Date

Lecture Topic

Readings

Tutorials & Assignments

Jan. 17th

· Course Overview and Introduction

(1) Schlick Chapter 1

(2) Hunter L, Molecular biology for computer scientists, pp. 1-46

T1

T1 files

Jan. 19th

·  Protein Folding I

The problem of protein folding will provide a template to understand what molecular simulation, particularly in combination with experiments, can elucidate about questions of biochemical or biological relevance. Here we introduce three problems associated with protein folding: predicting the highly specific folded structure, estimating the kinetic rates of folding and unfolding, and most interestingly, the pathways of folding.

(1) Schlick Chapter 2.1-2.3

(2) Mayor U, Johnson CM, Daggett V, Fersht AR: Protein folding and unfolding in microseconds to nanoseconds by experiment and simulation. Proc. Natl. Acad. Sci. USA 2000, 97:13518-13522.

Jan. 24th

·  Protein Folding II

We introduce the statistical mechanical picture of protein folding, which starts with a folding funnel. We will also highlight some of the mathematical and computational difficulties associated with constructing this folding funnel: the integration over many degrees of freedom, the roughness of the resulting free energy surface, and the disparity of time scales present in folding. The rest of the course tries to address these questions using model reduction, specialized numerical methods, and vast computational resources.

(1) Schlick Chapter 3

(2) Gruebele M, Protein folding: the free energy surface. Current Opinion in Structural Biology 2002, 12:161-168

(3) Snow CD, Sorin EJ, Rhee YM, Pande VS, How well can simulation predict protein folding kinetics and thermodynamics? Annu. Rev. Biophys. Biomol. Struct. 2005. 34:43-69

A1 pdf word

T2

A1 Sol

Jan. 26th

·  *Guest Lecture: Dr. Samy Meroueh
Dept. of Chemistry and Biochemistry, Notre Dame

Dr. Meroueh will describe the related problem of protein-ligand and protein-protein interactions from the microscopic viewpoint.

(1) Schlick Chapter 2.4

(2) Halperin, Ma, Wolfson, and Nussinov. Principles of Docking: An Overview of Search Algorithms and a Guide to Scoring Functions. PROTEINS 47:409-443 2002

(3) Kitchen, Decornez, Furr, and Bajorath. Docking and scoring in virtual screening for drug discovery: methods and applications, Nature Reviews3935 2004

Jan. 31st

·  Protein-Protein Interactions I

Once a protein is folded, functional, and interacting with particular ligands or proteins, it is useful to study the metabolic, signaling, and other networks they form. Here we introduce proteomics, the study of entire protein systems, particularly the approach of systems biology: to build a scaffold of interactions to detect modules with particular functions. We briefly introduce the experimental techniques to study protein interaction networks and the statistical tools needed to make sense of these large scale studies.

(1) Ideker T, Lauffenburger D, Building with a scaffold: emerging strategies for high- to low-level cellular modeling, Trends in biotechnology 2003, 21:255-262.

T3

Feb. 2^nd

·  Protein-Protein Interactions II

We introduce computational methods to predict and validate networks of protein-protein interactions. These methods are based on sequence, structure, or evolutionary similarity, and are frequently probabilistic. Key issues are the validation of predictions, and the integration with other sources of information.

(1) Valencia A, Pazos F, Computational methods for the prediction of protein interactions, Current Opinion in Structural Biology 2002, 12:368$.1Žòó373.

Feb. 7th

· Molecular Dynamics Simulations I

We go down the scaffold to one of the most versatile low level modeling and simulation methodologies: molecular dynamics (MD). Starting with atomic coordinates of proteins and possibly solvents, one tries to infer dynamics (how the molecule moves), thermodynamics (characterize various states of the systems), and kinetics (rates of change).

(1) Schlick Chapter 7.1,7.3,7.4

(2) Hansson T, Oostenbrink C, van Gunsteren WF, Molecular dynamics simulations, Current Opinion in Structural Biology 2002, 12:190Žòó196.

T4

Feb. 9th

·  Molecular Dynamics Simulations II

We look in detail at the procedure of molecular dynamics: generation of force fields, equilibration, gathering of statistics, and analysis. We emphasize some of the pitfalls when using naïve numerical methods to perform MD: large discretization errors, instabilities due to linear and nonlinear resonances, destruction of conserved quantities by the numerical method, and systematic errors that may sample from the wrong probability density functions.

(1) Schlick Chapter 8

(2) van Gunsteren WF, Mark AE, Validation of molecular dynamics simulation, J. Chem. Phys. 1998, 108:6109-6116.

Feb. 14th

·  Molecular Dynamics Equilibration I

We show with practical examples the difficulties in evaluating equilibration and convergence of desired quantities in MD simulations. We will look at some of the most descriptive thermodynamic and dynamic properties of the biomolecular system, and at metrics to assess equilibration and convergence of these.

(1) Schlick Chapter 12.1-12.3

(2) Smith LJ, Daura X, van Gunsteren WF, Assessing Equilibration and Convergence in Biomolecular Simulations, PROTEINS: Structure, Function, and Genetics 2002 48:487-496.

Project Reviews

Feb. 16th

·  Molecular Dynamics Equilibration II

Here we study in detail some of the main statistical ensembles in which molecular dynamics is performed: microcanonical, canonical, and isobaric ensembles. We will see and compare two MD approaches for the canonical ensemble: Langevin dynamics and extended system Hamiltonians.

(1) Schlick Chapter 12.4-12.6

Feb. 21st

· Sampling: Replica Exchange/ Parallel Tempering

MD can be used not only to compute dynamic properties, but to sample the configurational space and thus compute thermodynamic or equilibrium properties as well. The problem of sampling in MD is difficult because of the dimensions of the sampling space and the nonlinearity and thus ruggedness of the free energy function. Here we describe the parallel tempering or replica exchange method, one of the most successful sampling procedures for biomolecules. This procedure simulates multiple replicas in parallel, each with a different value of a thermodynamic variable, typically temperature, and attempts exchanges between replicas periodically using a Monte Carlo Markov Chain procedure. This is a random walk in the thermodynamic variable that allows escaping local minima while being a rigorous sampling method. It is also highly parallelizable, even in distributed systems.

(1) Schlick Chapter 11

(2) Earl DJ, Deem MW, Parallel tempering: Theory, applications, and new perspectives, Phys . Chem. Chem. Phys . , 2005 , 7:3910-3916.

(3) Sugita Y, Okamoto Y. Replica-exchange molecular dynamics method for protein holding, Chem. Phys. Lett. 1999, 314:141-151.

T5

Feb. 23rd

·  Guest Lecture: Dr. Christopher Sweet

Dept. of Computer Science & Eng, Notre Dame

Molecular Dynamics Error Analysis

Dr. Sweet will explain methods to identify and quantify error in Molecular Dynamics integrators through utilization of backward error analysis techniques exploiting Shadow Hamiltonian properties. Error introduced through limited order cutoff switching functions will be examined.

(1) Dr. Chris Sweet, Switching Function Technical Report, 2006

Feb. 28th

· Multiple Time Stepping Molecular Dynamics

Multiple time stepping (MTS) integrators attempt to speed up MD by splitting the potential energy function and integrating different parts with different time steps. Linear and nonlinear resonances create instabilities that limit the longest time step, which cannot be greater than a third of the period of the fastest motion. We will see some ways of increasing the stability of the integrators without sacrificing the quality of the integration.

(1) Schlick Chapter 13

(2) Elber R, Long-timescale simulation methods, Current Opinion in Structural Biology 2005, 15:151-156.

(1) Skeel RD, Force evaluation, integrators, and propagators.

A2 Released

A2files

Mar. 2nd

·  Guest Lecture: Dr. Robert D. Skeel

Dept. of Computer Science, Purdue

Finite-temperature string method for transition pathways

Afternoon Seminar: Fast Electrostatics and Polarizable Forces
(DBRT 140 4pm)

The calculation of nonbonded, and especially electrostatic, interactions is a major bottleneck in molecular simulations. To make matters worse, a consensus is emerging among researchers concerning the general inadequacy of fixed point-charge models and the desirability of including electronic polarizability in the models. Presented here is a report of recent work on two projects, each yielding substantial performance gains. The first is the use of hierarchical interpolation of interaction potentials on nested grids to calculate energies and forces in linear time for both periodic or nonperiodic boundary conditions. The second is the self-consistent solution of large dense linear systems for the induced dipole model. This is joint work with David J. Hardy and Wei Wang.

(1) Skeel RD, The finite-temperature string method for computing transition paths. 2006

(2) W.Ren, E.Vanden-Eijnden, P.Maragakis, and W.E. Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide. J. Chem. Phys., 123, 134109, Oct.1, 2005.

Mar. 7th

·  Transition Path Sampling

These methods allow the study of rare events with fast transition times. It is based on a statistical mechanics study of trajectory or path space. This technique has proven to be extremely useful in the study of biomolecular systems. It is also an ideal problem for distributed computing given its embarrassing parallelism and high computational needs.

(1) Bolhuis PG, Chandler D, Dellago C, Geissler PL, Transition Path Sampling: Throwing Ropes Over Rough Mountain Passes, in the Dark, Annu. Rev. Phys. Chem. 2002. 53:291Žòó318.

Mar. 8th

·  Guest Lecture: Dr. Douglas Thain

Dept. of Computer Science & Eng, Notre Dame

System Services for Large Scale Computing and Storage
(DBRT 204 4PM)

Dr. Thain will explain how the computational and storage grid can be effectively utilized to perform distributed simulations, such as the parallel tempering procedure described above, and to store and analyze results from these simulations.

(1) "Condor and the Grid", Douglas Thain, Todd Tannenbaum, and Miron Livny, in Fran Berman, Anthony J.G. Hey, Geoffrey Fox, editors, Grid Computing: Making The Global Infrastructure a Reality, John Wiley, 2003. ISBN: 0-470-85319-0

(2) Separating Abstractions from Resources in a Tactical Storage System, Douglas Thain, Sander Klous, Justin Wozniak, Paul Brenner, Aaron Striegel, and Jesus Izaguirre, in Proceedings of the International Conference for High Performance Computing and Communications (Supercomputing), Nov 2005.

T6

T6 files

Mar. 9th

·  *Guest Lecture: Dr. Jeff Peng

Dept. of Chemistry & Biochemistry, Notre Dame

NMR Techniques to Resolve Biomolecular Motion

Dr. Peng will describe how NMR can be used to study both fast and slow dynamics of proteins. In particular, he will describe how MD simulations can help interpret, validate, and guide NMR experiments.

(1) Peng JW, Wagner G, Mapping of the Spectral Densities of N-H Bond Motions in Eglin c Using Heteronuclear Relaxation Experiments, Biochemistry 1992, 31:8571-8586.

Mar. 21st

·  Normal Mode Analysis and Elastic Models

Given the inherent difficulties with MTS integrators, elastic network models are an attractive coarsened model to obtain dynamics of large biomolecules. We will see how Gaussian Network Models have been used to study the slow dynamics of proteins, and how they can be connected to X-ray and NMR experiments.

(1) Bahar I, Rader AJ, Coarse-grained normal mode analysis in structural biology, Current Opinion in Structural Biology 2005, 15:1-7.

Mar. 23rd

· Reaction Paths by Optimization of Actions

In this approach, one starts with an initial trajectory as a guess for the minimization of an action. This produces an approximate trajectory that avoids several of the numerical resonances of MTS integrators. This approach is based on solving a boundary value problem, e.g., we need to know the starting and final configuration of the protein. We will describe some of the major successes of the method, and some of its limitations.

(1) Olender R, Elber R, Calculation of classical trajectories with a very large time step: Formalism and numerical examples, J. Chem. Phys. 1996, 105:9299-9315.

Midterm

Mar. 28th

·  Free Energy Calculations

·  *Afternoon Guest Lecture: Dr. Eric Darve

Dept. of Mechanical Engineering, Stanford

Computing free energy using thermodynamic integration.

The adaptive biasing force method is an efficient technique to compute the potential of mean force along a reaction coordinate and for alchemical transformations. We present recent developments of the method for vector free energy calculations (i.e. for several reaction coordinates or for multiple alchemical transformations). General formulas are derived and their relative merit is discussed. Our approach will be compared with other popular techniques such as metadynamics. Application examples will be provided for simple examples, such as alanine dipeptide, and a more advanced one: the insertion of an amphipathic helix inside a cell membrane. For the latter, we will examine the stability of the inserted peptide relative to the interfacial configuration and its role in the association of individual peptides into larger multimeric structures, such as cellular channels. Our candidate for studies is the synthetic peptide (LSLLLSL)3. It was shown experimentally that, in the presence of an electric field, the orientation changes from parallel to the membrane to perpendicular and the location of the center-of-mass (COM) changes from the membrane surface to the center of the lipid bilayer. Experimental results, however, provide no information about stability of individual helices in the transmembrane orientation.

(1) Darve E, Introduction to Free Energy Calculation, in press

Mar. 30th

· Free Energy Calculations II

Practical implementations for free energy calculation using Jarsynski and ABF methods will we reviewed. Output data from calculations made using these two methods in NAMD will be evaluated.

Input and Configuration Files from DEMOS

(1) Rodriguez-Gomez D, Darve E, Pohorille A, Assessing the efficiency of free energy calculation methods, J. Chem. Phys. 2004, 120: 3563-3578.

Final Project Paper Requirements Released

Apr. 4th

·  Langevin and Brownian Dynamics

(1) Schlick Chapter 13.4-13.5

Apr. 6th

·  Constraint Dynamics

(1) Schlick Chapter 12.5

(1) B. Leimkuhler and R. D. Skeel, Symplectic numerical integrators in constrained Hamiltonian systems, J. Comput. Phys. 1994, 112:117-125.

Apr. 11th

·  Force Fields for Molecular Modeling

(1)Rommie Amaro, Brijeet Dhaliwal, Zaida Luthey-Schulten, Parameterizing a Novel Residue, UIUC Comp Bio Workshop 2005

Apr. 13th

·  Perspective: Flexible Protein Docking

We consider results of incorporating protein flexibility into docking protocol. These results show statistically significant improvement in accuracy over not including protein flexibility. We bring several of the topics discussed in the course to bear on this problem, and discuss possible lines of research in this subject.

(1) Carlson HA, Protein flexibility and drug design: how to hit a moving target, Current Opinion in Chemical Biology 2002, 6:447Žòó452.

(2) Cavasotto CN, Abagyan RA, Protein Flexibility in Ligand Docking and Virtual Screening to Protein Kinases, J. Mol. Biol. 2004, 337, 209Žòó225.

Apr. 18th

·  Fast Electrostatics

The incorporation of long-range electrostatics has been shown to be important for the stability and accuracy of MD simulations of biomolecules. We will review two methods that can be used for computing long-range electrostatics quickly: first, the classical Particle Mesh Ewald method, an O(N lg N) method, and the more recent fast multigrid summation, an O(N) method. We will compare their scalability in large parallel environments and their accuracy in periodic boundary condition simulations.

(1) Schlick Chapter 9.1-9.5

(2) Sagui C, Darden TA, Molecular Dynamics Simulations of Biomolecules: Long-Range Electrostatic Effects, Annu. Rev. Biophys. Biomol. Struct. 1999. 28:155Žòó79.

(3) Skeel RD, Tezcan I, Hardy DJ, Multiple Grid Methods for Classical Molecular Dynamics, J. Comp. Chem., 2002, 23:673-684.

Final Project Draft Paper Due

Apr. 20th

·  Continuum Electrostatics

An alternative to the explicit treatment of electrostatics is to use an implicit, continuum model to describe the electrostatics. We will discuss the Poisson-Boltzmann equation treatment, and mathematical and computational issues of interfacing a continuum solver with an MD simulation.

 *Afternoon: Guest Lecture: Dr. Ivet Bahar

Dept. of Computational Biology, Pittsburgh

Protein Dynamics and Allostery Explored by Network Models

Elastic network models have proven in recent years to serve as useful tools for understanding the collective machinery of proteins and their complexes (1). Inspired by the success of such network models, we recently proposed a new approach based on a Markovian propagation of signals to model the process of allosteric communication in complex structures. Application to GroEL-GroES unravels several conserved residues playing a key role in the ATP-mediation of chaperonin cycle (2)

(1) Schlick Chapter 9.6

(2) Baker NA, Sept D, Joseph S, Holst MJ, McCammon JA, Electrostatics of Nanosystems: Application to Microtubules and the Ribosome, Proc. Natl. Acad. Sci. USA, 2001, 98:10037-10041.

(1) Chennubhotla C, Rader AJ, Yang L, Bahar I. Elastic network models for understanding biomolecular machinery: from enzymes to supramolecular assemblies,  Physical Biology 2005, 2:S173-S180.

(2) Chennubhotla C, Bahar I. Markov Models for Hierarchical Coarse-Graining of Large Protein Dynamics. RECOMB'06, accepted.

Apr. 25th

·  *Guest Lecture: Dr. Ron Elber

Dept. of Computer Science, Computational Biology Service Unit,
Cornell University

Enhanced sampling in space and time for biophysical simulations

In complex systems, the transition from a reaction coordinate or order parameter to experimentally determined rate constant is far from trivial. I will also described a novel approach that we introduced recently -- "Milestoning" that enhances sampling in the neighborhood of dominant transition pathways and enable efficient calculations of rates. It is of particular interest when a clear transition state or a significant free energy energy barrier are not obvious

Afternoon Seminar: Computational Molecular Biophysics at broad range of time scales
(DBRT 140 4pm)

One of the long standing problems in computer simulations of biochemical function is of time scales. Straightforward molecular dynamics approaches are restricted to time scales which are below microseconds, far shorter than the time scale of many interesting biophysical processes. I shall discuss path finding approaches that provide unique view into atomically detailed mechanisms of biological function at extended timescales. These approaches are based on boundary value, action formulation of classical mechanics and they make it possible to take very large integration steps. The large integration step provides approximate trajectories and hierarchy of approximations which are not possible using straightforward Molecular Dynamics. This technique is especially useful to study mechanisms when the two end states are known, regardless of the time scale of the process. I will present the following concrete examples: (i) ion transport in the gramicidin channel (hundreds of nanoseconds), and (ii) the folding of the proteins: protein A and cytochrome c (milliseconds)

(1)Alfredo Cardenas and Ron Elber, "Kinetics of Cytochrome C Folding: Atomically Detailed Simulations", Proteins, Structure Function and Genetics, 51,245-257(2003)

(2) Ron Elber, Avijit Ghosh, Alfredo Cardenas and Harry Stern, "Bridging the gap between reaction pathways, long time dynamics and calculation of rates", Advances in Chemical Physics, 126,93-129(2003)

(3)Anton K. Faradjian and Ron Elber, "Computing time scales from reaction coordinates by milestoning", J. Chem. Phys. 120:10880-10889(2004)

Apr. 27th

·  *Guest Lecture: Dr. Nathan Baker

Dept. of Biochemistry & Molecular Biophysics, Washington Univ. St. Louis
Modeling solvation for biomolecular systems

Afternoon Seminar: Theory and modeling of biomolecular solvation: applications to ion-membrane interactions
(DBRT 140 4pm)
Biological phenomena occur over a wide range of length and time scales. However, current computational methods are typically constrained to sample rather narrow windows of these scales. This constraint can lead to significant disparities between experimental and computational observations. Our goal is to develop theories, algorithms, and software which combine the strengths of different computational methods to study biological phenomena in a multiscale fashion. In particular, I will present our work on two aspects of this research: (1) the critical investigation of current implicit solvent models and suggestions for improvement and (2) the influence of salicylate binding on membrane electromechanical coupling.

 (1) Nathan A Baker, Improving implicit solvent simulations: a Poisson-centric view, Current Opinion in Structural Biology, Volume 15, Issue 2, April 2005, Pages 137-143.

 (2) Baker NA. Poisson-Boltzmann methods for biomolecular electrostatics. In: Methods in Enzymology. Academic Press: San Diego, CA (2004)

May 2nd

·Student Project Presentations

Final Project Papers Due