Folding simulation: self-organization of 4-helix bundle protein. yellow = helical turns

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1 Folding simulation: self-organization of 4-helix bundle protein yellow = helical turns

2 Protein structure Protein: heteropolymer chain made of amino acid residues R + H 3 N - C - COO - H φ ψ Chain of amino acid residues 20 different amino acids More than 50,000 different proteins in human body alone

3 Protein structure Hierarchical levels of structure: α-helix β-strand primary secondary tertiary myoglobin Linear chain of amino acids Local regular structures 3-D compact structure with long-range contacts The biological function is determined by shape. The shape is determined by primary sequence. How? ( Protein Folding Problem )

4 Protein Folding Protein folding : Primary sequence Native state S<0 Random coil Highly organized Compact 3-d structure Huge variation in the possible primary sequence: 20 N (20 different amino acids, N is # of amino acids in a chain) Most sequences do not fold; primary sequence must be carefully chosen Methods for finding primary sequences that fold to specific shapes: Evolution: trial and error, requires lots of time Engineering: Understand underlying principles of Self-organization

5 Protein Folding Problem Proteins are long (>50) chains of amino acid residues Biological functioning requires protein chain to fold to very specific compact shape: native state Chain is very flexible: each amino acid has internal degrees of freedom (Φ, Ψ, sidechain, e.g. 4 states each) > 64 configurations Ex: Myoglobin (153 amino acids) = configs Paradox: Even with super-fast sampling rate sec/config seconds ( yrs) to randomly find native state. (degeneracy of native state reduces this to years) Actual real protein folding times: milli-seconds!! How?? Folding must be a guided deterministic process, not random. Configuration space is frustrated, ultra-metric. Different initial configurations converge to native state. How does primary sequence determine folding dynamics. Interactions are non-linear: Anti-chaotic dynamics!?

6 Energy Landscape Funnel shaped, different initial configurations guide system to the same native state. Anti-Chaos? Is this a valid and useful approach? (B. Gerstman and Y. Garbourg, Journal of Polymer Science B: Polymer Physics, 36, , 1998.) -- 0 Many other axes are necessary to represent all the structural degrees of freedom. Which are most important?

7 Ultimate Physics Aim: Determine which aspects of 1-D sequence of amino acids in peptide chain determine efficient folding pathway and final shape (native state). Immediate Aim: Determine if formalism of non-linear dynamics is useful for investigating protein folding. This work: Can formalism of non-linear dynamics show that large scale un-folding is deterministic (and is it mathematically anti-chaotic) and distinguish random thermal fluctuations? Use data from lattice simulations of protein unfolding (realistic folding simulations of full proteins not available) First check to confirm that model realistically simulates protein dynamics. Compare results from model for characteristics that have been experimentally measured; e.g. Heat Capacity

8 Why use computer model? The system is complex - Huge number of degrees of structural freedom - Many terms in the Hamiltonian - System is not solvable analytically Monte Carlo simulations are very useful for these kinds of systems - Interested in relaxation times (non-equilibrium dynamics), as well as final configurations (equilibrium).

9 Lattice model and interaction Hamiltonian Red: backbone Green: side chain Interaction Hamiltonian: H = i j> i a ij ss p E ij ssp + a ij bb E bb + a ij rep E rep close enough contact (or preferred state)? Yes: a = 1; No: a = 0. ss : sidechain-sidechain bb: backbone-backbone l : local m : cooperative p : hydrophobic or polar or hydrophilic + l a l i E l + a m i E m m

10 Protein Configuration Energy Determined by Interaction Hamiltonian i,j : amino acid residue number in the primary sequence. a ss ij : are sidechains of i and j close enough to interact; yes = 1, no = 0. E ij ssp : sidechain-sidechain energy (p = 1 hydrophobic-hydrophobic, p = 2 hydrophilic-hydrophilic, p = 3 hydrophobic-hydrophilic). a ij bb : are backbones i and j close enough to interact; y=1, n=0. E bb : a l i : E l : a m i : E m : backbone-backbone interaction energy ( hydrogen bond, dipole, soft core repulsion combined together) are residues i-1, i, i+1, arranged so that i is in its preferred user-defined local configuration (i.e. α-helix, β-sheet, turn); y=1, n=0. local propensity energy. are residues i-1, i, i+1, i+2 arranged so that i and i+1 are both in the same preferred local configuration; y=1, n=0 medium range (cooperative) propensity energy

11 Nucleus DNA

12 DNA Packaging Inside Nucleus Nucleosome Supercoil Chromosome Protein Scaffold

13 Double Helix (Partially Disrupted) 2 nanometers 1 turn = 10 base pairs = 3.4 nanometers Minor Groove Major Groove

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16 NUCLEOTIDES Phosphate Base Sugar

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18 TRIPLET CODONS

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20 GENETIC CODE Initiation Codon Termination Codons U C A G UUU Phe UCU Ser UAU Tyr UGU Cys U UUC Phe UCC Ser UAC Tyr UGC Cys UUA Leu UCA Ser UAA UGA UUG Leu UCG Ser UGA UAG UGG Trp First Base in Codon C CUU Leu CCU Pro CAU His CGU Arg CUC Leu CCC Pro CAC His CGC Arg CUA Leu CCA Pro CAA Gln CGA Arg CUG Leu CCG Pro CAG Gln CGG Arg Third Base in Codon AUU Ile ACU Thr AAU Asn AGU Ser A AUC Ile ACC Thr AAC Asn AGC Ser AUA Ile ACA Thr AAA Lys AGA Arg AUG Met ACG Thr AAG Lys AGG Arg GUU Val GCU Ala GAU Asp GGU Gly G GUC Val GCC Ala GAC Asp GGC Gly GUA Val GCA Ala GAA Glu GGA Gly GUG Val GCG Ala GAG Glu GGG Gly

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