The foldability landscape of model proteins

Molecular evolution may be considered as a walk in a multidimensional fitness landscape, where the fitness at each point is associated with features such as the function, stability, and survivability of these molecules. We present a simple model for the evolution of protein sequences on a landscape with a precisely defined fitness function. We use simple lattice models to represent protein structures, with the ability of a protein sequence to fold into the structure with lowest energy, quantified as the foldability, representing the fitness of the sequence. The foldability of the sequence is characterized based on the spin glass model of protein folding. We consider evolution as a walk in this foldability landscape and study the nature of the landscape and the resulting dynamics. Selective pressure is explicitly included in this model in the form of a minimum foldability requirement. We find that different native structures are not evenly distributed in interaction space, with similar structures and structures with similar optimal foldabilities clustered together. Evolving proteins marginally fulfill the selective criteria of foldability. As the selective pressure is increased, evolutionary trajectories become increasingly confined to “neutral networks,” where the sequence and the interactions can be significantly changed while a constant structure is maintained. © 1997 John Wiley & Sons, Inc. Biopoly 42: 427–438, 1997

[1]  M. Karplus,et al.  Kinetics of protein folding. A lattice model study of the requirements for folding to the native state. , 1994, Journal of molecular biology.

[2]  C. A. Macken,et al.  Protein evolution on rugged landscapes. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[3]  B. Derrida,et al.  Evolution in a flat fitness landscape , 1991 .

[4]  R A Goldstein,et al.  Context-dependent optimal substitution matrices. , 1995, Protein engineering.

[5]  E. Shakhnovich,et al.  Engineering of stable and fast-folding sequences of model proteins. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[6]  E. Shakhnovich,et al.  Proteins with selected sequences fold into unique native conformation. , 1994, Physical review letters.

[7]  Richard A. Goldstein,et al.  Searching for foldable protein structures using optimized energy functions , 1995 .

[8]  D. Yee,et al.  Principles of protein folding — A perspective from simple exact models , 1995, Protein science : a publication of the Protein Society.

[9]  P. Wolynes,et al.  Optimal protein-folding codes from spin-glass theory. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Weinberger,et al.  RNA folding and combinatory landscapes. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  J. Onuchic,et al.  Funnels, pathways, and the energy landscape of protein folding: A synthesis , 1994, Proteins.

[12]  Steven A. Benner,et al.  Reconstructing the evolutionary history of the artiodactyl ribonuclease superfamily , 1995, Nature.

[13]  P. Wolynes,et al.  The energy landscapes and motions of proteins. , 1991, Science.

[14]  P. Wolynes,et al.  Protein tertiary structure recognition using optimized Hamiltonians with local interactions. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[15]  John Maynard Smith,et al.  Natural Selection and the Concept of a Protein Space , 1970, Nature.

[16]  D. Lipman,et al.  Modelling neutral and selective evolution of protein folding , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[17]  E. Shakhnovich,et al.  Implications of thermodynamics of protein folding for evolution of primary sequences , 1990, Nature.

[18]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[19]  E I Shakhnovich,et al.  Evolution-like selection of fast-folding model proteins. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Flyvbjerg,et al.  Coevolution in a rugged fitness landscape. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[21]  R A Goldstein,et al.  Mutation matrices and physical‐chemical properties: Correlations and implications , 1997, Proteins.

[22]  Linus Pauling,et al.  Chemical Paleogenetics. Molecular "Restoration Studies" of Extinct Forms of Life. , 1963 .

[23]  R A Goldstein,et al.  Why are some proteins structures so common? , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[24]  K. Dill,et al.  Transition states and folding dynamics of proteins and heteropolymers , 1994 .

[25]  M Levitt,et al.  Different protein sequences can give rise to highly similar folds through different stabilizing interactions , 1994, Protein science : a publication of the Protein Society.

[26]  M. Karplus,et al.  How does a protein fold? , 1994, Nature.

[27]  E. Shakhnovich,et al.  A new approach to the design of stable proteins. , 1993, Protein engineering.

[28]  M. Thompson,et al.  Constructing amino acid residue substitution classes maximally indicative of local protein structure , 1996, Proteins.

[29]  M Karplus,et al.  Theoretical studies of protein folding and unfolding. , 1995, Current opinion in structural biology.

[30]  R A Goldstein,et al.  Optimal local propensities for model proteins , 1995, Proteins.

[31]  Brian W. Matthews,et al.  Ancestral lysozymes reconstructed, neutrality tested, and thermostability linked to hydrocarbon packing , 1990, Nature.

[32]  N. Go.  Theoretical studies of protein folding. , 1983, Annual review of biophysics and bioengineering.

[33]  M. Nei,et al.  A new method of inference of ancestral nucleotide and amino acid sequences. , 1995, Genetics.

[34]  Peter F. Stadler,et al.  Landscapes: Complex Optimization Problems and Biopolymer Structures , 1994, Comput. Chem..

[35]  C. Branden,et al.  Introduction to protein structure , 1991 .

[36]  P. Schuster,et al.  Statistics of RNA secondary structures , 1993, Biopolymers.

[37]  Scott R. Presnell,et al.  The ribonuclease from an extinct bovid ruminant , 1990, FEBS letters.

[38]  N. Wingreen,et al.  Emergence of Preferred Structures in a Simple Model of Protein Folding , 1996, Science.

[39]  W. Hendrickson,et al.  Quantification of tertiary structural conservation despite primary sequence drift in the globin fold , 1994, Protein science : a publication of the Protein Society.

[40]  P. Argos,et al.  Protein structure prediction: recognition of primary, secondary, and tertiary structural features from amino acid sequence. , 1995, Critical reviews in biochemistry and molecular biology.

[41]  P. Schuster,et al.  From sequences to shapes and back: a case study in RNA secondary structures , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[42]  A. Wilson,et al.  Reconstruction and testing of ancestral proteins. , 1993, Methods in enzymology.

[43]  R. Jernigan,et al.  Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation , 1985 .

[44]  P. Wolynes,et al.  Spin glasses and the statistical mechanics of protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.