Absolute Entropy of a 2D Lattice Model for a Denatured Protein

Size: px
Start display at page:

Download "Absolute Entropy of a 2D Lattice Model for a Denatured Protein"

Transcription

1 Absolute Entropy of a 2D Lattice Model for a Denatured Protein Jason Funt 1,4 and Hagai Meirovitch 2,3 1 Bioengineering and Bioinformatics Summer Institute 2 Center for Computational Biology and Bioinformatics, 3 Department of Molecular Genetics and Biochemistry, University of Pittsburgh, Pittsburgh, PA Department of Biology, Case Western Reserve University

2 Why Study This? Protein Folding Problem Conformation dictates functionality As yet, the mechanism and kinetics for this process are not elucidated Future Application Protein folding is essential for molecular medicine and disease research

3 F, free energy, F = E TS (Helmholtz Free Energy) E, the average energy T, the absolute temperature S, the absolute entropy It is easy to calculate E in simulations, but very difficult to obtain S, hence calculation of F proves to be difficult. F is a criterion of stability. When F is minimized, the proteins conformation is favorable.

4 How do you calculate S? From statistical mechanics we know that: F = - k T ln(z) Z = Σ e βei This information tells us the potential energy of bond i, however, Z, the partition function proves difficult to calculate in complex systems

5 How do you calculate S? From the realization of the following graph, relative abstractions may be made T

6 How do you calculate S? Generalizations: Average Energy of the system is assumed 0. This makes Z =1 at each configuration. Because of this, the partition function is approximately the multiplicity of the system at a given total energy. A formula to calculate entropy then arises Z T = n(e* T )e -βe* F = - kt ln(n(e* T )) + E* S = - kt ln(n(e* T )) T

7 How do you calculate S? If S is proportional to Z, and Z is proportional to N(E*) How do you calculate N(E*)? Our approach: String of Beads on a lattice 2 Dimensional, No interactions Idea: 3D Continuous Space With Full Interactions 3D Discrete Space with no interactions 2D Discrete Space with no interactions Go from least complex to most complex

8 How you calculate S! Self Avoiding Random Walk has been used to estimate the multiplicity N SUC N TOT N ACT α 4 N

9 A new way to calculate S? Enter, my research: Example 1: Hypothetical Scanning MC Example 2: Corners and Crankshafts MMC Example 3: Pivots different MC BBSI_ATTEMPT_1.exe Pivotapp.exe Other methods include Series Expansion

10 Methodology The methodology for analysis is the same, regardless of technique or combinations of techniques. Entropy is calculated per bond Actual Chain Successful Outcome Unsuccessful Outcome

11 Methodology The probability is calculated, and then a final entropy value is calculated S = (N-2)ln(3) + ln(4) - ln(p) (N-1) (N-1) (derivation of formula not shown)

12 Results: Corner N = 50 Beads Scanning Method: Series Expansion: Without Rejection Criteria Monte Carlo Steps S With Rejection Criteria Monte Carlo Steps S

13 Results: Corner Data Processing MC Steps required to be very high Proved to be futile because the approximation would not reach the same accuracy as previous methods

14 Results: Crankshaft N = 50 Beads Scanning Method: Series Expansion: Without Rejection Criteria Monte Carlo Steps S With Rejection Criteria Monte Carlo Steps S

15 Results: Crankshaft Seems to not move enough Because of its sluggishness, it cannot be used exclusively for this purpose

16 Results: Corner and Crankshaft N = 50 Beads Scanning Method: Series Expansion: Without Rejection Criteria Monte Carlo Steps S With Rejection Criteria Monte Carlo Steps S

17 Results: Corner and Crankshaft Sluggishness solved, but too difficult for the chain to return, evidently The trend in values get worse as MC steps increase, instead of getting better

18 Results: Pivot N = 50 Beads Scanning Method: Series Expansion: Without Rejection Criteria Monte Carlo Steps 5 S So with relatively few Monte Carlo steps, the value is already zeroing on the correct value

19 Results Pivot MC 5M 16M 16M 32 M 32 M 32 M N Chains S Scan Series Scan E Fluc

20 Results: Pivot So, this looked promising, but there is another point of interest Straight Chains MC N S Scanning Series Scan

21 Analysis and Conclusion Strengths Shuffles the chain sufficiently well One straight chain = Several Chains More work will be done on the pivot technique This may be allowed to expand to a 3D lattice, to see if values are as strong

22 Questions & Comments

23 Acknowledgements NIH-NSF Dr. Hagai Meirovitch Dr. Agnieszka Szarecka (UNIX help) Dr. Rajan Munshi Jerome, Mark, and the other researchers in the 1095 Lab BBSI

Monte Carlo Simulations of Protein Folding using Lattice Models

Monte Carlo Simulations of Protein Folding using Lattice Models Monte Carlo Simulations of Protein Folding using Lattice Models Ryan Cheng 1,2 and Kenneth Jordan 1,3 1 Bioengineering and Bioinformatics Summer Institute, Department of Computational Biology, University

More information

Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water?

Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water? Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water? Ruhong Zhou 1 and Bruce J. Berne 2 1 IBM Thomas J. Watson Research Center; and 2 Department of Chemistry,

More information

Identification of core amino acids stabilizing rhodopsin

Identification of core amino acids stabilizing rhodopsin Identification of core amino acids stabilizing rhodopsin A. J. Rader, Gulsum Anderson, Basak Isin, H. Gobind Khorana, Ivet Bahar, and Judith Klein- Seetharaman Anes Aref BBSI 2004 Outline Introduction

More information

Engineering of Repressilator

Engineering of Repressilator The Utilization of Monte Carlo Techniques to Simulate the Repressilator: A Cyclic Oscillatory System Seetal Erramilli 1,2 and Joel R. Stiles 1,3,4 1 Bioengineering and Bioinformatics Summer Institute,

More information

Monte Carlo (MC) Simulation Methods. Elisa Fadda

Monte Carlo (MC) Simulation Methods. Elisa Fadda Monte Carlo (MC) Simulation Methods Elisa Fadda 1011-CH328, Molecular Modelling & Drug Design 2011 Experimental Observables A system observable is a property of the system state. The system state i is

More information

Lattice protein models

Lattice protein models Lattice protein models Marc R. Roussel epartment of Chemistry and Biochemistry University of Lethbridge March 5, 2009 1 Model and assumptions The ideas developed in the last few lectures can be applied

More information

Novel Monte Carlo Methods for Protein Structure Modeling. Jinfeng Zhang Department of Statistics Harvard University

Novel Monte Carlo Methods for Protein Structure Modeling. Jinfeng Zhang Department of Statistics Harvard University Novel Monte Carlo Methods for Protein Structure Modeling Jinfeng Zhang Department of Statistics Harvard University Introduction Machines of life Proteins play crucial roles in virtually all biological

More information

Expectations, Markov chains, and the Metropolis algorithm

Expectations, Markov chains, and the Metropolis algorithm Expectations, Markov chains, and the Metropolis algorithm Peter Hoff Departments of Statistics and Biostatistics and the Center for Statistics and the Social Sciences University of Washington 7-27-05 1

More information

Protein Folding Prof. Eugene Shakhnovich

Protein Folding Prof. Eugene Shakhnovich Protein Folding Eugene Shakhnovich Department of Chemistry and Chemical Biology Harvard University 1 Proteins are folded on various scales As of now we know hundreds of thousands of sequences (Swissprot)

More information

3D HP Protein Folding Problem using Ant Algorithm

3D HP Protein Folding Problem using Ant Algorithm 3D HP Protein Folding Problem using Ant Algorithm Fidanova S. Institute of Parallel Processing BAS 25A Acad. G. Bonchev Str., 1113 Sofia, Bulgaria Phone: +359 2 979 66 42 E-mail: stefka@parallel.bas.bg

More information

Short Announcements. 1 st Quiz today: 15 minutes. Homework 3: Due next Wednesday.

Short Announcements. 1 st Quiz today: 15 minutes. Homework 3: Due next Wednesday. Short Announcements 1 st Quiz today: 15 minutes Homework 3: Due next Wednesday. Next Lecture, on Visualizing Molecular Dynamics (VMD) by Klaus Schulten Today s Lecture: Protein Folding, Misfolding, Aggregation

More information

Objectives. Comparison and Analysis of Heat Shock Proteins in Organisms of the Kingdom Viridiplantae. Emily Germain 1,2 Mentor Dr.

Objectives. Comparison and Analysis of Heat Shock Proteins in Organisms of the Kingdom Viridiplantae. Emily Germain 1,2 Mentor Dr. Comparison and Analysis of Heat Shock Proteins in Organisms of the Kingdom Viridiplantae Emily Germain 1,2 Mentor Dr. Hugh Nicholas 3 1 Bioengineering & Bioinformatics Summer Institute, Department of Computational

More information

Goals. Structural Analysis of the EGR Family of Transcription Factors: Templates for Predicting Protein DNA Interactions

Goals. Structural Analysis of the EGR Family of Transcription Factors: Templates for Predicting Protein DNA Interactions Structural Analysis of the EGR Family of Transcription Factors: Templates for Predicting Protein DNA Interactions Jamie Duke 1,2 and Carlos Camacho 3 1 Bioengineering and Bioinformatics Summer Institute,

More information

5th CCPN Matt Crump. Thermodynamic quantities derived from protein dynamics

5th CCPN Matt Crump. Thermodynamic quantities derived from protein dynamics 5th CCPN 2005 -Matt Crump Thermodynamic quantities derived from protein dynamics Relaxation in Liquids (briefly!) The fluctuations of each bond vector can be described in terms of an angular correlation

More information

Local Interactions Dominate Folding in a Simple Protein Model

Local Interactions Dominate Folding in a Simple Protein Model J. Mol. Biol. (1996) 259, 988 994 Local Interactions Dominate Folding in a Simple Protein Model Ron Unger 1,2 * and John Moult 2 1 Department of Life Sciences Bar-Ilan University Ramat-Gan, 52900, Israel

More information

Lecture 2 and 3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability

Lecture 2 and 3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Lecture 2 and 3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Part I. Review of forces Covalent bonds Non-covalent Interactions: Van der Waals Interactions

More information

Bioengineering & Bioinformatics Summer Institute, Dept. Computational Biology, University of Pittsburgh, PGH, PA

Bioengineering & Bioinformatics Summer Institute, Dept. Computational Biology, University of Pittsburgh, PGH, PA Pharmacophore Model Development for the Identification of Novel Acetylcholinesterase Inhibitors Edwin Kamau Dept Chem & Biochem Kennesa State Uni ersit Kennesa GA 30144 Dept. Chem. & Biochem. Kennesaw

More information

Building a Homology Model of the Transmembrane Domain of the Human Glycine α-1 Receptor

Building a Homology Model of the Transmembrane Domain of the Human Glycine α-1 Receptor Building a Homology Model of the Transmembrane Domain of the Human Glycine α-1 Receptor Presented by Stephanie Lee Research Mentor: Dr. Rob Coalson Glycine Alpha 1 Receptor (GlyRa1) Member of the superfamily

More information

Lecture V: Multicanonical Simulations.

Lecture V: Multicanonical Simulations. Lecture V: Multicanonical Simulations. 1. Multicanonical Ensemble 2. How to get the Weights? 3. Example Runs (2d Ising and Potts models) 4. Re-Weighting to the Canonical Ensemble 5. Energy and Specific

More information

Statistical Thermodynamics and Monte-Carlo Evgenii B. Rudnyi and Jan G. Korvink IMTEK Albert Ludwig University Freiburg, Germany

Statistical Thermodynamics and Monte-Carlo Evgenii B. Rudnyi and Jan G. Korvink IMTEK Albert Ludwig University Freiburg, Germany Statistical Thermodynamics and Monte-Carlo Evgenii B. Rudnyi and Jan G. Korvink IMTEK Albert Ludwig University Freiburg, Germany Preliminaries Learning Goals From Micro to Macro Statistical Mechanics (Statistical

More information

Importance of chirality and reduced flexibility of protein side chains: A study with square and tetrahedral lattice models

Importance of chirality and reduced flexibility of protein side chains: A study with square and tetrahedral lattice models JOURNAL OF CHEMICAL PHYSICS VOLUME 121, NUMBER 1 1 JULY 2004 Importance of chirality and reduced flexibility of protein side chains: A study with square and tetrahedral lattice models Jinfeng Zhang Department

More information

Computer Simulation of Peptide Adsorption

Computer Simulation of Peptide Adsorption Computer Simulation of Peptide Adsorption M P Allen Department of Physics University of Warwick Leipzig, 28 November 2013 1 Peptides Leipzig, 28 November 2013 Outline Lattice Peptide Monte Carlo 1 Lattice

More information

End-to-end length of a stiff polymer

End-to-end length of a stiff polymer End-to-end length of a stiff polymer Jellie de Vries April 21st, 2005 Bachelor Thesis Supervisor: dr. G.T. Barkema Faculteit Btawetenschappen/Departement Natuur- en Sterrenkunde Institute for Theoretical

More information

Protein Structure Analysis with Sequential Monte Carlo Method. Jinfeng Zhang Computational Biology Lab Department of Statistics Harvard University

Protein Structure Analysis with Sequential Monte Carlo Method. Jinfeng Zhang Computational Biology Lab Department of Statistics Harvard University Protein Structure Analysis with Sequential Monte Carlo Method Jinfeng Zhang Computational Biology Lab Department of Statistics Harvard University Introduction Structure Function & Interaction Protein structure

More information

Phase Equilibria and Molecular Solutions Jan G. Korvink and Evgenii Rudnyi IMTEK Albert Ludwig University Freiburg, Germany

Phase Equilibria and Molecular Solutions Jan G. Korvink and Evgenii Rudnyi IMTEK Albert Ludwig University Freiburg, Germany Phase Equilibria and Molecular Solutions Jan G. Korvink and Evgenii Rudnyi IMTEK Albert Ludwig University Freiburg, Germany Preliminaries Learning Goals Phase Equilibria Phase diagrams and classical thermodynamics

More information

Computational Biology 1

Computational Biology 1 Computational Biology 1 Protein Function & nzyme inetics Guna Rajagopal, Bioinformatics Institute, guna@bii.a-star.edu.sg References : Molecular Biology of the Cell, 4 th d. Alberts et. al. Pg. 129 190

More information

CHAPTER 13 (MOORE) CHEMICAL KINETICS: RATES AND MECHANISMS OF CHEMICAL REACTIONS

CHAPTER 13 (MOORE) CHEMICAL KINETICS: RATES AND MECHANISMS OF CHEMICAL REACTIONS CHAPTER 13 (MOORE) CHEMICAL KINETICS: RATES AND MECHANISMS OF CHEMICAL REACTIONS This chapter deals with reaction rates, or how fast chemical reactions occur. Reaction rates vary greatly some are very

More information

Sequence Based Bioinformatics

Sequence Based Bioinformatics Structural and Functional Analysis of Inosine Monophosphate Dehydrogenase using Sequence-Based Bioinformatics Barry Sexton 1,2 and Troy Wymore 3 1 Bioengineering and Bioinformatics Summer Institute, Department

More information

Statistical thermodynamics for MD and MC simulations

Statistical thermodynamics for MD and MC simulations Statistical thermodynamics for MD and MC simulations knowing 2 atoms and wishing to know 10 23 of them Marcus Elstner and Tomáš Kubař 22 June 2016 Introduction Thermodynamic properties of molecular systems

More information

Lecture 2-3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability

Lecture 2-3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Lecture 2-3: Review of forces (ctd.) and elementary statistical mechanics. Contributions to protein stability Part I. Review of forces Covalent bonds Non-covalent Interactions Van der Waals Interactions

More information

Protein Folding Challenge and Theoretical Computer Science

Protein Folding Challenge and Theoretical Computer Science Protein Folding Challenge and Theoretical Computer Science Somenath Biswas Department of Computer Science and Engineering, Indian Institute of Technology Kanpur. (Extended Abstract) September 2011 Almost

More information

Monte Carlo simulation of proteins through a random walk in energy space

Monte Carlo simulation of proteins through a random walk in energy space JOURNAL OF CHEMICAL PHYSICS VOLUME 116, NUMBER 16 22 APRIL 2002 Monte Carlo simulation of proteins through a random walk in energy space Nitin Rathore and Juan J. de Pablo a) Department of Chemical Engineering,

More information

Frontiers in Physics 27-29, Sept Self Avoiding Growth Walks and Protein Folding

Frontiers in Physics 27-29, Sept Self Avoiding Growth Walks and Protein Folding Frontiers in Physics 27-29, Sept. 2012 Self Avoiding Growth Walks and Protein Folding K P N Murthy, K Manasa, and K V K Srinath School of Physics, School of Life Sciences University of Hyderabad September

More information

Molecular Interactions F14NMI. Lecture 4: worked answers to practice questions

Molecular Interactions F14NMI. Lecture 4: worked answers to practice questions Molecular Interactions F14NMI Lecture 4: worked answers to practice questions http://comp.chem.nottingham.ac.uk/teaching/f14nmi jonathan.hirst@nottingham.ac.uk (1) (a) Describe the Monte Carlo algorithm

More information

Assignment 6: MCMC Simulation and Review Problems

Assignment 6: MCMC Simulation and Review Problems Massachusetts Institute of Technology MITES 2018 Physics III Assignment 6: MCMC Simulation and Review Problems Due Monday July 30 at 11:59PM in Instructor s Inbox Preface: In this assignment, you will

More information

Chapter 4: Going from microcanonical to canonical ensemble, from energy to temperature.

Chapter 4: Going from microcanonical to canonical ensemble, from energy to temperature. Chapter 4: Going from microcanonical to canonical ensemble, from energy to temperature. All calculations in statistical mechanics can be done in the microcanonical ensemble, where all copies of the system

More information

ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below

ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below Introduction In statistical physics Monte Carlo methods are considered to have started in the Manhattan project (1940

More information

STRUCTURAL BIOINFORMATICS I. Fall 2015

STRUCTURAL BIOINFORMATICS I. Fall 2015 STRUCTURAL BIOINFORMATICS I Fall 2015 Info Course Number - Classification: Biology 5411 Class Schedule: Monday 5:30-7:50 PM, SERC Room 456 (4 th floor) Instructors: Vincenzo Carnevale - SERC, Room 704C;

More information

Phase Transition in a Bond. Fluctuating Lattice Polymer

Phase Transition in a Bond. Fluctuating Lattice Polymer Phase Transition in a Bond arxiv:1204.2691v2 [cond-mat.soft] 13 Apr 2012 Fluctuating Lattice Polymer Hima Bindu Kolli and K.P.N.Murthy School of Physics, University of Hyderabad Hyderabad 500046 November

More information

MCB100A/Chem130 MidTerm Exam 2 April 4, 2013

MCB100A/Chem130 MidTerm Exam 2 April 4, 2013 MCB1A/Chem13 MidTerm Exam 2 April 4, 213 Name Student ID True/False (2 points each). 1. The Boltzmann constant, k b T sets the energy scale for observing energy microstates 2. Atoms with favorable electronic

More information

Enzymes. Lab Exercise 7. Introduction. Contents. Objectives

Enzymes. Lab Exercise 7. Introduction. Contents. Objectives Lab Exercise Enzymes Contents Objectives 1 Introduction 1 Activity.1 Optimal ph 3 Activity.2 Optimal Temperature 4 Activity.3 Reaction Rates 4 Resutls Section 5 Objectives - Appreciate the sensitivity

More information

Protein Folding experiments and theory

Protein Folding experiments and theory Protein Folding experiments and theory 1, 2,and 3 Protein Structure Fig. 3-16 from Lehninger Biochemistry, 4 th ed. The 3D structure is not encoded at the single aa level Hydrogen Bonding Shared H atom

More information

PY Introduction to thermodynamics and statistical physics Summer Examination suggested solutions Dr. Asaf Pe er

PY Introduction to thermodynamics and statistical physics Summer Examination suggested solutions Dr. Asaf Pe er PY2104 - Introduction to thermodynamics and statistical physics Summer Examination 2014 - suggested solutions Dr. Asaf Pe er 1) Onemoleofwater(H 2 O)isbeingheatedfrom 20 Cto+80 C,atconstant atmospheric

More information

Quiz 2 Morphology of Complex Materials

Quiz 2 Morphology of Complex Materials 071003 Quiz 2 Morphology of Complex Materials 1) Explain the following terms: (for states comment on biological activity and relative size of the structure) a) Native State b) Unfolded State c) Denatured

More information

) is the interaction energy between a pair of chain units in the state ψ i 1

) is the interaction energy between a pair of chain units in the state ψ i 1 Persistence Length, One Application of the Ising-Chain and the RIS Model. Local features of a polymer chain such as the chain persistence, and the pair correlation function, g(r), and the associated high-q

More information

Coupling Hair Follicle Cycles to Produce Traveling Waves

Coupling Hair Follicle Cycles to Produce Traveling Waves Coupling Hair Follicle Cycles to Produce Traveling Waves Megan Jeans 1,2 and Dr. G. Bard Ermentrout 3 1 Bioengineering and Bioinformatics Summer Institute, Department of Computational Biology, University

More information

Chemistry 431. Lecture 27 The Ensemble Partition Function Statistical Thermodynamics. NC State University

Chemistry 431. Lecture 27 The Ensemble Partition Function Statistical Thermodynamics. NC State University Chemistry 431 Lecture 27 The Ensemble Partition Function Statistical Thermodynamics NC State University Representation of an Ensemble N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T N,V,T

More information

Total

Total Student Performance by Question Biology (Multiple-Choice ONLY) Teacher: Core 1 / S-14 Scientific Investigation Life at the Molecular and Cellular Level Analysis of Performance by Question of each student

More information

Vance County Early College High School Pacing Guide Course: Introduction to Biology (Semester I)

Vance County Early College High School Pacing Guide Course: Introduction to Biology (Semester I) Vance County Early College High School Pacing Guide Course: Introduction to Biology (Semester I) Week(s ) Dates Unit Unit Title Essential Questions / Topic Questions 1 1 Introduction to Biology 1. How

More information

DNA/RNA structure and packing

DNA/RNA structure and packing DNA/RNA structure and packing Reminder: Nucleic acids one oxygen atom distinguishes RNA from DNA, increases reactivity (so DNA is more stable) base attaches at 1, phosphate at 5 purines pyrimidines Replace

More information

Ideal gases. Asaf Pe er Classical ideal gas

Ideal gases. Asaf Pe er Classical ideal gas Ideal gases Asaf Pe er 1 November 2, 213 1. Classical ideal gas A classical gas is generally referred to as a gas in which its molecules move freely in space; namely, the mean separation between the molecules

More information

Protein Folding by Robotics

Protein Folding by Robotics Protein Folding by Robotics 1 TBI Winterseminar 2006 February 21, 2006 Protein Folding by Robotics 1 TBI Winterseminar 2006 February 21, 2006 Protein Folding by Robotics Probabilistic Roadmap Planning

More information

Context of the project...3. What is protein design?...3. I The algorithms...3 A Dead-end elimination procedure...4. B Monte-Carlo simulation...

Context of the project...3. What is protein design?...3. I The algorithms...3 A Dead-end elimination procedure...4. B Monte-Carlo simulation... Laidebeure Stéphane Context of the project...3 What is protein design?...3 I The algorithms...3 A Dead-end elimination procedure...4 B Monte-Carlo simulation...5 II The model...6 A The molecular model...6

More information

Announcements. Homework 3 (Klaus Schulten s Lecture): Due Wednesday at noon. Next homework assigned. Due Wednesday March 1.

Announcements. Homework 3 (Klaus Schulten s Lecture): Due Wednesday at noon. Next homework assigned. Due Wednesday March 1. Announcements Homework 3 (Klaus Schulten s Lecture): Due Wednesday at noon. Next homework assigned. Due Wednesday March 1. No lecture next Monday, Feb. 27 th! (Homework is a bit longer.) Marco will have

More information

Homework 9: Protein Folding & Simulated Annealing : Programming for Scientists Due: Thursday, April 14, 2016 at 11:59 PM

Homework 9: Protein Folding & Simulated Annealing : Programming for Scientists Due: Thursday, April 14, 2016 at 11:59 PM Homework 9: Protein Folding & Simulated Annealing 02-201: Programming for Scientists Due: Thursday, April 14, 2016 at 11:59 PM 1. Set up We re back to Go for this assignment. 1. Inside of your src directory,

More information

Swelling and Collapse of Single Polymer Molecules and Gels.

Swelling and Collapse of Single Polymer Molecules and Gels. Swelling and Collapse of Single Polymer Molecules and Gels. Coil-Globule Transition in Single Polymer Molecules. the coil-globule transition If polymer chains are not ideal, interactions of non-neighboring

More information

A new combination of replica exchange Monte Carlo and histogram analysis for protein folding and thermodynamics

A new combination of replica exchange Monte Carlo and histogram analysis for protein folding and thermodynamics JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 3 15 JULY 2001 A new combination of replica exchange Monte Carlo and histogram analysis for protein folding and thermodynamics Dominik Gront Department of

More information

Basics of Experimental Design. Review of Statistics. Basic Study. Experimental Design. When an Experiment is Not Possible. Studying Relations

Basics of Experimental Design. Review of Statistics. Basic Study. Experimental Design. When an Experiment is Not Possible. Studying Relations Basics of Experimental Design Review of Statistics And Experimental Design Scientists study relation between variables In the context of experiments these variables are called independent and dependent

More information

Statistical Mechanics Primer

Statistical Mechanics Primer Statistical Mechanics Primer David an alen January 7, 2007 As the data produced by experimental biologists becomes more quantitative, there becomes a need for more quantitative models. There are many ways

More information

Computational Physics (6810): Session 13

Computational Physics (6810): Session 13 Computational Physics (6810): Session 13 Dick Furnstahl Nuclear Theory Group OSU Physics Department April 14, 2017 6810 Endgame Various recaps and followups Random stuff (like RNGs :) Session 13 stuff

More information

Full file at https://fratstock.eu

Full file at https://fratstock.eu Chapter 03 1. a. DG=DH-TDS Δ G = 80 kj ( 98 K) 0.790 kj = 44.6 kj K b. ΔG = 0 @ T m. Unfolding will be favorable at temperatures above the T m. Δ G =Δ H TΔ S 0 kj kj 80 ( xk) 0.790 K 0 Δ G = = 354.4 K

More information

Thermodynamics. Energy is driving life. Energy of sun ultimately drives most of life on Earth

Thermodynamics. Energy is driving life. Energy of sun ultimately drives most of life on Earth Sci 190E Lecture 09 Thermodynamics Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown.

More information

Molecular simulation and structure prediction using CHARMM and the MMTSB Tool Set Free Energy Methods

Molecular simulation and structure prediction using CHARMM and the MMTSB Tool Set Free Energy Methods Molecular simulation and structure prediction using CHARMM and the MMTSB Tool Set Free Energy Methods Charles L. Brooks III MMTSB/CTBP 2006 Summer Workshop CHARMM Simulations The flow of data and information

More information

2. Thermodynamics. Introduction. Understanding Molecular Simulation

2. Thermodynamics. Introduction. Understanding Molecular Simulation 2. Thermodynamics Introduction Molecular Simulations Molecular dynamics: solve equations of motion r 1 r 2 r n Monte Carlo: importance sampling r 1 r 2 r n How do we know our simulation is correct? Molecular

More information

Free Energy. because H is negative doesn't mean that G will be negative and just because S is positive doesn't mean that G will be negative.

Free Energy. because H is negative doesn't mean that G will be negative and just because S is positive doesn't mean that G will be negative. Biochemistry 462a Bioenergetics Reading - Lehninger Principles, Chapter 14, pp. 485-512 Practice problems - Chapter 14: 2-8, 10, 12, 13; Physical Chemistry extra problems, free energy problems Free Energy

More information

Basics of Statistical Mechanics

Basics of Statistical Mechanics Basics of Statistical Mechanics Review of ensembles Microcanonical, canonical, Maxwell-Boltzmann Constant pressure, temperature, volume, Thermodynamic limit Ergodicity (see online notes also) Reading assignment:

More information

PHY 5524: Statistical Mechanics, Spring February 11 th, 2013 Midterm Exam # 1

PHY 5524: Statistical Mechanics, Spring February 11 th, 2013 Midterm Exam # 1 PHY 554: Statistical Mechanics, Spring 013 February 11 th, 013 Midterm Exam # 1 Always remember to write full work for what you do. This will help your grade in case of incomplete or wrong answers. Also,

More information

Practical Numerical Methods in Physics and Astronomy. Lecture 5 Optimisation and Search Techniques

Practical Numerical Methods in Physics and Astronomy. Lecture 5 Optimisation and Search Techniques Practical Numerical Methods in Physics and Astronomy Lecture 5 Optimisation and Search Techniques Pat Scott Department of Physics, McGill University January 30, 2013 Slides available from http://www.physics.mcgill.ca/

More information

Termination in Rule Based Approach to Signaling Systems

Termination in Rule Based Approach to Signaling Systems Termination in Rule Based Approach to Signaling Systems Davis Buenger and Jim Faeder Bioengineering & Bioinformatics Summer Institute Dept of Bioengineering & Bioinformatics Summer Institute, Dept. of

More information

Wang-Landau sampling for Quantum Monte Carlo. Stefan Wessel Institut für Theoretische Physik III Universität Stuttgart

Wang-Landau sampling for Quantum Monte Carlo. Stefan Wessel Institut für Theoretische Physik III Universität Stuttgart Wang-Landau sampling for Quantum Monte Carlo Stefan Wessel Institut für Theoretische Physik III Universität Stuttgart Overview Classical Monte Carlo First order phase transitions Classical Wang-Landau

More information

Predicting free energy landscapes for complexes of double-stranded chain molecules

Predicting free energy landscapes for complexes of double-stranded chain molecules JOURNAL OF CHEMICAL PHYSICS VOLUME 114, NUMBER 9 1 MARCH 2001 Predicting free energy landscapes for complexes of double-stranded chain molecules Wenbing Zhang and Shi-Jie Chen a) Department of Physics

More information

How do we compare the relative performance among competing models?

How do we compare the relative performance among competing models? How do we compare the relative performance among competing models? 1 Comparing Data Mining Methods Frequent problem: we want to know which of the two learning techniques is better How to reliably say Model

More information

Many proteins spontaneously refold into native form in vitro with high fidelity and high speed.

Many proteins spontaneously refold into native form in vitro with high fidelity and high speed. Macromolecular Processes 20. Protein Folding Composed of 50 500 amino acids linked in 1D sequence by the polypeptide backbone The amino acid physical and chemical properties of the 20 amino acids dictate

More information

Generalized Ensembles: Multicanonical Simulations

Generalized Ensembles: Multicanonical Simulations Generalized Ensembles: Multicanonical Simulations 1. Multicanonical Ensemble 2. How to get the Weights? 3. Example Runs and Re-Weighting to the Canonical Ensemble 4. Energy and Specific Heat Calculation

More information

Colligative Properties of Solutions

Colligative Properties of Solutions CHAPTER 16. Colligative Properties of Solutions 16-1. The number of moles of KMnO 4 (aq) is ( ) 1 mol KMnO4 moles KMnO 4 (5.25 g KMnO 4 ) 0.0332 mol 158.04 g KMnO 4 molality m 0.0332 mol 0.250 kg 0.133

More information

ON BROWNIAN COMPUTATION

ON BROWNIAN COMPUTATION ON BROWNIAN COMPUTATION JOHN D. NORTON Department of History and Philosophy of Science Center for Philosophy of Science University of Pittsburgh Pittsburgh PA USA 15260 jdnorton@pitt.edu Draft: October10,

More information

Chapter 5 - Systems under pressure 62

Chapter 5 - Systems under pressure 62 Chapter 5 - Systems under pressure 62 CHAPTER 5 - SYSTEMS UNDER PRESSURE 5.1 Ideal gas law The quantitative study of gases goes back more than three centuries. In 1662, Robert Boyle showed that at a fixed

More information

Algorithm for protein folding problem in 3D lattice HP model

Algorithm for protein folding problem in 3D lattice HP model Algorithm for protein folding problem in 3D lattice HP model METODI TRAYKOV Department of Electrical Engineering, Electronics and Automatics University Center for Advanced Bioinformatics Research South-West

More information

Biophysical Model Building

Biophysical Model Building Biophysical Model Building Step 1: Come up with a hypothesis about how a system works How many binding sites? Is there cooperativity? Step 2: Translate the qualitative hypotheses into an observable mathematical

More information

Dihedral Angles. Homayoun Valafar. Department of Computer Science and Engineering, USC 02/03/10 CSCE 769

Dihedral Angles. Homayoun Valafar. Department of Computer Science and Engineering, USC 02/03/10 CSCE 769 Dihedral Angles Homayoun Valafar Department of Computer Science and Engineering, USC The precise definition of a dihedral or torsion angle can be found in spatial geometry Angle between to planes Dihedral

More information

= (-22) = +2kJ /mol

= (-22) = +2kJ /mol Lecture 8: Thermodynamics & Protein Stability Assigned reading in Campbell: Chapter 4.4-4.6 Key Terms: DG = -RT lnk eq = DH - TDS Transition Curve, Melting Curve, Tm DH calculation DS calculation van der

More information

to satisfy the large number approximations, W W sys can be small.

to satisfy the large number approximations, W W sys can be small. Chapter 12. The canonical ensemble To discuss systems at constant T, we need to embed them with a diathermal wall in a heat bath. Note that only the system and bath need to be large for W tot and W bath

More information

Physics 333, Thermal and Statistical Physics: Homework #2 Solutions Manual

Physics 333, Thermal and Statistical Physics: Homework #2 Solutions Manual Physics 333, Thermal and Statistical Physics: Homework #2 Solutions Manual 1. n 5 = 0 n 5 = 1 n 5 = 2 n 5 = 3 n 5 = 4 n 5 = 5 d n 5,0,0,0,0 4 0 0 0 0 1 5 4,1,0,0,0 12 4 0 0 4 0 20 3,2,0,0,0 12 0 4 4 0

More information

UC Berkeley. Chem 130A. Spring nd Exam. March 10, 2004 Instructor: John Kuriyan

UC Berkeley. Chem 130A. Spring nd Exam. March 10, 2004 Instructor: John Kuriyan UC Berkeley. Chem 130A. Spring 2004 2nd Exam. March 10, 2004 Instructor: John Kuriyan (kuriyan@uclink.berkeley.edu) Enter your name & student ID number above the line, in ink. Sign your name above the

More information

Coarse-Grained Models!

Coarse-Grained Models! Coarse-Grained Models! Large and complex molecules (e.g. long polymers) can not be simulated on the all-atom level! Requires coarse-graining of the model! Coarse-grained models are usually also particles

More information

2m + U( q i), (IV.26) i=1

2m + U( q i), (IV.26) i=1 I.D The Ideal Gas As discussed in chapter II, micro-states of a gas of N particles correspond to points { p i, q i }, in the 6N-dimensional phase space. Ignoring the potential energy of interactions, the

More information

Computational Biology & Computational Medicine

Computational Biology & Computational Medicine Computational Biology & Computational Medicine Homayoun Valafar Outline Why proteins? What are proteins? How do we compute them? How do we use computational approaches? Why Proteins? Molecular basis of

More information

arxiv:cond-mat/ v1 [cond-mat.soft] 19 Mar 2001

arxiv:cond-mat/ v1 [cond-mat.soft] 19 Mar 2001 Modeling two-state cooperativity in protein folding Ke Fan, Jun Wang, and Wei Wang arxiv:cond-mat/0103385v1 [cond-mat.soft] 19 Mar 2001 National Laboratory of Solid State Microstructure and Department

More information

Lecture 34 Protein Unfolding Thermodynamics

Lecture 34 Protein Unfolding Thermodynamics Physical Principles in Biology Biology 3550 Fall 2018 Lecture 34 Protein Unfolding Thermodynamics Wednesday, 21 November c David P. Goldenberg University of Utah goldenberg@biology.utah.edu Clicker Question

More information

Protein Structure Prediction

Protein Structure Prediction Page 1 Protein Structure Prediction Russ B. Altman BMI 214 CS 274 Protein Folding is different from structure prediction --Folding is concerned with the process of taking the 3D shape, usually based on

More information

Statistical Mechanics for Proteins

Statistical Mechanics for Proteins The Partition Function From Q all relevant thermodynamic properties can be obtained by differentiation of the free energy F: = kt q p E q pd d h T V Q ), ( exp 1! 1 ),, ( 3 3 3 ),, ( ln ),, ( T V Q kt

More information

3.320: Lecture 19 (4/14/05) Free Energies and physical Coarse-graining. ,T) + < σ > dµ

3.320: Lecture 19 (4/14/05) Free Energies and physical Coarse-graining. ,T) + < σ > dµ 3.320: Lecture 19 (4/14/05) F(µ,T) = F(µ ref,t) + < σ > dµ µ µ ref Free Energies and physical Coarse-graining T S(T) = S(T ref ) + T T ref C V T dt Non-Boltzmann sampling and Umbrella sampling Simple

More information

MONTE CARLO METHODS IN SEQUENTIAL AND PARALLEL COMPUTING OF 2D AND 3D ISING MODEL

MONTE CARLO METHODS IN SEQUENTIAL AND PARALLEL COMPUTING OF 2D AND 3D ISING MODEL Journal of Optoelectronics and Advanced Materials Vol. 5, No. 4, December 003, p. 971-976 MONTE CARLO METHODS IN SEQUENTIAL AND PARALLEL COMPUTING OF D AND 3D ISING MODEL M. Diaconu *, R. Puscasu, A. Stancu

More information

Presenter: She Zhang

Presenter: She Zhang Presenter: She Zhang Introduction Dr. David Baker Introduction Why design proteins de novo? It is not clear how non-covalent interactions favor one specific native structure over many other non-native

More information

Chapter 16: Spontaneity, Entropy, and Free Energy Spontaneous Processes and Entropy

Chapter 16: Spontaneity, Entropy, and Free Energy Spontaneous Processes and Entropy Chapter 16: Spontaneity, Entropy, and Free Energy 16.1 Spontaneous Processes and Entropy 1 3 The first law of thermodynamics the law of conservation of energy: Energy can be neither created nor destroyed

More information

How is the melting point of a molecular compound affected by its structure?

How is the melting point of a molecular compound affected by its structure? How is the melting point of a molecular compound affected by its structure? Pre-experiment Questions (Please come to class prepared to discuss your answers to questions 1-4.) 1. Compile a table, Table

More information

Polymer solutions and melts

Polymer solutions and melts Course M6 Lecture 9//004 (JAE) Course M6 Lecture 9//004 Polymer solutions and melts Scattering methods Effects of excluded volume and solvents Dr James Elliott Online teaching material reminder Overheads

More information

Olle Inganäs: Polymers structure and dynamics. Polymer physics

Olle Inganäs: Polymers structure and dynamics. Polymer physics Polymer physics Polymers are macromolecules formed by many identical monomers, connected through covalent bonds, to make a linear chain of mers a polymer. The length of the chain specifies the weight of

More information

Design of sequences with good folding properties in coarse-grained protein models Anders Irbäck*, Carsten Peterson, Frank Potthast and Erik Sandelin

Design of sequences with good folding properties in coarse-grained protein models Anders Irbäck*, Carsten Peterson, Frank Potthast and Erik Sandelin Research Article 347 Design of sequences with good folding properties in coarse-grained protein models Anders Irbäck*, Carsten Peterson, Frank Potthast and Erik Sandelin Background: Designing amino acid

More information

Size of rings in two dimensions

Size of rings in two dimensions J. Phys. A: Math. Gen. () L-L. Printed in Great Britain LETTER TO THE EDITOR Size of rings in two dimensions V Privmant and J RudnickS t Department of Physics, 0-, California Institute of Technology, Pasadena,

More information