Theoretical approaches to designing and understanding proteins
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1 Theoretical approaches to designing and understanding proteins Jeffery G. Saven University of Pennsylvania Department of Chemistry
2 Design Challenges of Beratan 1. How to explore and characterize chemical space? 2. Discovering structures with excellent properties 3. How to capitalize on iterating theory and experiment? 4. Metrics for diversity? 5. Geometry and energetics of underlying design landscape
3 Proteins: many length scales and functions Multiple environments: solution, membranes, surfaces! Many functionalities Solution: catalysis, recognition, signals, pigments! Membranes: channels, energy transduction, light harvesting, signaling! Å! nm! > 10 nm!
4 Sequence degeneracy Sequence! Structure! Sequences folding to a common structure! 20 N possible! sequences! Known sequences folding to a common structure!
5 Elements of protein design Template structures: redesign of existing structure novel structure Monomer (residue) degrees of freedom Backbone structure amino acids (identity) amino acid conformations (rotamers) Energy functions: quantifying interactions within a structure Folding criteria and negative design Energy based: sequence structure compatibility Competing structures Characterizing sequences Searching sequence space with optimization based methods Estimating the frequencies of the amino acids A. Lehmann, et al, in Protein Folding and Misfolding (ed. V. Munoz; Royal Society of Chemistry), S. Park et al, Annual Reports of the Royal Society of Chemistry, Section C, (Physical Chemistry), 2004, pp J. G. Saven, Chemical Reviews (10): Samish et al, Annu. Rev. Phys. Chem 2011.!
6 Sequence design: search methods Simulated annealing! Monte Carlo methods! Genetic algorithms!! Objective! Function!! Energy!! Foldability! Pruning methods! (dead end elimination)!! Fix target structure! Vary sequence! Folded! state! S. Mayo (Caltech), H. Hellinga (Duke); D. Baker (UW Seattle); T. Alber (UC Berkeley), P. Kim, B. Tidor, A. Keating (MIT); P. Harbury (Stanford); J. Desjarlais (Xencor); C. Floudas (Princeton); L. Lai (Beijing); S. Takada (Kyoto)!
7 Difficulties protein design Large numbers of degrees of freedom 20 amino acids, most have multiple side-chain conformations: 100 s of states per residue position: (20 x 100) 100 configurations Calculations can become demanding even for small proteins Imperfect energy functions Imperfect structures Optimization? Natural proteins are marginally stable Biological function may compete with stability Scoring functions are approximate Sequence variability Incomplete information guides directed design of protein sequences Potentials contain (partial) information about stabilizing forces: van der Waals interactions, electrostatics, structural propensities,... A probabilistic approach seems appropriate to broadly understand sequences consistent with a chosen structure!!and combinatorial experiments (10 7 sequences)!
8 Theory and Design of Proteins (and Self-Organizing Macromolecules) Methods for probabilistic protein design! Input:! Target tertiary and quaternary structure! Features, e.g., well-packed, hydrophobic interior! Atomistic energy functions! Physical, synthetic and functional constraints on sequences! Output: Site-specific probabilities of the amino acids for a given structure! Advantages:! Large structures and diversity! Application to de novo protein design and combinatorial design! Transferable to nonbiological systems! Target structure! Atomistic model of structure and monomers! Site-specific monomer probabilities!
9 Thermodynamic analogy Thermodynamic ensemble Sequence ensemble!=no. configurations!=no. sequences!(x) N,V,E w i (a) Apply methods from statistical thermodynamics to estimate probabilities (effective thermodynamic quantities: T, E, S!) Solve for probabilities w i (a) subject to constraints on sequences Self-consistent field methods based on entropy maximization H. Kono and J. G. Saven. J Mol. Biol.,. 306: (2001). J. Zou and J. G. Saven, J. Mol. Biol., 296: (2000). Sample sequences and count frequencies of amino acids Efficient (biased with replica exchange) Monte Carlo methods X. Yang and J. G. Saven, Chem. Phys. Lett., 401: (2005). J. Zou and J. G. Saven, J. Chem. Phys. 118: p (2003).
10 Entropy maximization Sequence ensemble: other variables include amino acid probabilities
11 Entropy maximization Fix Number, Volume, and Energy! Case 1: permeable wall! Case 2: impermeable wall! S 1 (E) < S 2 (E)!! 1 (E) <! 2 (E)!
12 Factorization (Hartree) approximation W(a)! w i (a i ) " i ln # = S = $ % W(a)ln W(a)! $ % w i (a i )ln w i (a i ) constraints on sequences couple site probabilities!
13 Maximize Effective Entropy Maximize sequence entropy for fixed structure S =! " i " a w i (a)ln w i (a) Sum over sites! Sum over states at each site! Solve for probabilities w i (a) i = position in sequence a = amino acid state Maximize subject to constraints on sequences Sequences are not enumerated
14 Maximize entropy subject to constraints Probabilities are normalized Overall Energy of sequence in target structure! w i (a) = 1 a E = E seq Overall composition: number of each amino acid Patterning constraints! w i (a) = n(a) i w i (a) =1
15 Self-consistent, entropy maximization Sequences are not enumerated Solve for probabilities w i (a): a = amino acid state, i = position in sequence Maximize subject to physical and synthetic constraints on sequences: E i, f i Constrain effective energies E i (low energy sequences for target structure) Other possible constraints: Pattern amino acids: hydrophobic inside, hydrophilic outside Specify identities and/or conformations of functionally important residues V ({w i (a)}) = S " # 1 E 1 " # 2 E 2 "..." $ 1 f 1 " $ 2 f 2 "... S = " ## i a w i (a)lnw i (a) E 1 = E folded ({ a}) " F unfolded ({ a}) E 2 = E solvation ({ a}) Atomic potential energy! Solvation energy! "V "w i (a) = 0, and E i = E i sequence H. Kono and J. G. Saven. J Mol. Biol.,. 306: (2001).! J. Zou and J. G. Saven, J. Mol. Biol., 296: (2000).!
16 () 1 ( 2) Ea (,..., a )! " ( a) " " ( a, a) 1 N!! i i i# j i j
17 Local average energy Energy of sequence (a 1,, a N ) in structure! () 1 ( 2) Ea (,..., a )! " ( a) " " ( a, a) 1 N! i! i i# j i j Local energy of a at site i!! ( a) " () 1 ( a) " ( 2 ) ( a, a ) i! "# j j...!! i( a)! i( a) " () 1 ( a) " ( 2 #! " $ $ ) ( a, aj) wj( aj) j a j Average over sequences!
![Biol, 306:607 (2001)] Discrete conformational states for amino acids (rotamers) Dunbrack &](/docs-images/90/103077263/images/18-1.jpg "Cohen, Protein Sci., 6:1661 (1997) Ala Arg Asn.")
18 Atomistic Models of Proteins Amino acid and side chain conformation Energy Atomic interactions (AMBER) Solvation (Hydrophobic effect) [Kono & Saven, J. Mol. Biol, 306:607 (2001)] Discrete conformational states for amino acids (rotamers) Dunbrack & Cohen, Protein Sci., 6:1661 (1997) Ala Arg Asn... w i (a) w i (a, r a i ) rotamer states w i (a) = " w i (a,r a ) r a
19 Relative entropy: SH3 domain - 57 residue protein! - Allow all amino acids at each position! - Compare with multiple sequence alignment!
20 Effective heat capacity C v plotted against effective temperature T! all buried exposed Heat Capacity / a.a SH3 domain! Temperature kt
21 Functional metalloproteins! Protein complexes with nonbiological cofactors! JACS, : 1346! JACS, : 5804! J. Mol. Biol., : 1101! Ultrafast (µs) (b) folding proteins! Nonbiological foldamers! J Phys Chem B, : 11988! Solubilized integral membrane proteins! Membrane bilayer! PNAS, : 1828! Membrane protein association!
22 Computational design of protein assemblies DpsWT Dps10 Designing protein crystals! Designing proteins with icosohedral symmetry (ferritins)! JACS, 2006.! Biochemistry, 2008.!
23 Water-Solubilization of Membrane Proteins
24 Membrane proteins Membrane proteins! Few structures! 30% of genome! 30-50% of drug targets! Poor expression, low solubility! Often solubilized for biophysical studies and structure determination!!
25 Water solubilization of membrane proteins: KcsA Humanized version of a bacterial K-channel, tkcsa.! tkcsa: extracellular loops contain residues (from human K-channels) required for binding to a scorpion toxin, agitoxin 2.! Selective toxin binding! R. MacKinnon, S. L. Cohen, A. Kuo, A. Lee, B. T. Chait, Science 280, (1998)
26 Designing WSK: soluble variant of the potassium channel KcsA! KcsA structure (Mackinnon & coworkers)! Tetramer of 103 residue helical protomers (412 total residues)! Computationally design 29 exterior amino acids of each subunit!! Agitoxin binding site! membrane! wild type! WSK! A. Slovic, H. Kono, J. Lear, J. G. Saven, and W. F. DeGrado, Proc. Natl. Acad Sci., 101: (2004)!
27 Solubilization of membrane protein Solvation! energy! Soluble! proteins! Membrane protein! Solubilized! design! Calculations simultaneously consider solvation properties and inter-residue interactions of mutated residues! A. Slovic et al, Proc. Natl. Acad Sci., 2004!
28 Characterization of soluble variant Express in soluble form!! Properties shared with membrane soluble tkcsa! Structural criteria:! Secondary structure! Tetrameric! Functional criteria:! Binds toxin specifically with same K d! Binds protein toxin stoichiometrically! Binds small molecule channel blocker (TEA)! A. Slovic, H. Kono, J. Lear, J. G. Saven, and W. F. DeGrado, Proc. Natl. Acad Sci., 101: (2004)!
29 Solution structure of water soluble variant of K-channel (WSK-3) D. Ma, et al PNAS (2008), 105:
30 Designing protein complexes with nonbiological cofactors Groups of Michael Therien, William DeGrado, & J. Saven
31 Protein complexes with nonbiological cofactors H O 2 C CO 2 H Cofactors confer function to proteins e.g., Heme (oxygen binding, catalysis) New function and materials: proteins containing nonbiological cofactors Controlled cofactor environment Controlled protein assembly H 3 C N N CH 3 Fe N N CH 3 CH 3 PPIX-Fe O CH 2 COOH N N N Ru N N N N N R Zn R N N 2+ N N Fe N N DPP-Fe - near IR emitters! - large molecular hyperpolarizability (NLO)! - long lived charge separated states! (M. J. Therien)! O CH 2 COOH
32 Acknowledgments J. G. Saven group (Penn) Present Chris Lanci Chris MacDermaid Jose Manuel Perez Aguilar Former Hidetoshi Kono (Japan Atomic Energy Res. Inst. ) Andreas Lehmann (Fox Chase Cancer Center) Wei Wang (Colgate-Palmolive, Inc.) Xi Yang (Standard & Poors) Support National Science Foundation (MRSEC) (NSEC) Department of Energy National Institutes of Health University of Pennsylvania William F. DeGrado group (Penn) Michael J. Therien group (Penn & Duke) Christopher Fry (Argonne Nat l Lab) Feng Gai group (Penn) Ivan Dmochowski group (Penn)
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