Proteins top–down: a statistical mechanics approach

Physical review letters, 2007

Within the frame of an effective, coarse-grained hydrophobic-polar protein model, we employ multicanonical Monte Carlo simulations to investigate free-energy landscapes and folding channels of exemplified heteropolymer sequences, which are permutations of each other. Despite ...

1 6 1 8 2 2 K a v a Figure 3. Plots of theoretical rw versus K at different Nl values, using the values of parameters listed in . The values of N1 are indicated on the curves. two ions. The dependence of the theoretical rMg on K was calculated for N1 values in the range 0.10-0.90. The resulting curves are shown in . The curvature is large and negative at Nl > 0.6 but is very small for Nl < 0.6, eventually becoming positive at Nl < 0.3. These results suggest that rMg versus K will be linear enough for a test of this type for territorial binding when N 1 lies between 0.25 and 0.50. This condition was satisfied in the PG experiment using a 1:l equivalent ratio of h4g* to Na2+ that did produce a linear relationship between r and K .

2003

How a unique three-dimensional structure is rapidly formed from the linear sequence of a polypeptide is one of the important questions in contemporary science. Apart from biological context of in vivo protein folding (which has been studied only for a few proteins), the roles of the fundamental physical forces in the in vitro folding remain largely unstudied. Despite a degree of success in using descriptions based on statistical and/or thermodynamic approaches, few of the current models explicitly include more basic physical forces (such as electrostatics and Van Der Waals forces). Moreover, the present-day models rarely take into account that the protein folding is, essentially, a rapid process that produces a highly specific architecture. This review considers several physical models that may provide more direct links between sequence and tertiary structure in terms of the physical forces. In particular, elaboration of such simple models is likely to produce extremely effective computational techniques with value for modern genomics.

Physica A: Statistical Mechanics and its Applications, 1999

We review a statistical mechanics treatment of the stability of globular proteins based on a simple model Hamiltonian taking into account protein self interactions and protein-water interactions. The model contains both hot and cold folding transitions. In addition it predicts a critical point at a given temperature and chemical potential of the surrounding water. The universality class of this critical point is new.

1990

Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics. C.L. Brooks III, M. Karplus, and B. M. Pettitt.

Reviews of Modern Physics, 2000

Protein folding has become one of the most actively studied problems in modern molecular biophysics. Approaches to the problem combine ideas from the physics of disordered systems, polymer physics, and molecular biology. Much can be learned from the statistical properties of model heteropolymers, the chain molecules having different monomers in irregular sequences. Even in highly evolved proteins, there is a strong random element in the sequences, which gives rise to a statistical ensemble of sequences for a given folded shape. Simple analytic models give rise to phase transitions between random, glassy, and folded states, depending on the temperature T and the design temperature T des of the ensemble of sequences. Besides considering the analytic results obtainable in a random-energy model and in the Flory mean-field model of polymers, the article reports on confirming numerical simulations.

The European Physical Journal B, 1998

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins.

Proceedings of the National …, 1993

Monte Carlo simulations on a class of lattice models are used to probe the thermodynamics and kinetics of protein folding. We find two transition temperatures: one at To, when chains collapse from a coil to a compact phase, and the other at Tf (< TO), when chains adopt a conformation corresponding to their native state. The kinetics are probed by several correlation functions and are interpreted in terms ofthe underlying energy landscape. The transition from the coil to the native state occurs in three distinct stages. The initial stage corresponds to a random collapse of the protein chain. At intermediate times i¢, during which much of the native structure is acquired, there are multiple pathways. For longer times rr (>> r,) the decay is exponential, suggestive of a late transition state. The folding time scale (= rr) varies greatly depending on the model. Implications of our results for in vitro folding of proteins are discussed.

Physical Review E, 2004

We study a physical system which, while devoid of the complexity one usually associates with proteins, nevertheless displays a remarkable array of protein-like properties. The constructive hypothesis that this striking resemblance is not accidental leads not only to a unified framework for understanding protein folding, amyloid formation and protein interactions but also has implications for natural selection.

Brazilian Journal of Physics, 2003

We review some results concerning the energetic and dynamical consequences of taking a generic hydrophobic model of a random polypeptide chain, where the effective hydrophobic interactions are represented by Hookean springs. Then we present a set of calculations on a microscopic model of hydrophobic interactions, investigating the behaviour of a hydrophobic chain in the vicinity of a hydrophobic boundary. We conclude with some speculations as to the thermodynamics of pre-biotic functions proteins may have discharged very early on in the evolutionary past.