems can be built based on a set of building blocks that includes all the amino acids and nucleotides A crystal builder is also provided to build a limited number of crystal lattices Atoms can be selected translated rotated duplicated and deleted as blocks There different views are available for the author to set the perspective to observe a simula tion These views include a regular view in which the model is viewed as a whole at different zooming distance a navigation view in which the user can move the camera around within the molecular system to experience an immersive effect and a rover view in which the camera is attached to an atom to mimic the effect of riding on an atom There are many pre made models that cover a breadth of science and are freely available in MW The collection constitutes a solid scientific foundation of MW As the software development continues more examples will be added to consolidate and expand this foundation Simulations should be embedded in a learning environment Simulations are not broadly useful in classroom without accompanying instructional materials Many educational applications provide lesson plans or worksheets for students to use separated from the so
16. ly reinforced 11 In the process of building sharing or collaborating students learn their subjects well because they have to think hard about them and figure out how to present their modeling ideas to others MW allows users to share and publish their modeling work through the MW Space a web applica tion that facilitates social interactions in virtual classrooms in a culture where models are the central elements Students can easily submit their models to their MW accounts and decide with whom they will be shared They can choose to share with their classmates their teachers or the world users of MW With the authoring system students can also introduce their motivations explain what their simulations will show and tell how they were constructed This makes a submission read more like a presentation instead of just a plain model How do we know if students learn To some extent going through an MW activity for a student is similar to going through an experi mental procedure in a wet lab The common things are that a student needs to read instructions follow certain procedures operate some instruments observe what happens record some data and write a report at the end The Report System in MW monitors what students do during this process automatically generates reports and allows teachers to track down students progresses The Report System consists of five parts The first one is questions which can be embedded into a learning
17. n MW we call these constructs radial bonds angular bonds and torsional bonds The first two terms the Lennard Jones potential and the electrostatic potential are called the non bonded interactions In MD simulations they are more important than the bonded interactions It is the non bonded interactions among the atoms of a macromolecule that affect its secondary structure It is the non bonded interactions among the atoms of different molecules that organize them into crystals complexes and other assemblies Molecular dynamics simulations Having defined the interactions among atoms the position velocity and acceleration of each atom are calculated using a numerical method e g the Verlet method or the Runge Kutta method to solve Newton s equations of motion according to the forces derived from the gradients of the interaction potentials involving the atom mR V U R R R where R is the position vector of the i th atom and mi is its mass The numeric integration is carried out stepwisely The process is repeated at each discretized time step The time evolution of the system is approximated by a sequence of results calculated consecutively The trajectory of each individual object can be tracked by connecting its states into a time series That is all you need to do to get an MD simulation up and running For advanced topics such as boundary conditions thermostats pistons statistical mechanics and so on interested re
18. nsfer and phase transition clearly show that the entropy of an isolated molecular system always tends to maximize Despite of the fact that it is possible to create special initial conditions that lead to a process of entropy reduction in an isolated system in practice we have never found that such special conditions can sponta neously arise during an MD simulation e The Law of Momentum Conservation As the Law of Conservation of Energy this Law also automatically emerges in an MD simulation This Law dictates each collision among atoms The overall result is that the total linear and angular momentum of the system conserves e Other statistical laws Important laws in statistical mechanics such as the Theorem of Energy Equipartition Maxwell s Theorem of Speed Distribution and the Boltzmann Distribution are all guaranteed in MD simulations We can even simulate the Galton Board that demonstrates the normal distribution What needs to be done to make molecular dynamics model ing accessible to students Most MD programs involve using a pre processor to prepare simulations and a post processor to analyze results When a calculation is actually being done after it is submitted to a computing service the user is rarely given a chance to intervene Moreover many programs require the user be able to work with command lines and scripts and feel comfortable dealing with raw data These require ments are prerequisites for scientists But they
19. om which the user can edit and modify the properties of an object of its type Draw a rectangle vast number of water molecules that have to be otherwise present in the simulations of molecules in aqueous solutions The blue window in Fig 2 shows a coarse grained model for micelle with implicit solvation Simulations should be easy to create Models are abstractions of data that are composed of different objects at different locations in the phase space under different conditions and with different initial settings A simulation engine if generic and powerful enough allows us to build as many models as permitted by its capacity to match the diversity of reality It becomes apparent that to harness the power of this theoretical capability users need to be able to turn their modeling ideas into computational models A user friendly system for constructing simulations has twofold importance First it allows educators to create simulations for teaching as alternatives to traditional drawings and illustrations Second it allows advanced students to design their own models a process during which their modeling skills and creative thinking can be trained MW has a What You See Is What You Get WYSIWYG 2D model builder that makes models in a way that is as easy as making shapes with a drawing program see Fig 2 With this model builder many types of objects can be added and every object in a model can be cut copied pasted dra
20. on of the Second Law of Thermodynamics at first glance See http mw concord org modeler1 3 mirror thermodynamics loschmidt html 6 http mw concord org modeler1 3 mirror mechanics galton html ate results on the fly Neither is there a need for the user to alter the parameters and conditions arbitrarily during a simulation Often a simulation starts with a fixed set of inputs and records the intermediate results while it is running When it completes the stored results can be analyzed to retrieve the needed information corresponding to the given set of inputs For a program to be educationally useful however opportunities must be provided to students to interact with simulations themselves To support inquiry students must be allowed to adjust parameters and add inputs at any time and see the emergent behaviors of the simulated systems instantane ously Only through interacting with simulations freely in many different ways and watching the results can students discover the cause and effect relationships revealed by the simulations and therefore construct their own mental pictures about the important physical and chemical concepts embodied in the simulations Technically an educational simulation is required to do both the calculations and the visualizations at the same time in order for students to see the entire process in all possible levels of details and in real time in order for them to manipulate it and observe the responses of the
21. system right away Translated into programming terms the MD code the visualization tool and the graphical user interface must be integrated seamlessly in the run time The requirement of interactivity however limits the sizes of simulatable systems on personal computers There are two solutions to this issue The first one counts on the continuous improve ments on computer power As the Era of Multicore Computing is upon us the parallelization of the software system based on multicore File Edit Toolbar Compute Analysis Options processors will allow larger systems MNES eee ehotststoMeoces to be simulated The second one uses a coarse grained approach to reduce large systems into models with a tractable number of particles each of which represents a large number of grouped atoms that form a stable structure These effective particles interact with each other to move join and break For example it is common to use a model in which an amino acid is represented by a single particle to study the mechanisms of protein folding 10 Implicit solvation that employs effective fields to simulate solvent solute O m 0 01D interactions can be used to save the computational cost needed for the Figure 2 A screenshot of the 2D Model Builder in action The menu bar and the tool bar above the view window provide many tools needed to construct models and set up simulations Each type of object also provides a pop up menu and a property editor fr
22. table proper and improper dihedral angle see Fig 1 Mas gt DK I A B mebonds 7 V 1 De k 0 0 AB 2 m m meangles 1 Vir dV 1 cos n a 7 metorsions C Vir 1 ee sok metorsions where Im is the distance between the two atoms of the m th bond lm is the equilibrium bond length km is the bond strength n is the m th Figure 1 A schematic illustration of the interactions that model co valent bonding A Bond stretching force B Angle bending force C Proper torsional force D Improper torsional force angle between the two adjacent bonds that share a common atom 6m is the equilibrium bond angle km is the strength m is the m th dihedral angle between the two adjacent angles that share a common bond mm is the periodicity factor which determines the number of equilibrium dihedral angles in a 360 rotation Yn is the phase shift Vm is the amplitude m is the m th improper dihedral angle among four atoms that are not 2 If a pair of atoms can react to form a covalent bond the length of the bond between them can be smaller than the collision diameter bonded successively to one another m is the equilibrium improper dihedral angle and km is the strength The last four items are called the bonded interactions which maintain the bond lengths the bond angles and the dihedral angles so that chemical groups will remain sterically stable in an MD simulation i
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