Highly Designable Protein Structures and Inter Monomer Interactions

By exact computer enumeration and combinatorial methods, we have calculated the designability of proteins in a simple lattice H-P model for the protein folding problem. We show that if the strength of the non-additive part of the interaction potential becomes larger than a critical value, the degree of designability of structures will depend on the parameters of potential. We also show that the existence of a unique ground state is highly sensitive to mutation in certain sites.Comment: 14 pages, Latex file, 3 latex and 6 eps figures are include

The effect of local thermal fluctuations on the folding kinetics: a study from the perspective of the nonextensive statistical mechanics

Protein folding is a universal process, very fast and accurate, which works consistently (as it should be) in a wide range of physiological conditions. The present work is based on three premises, namely: ($i$) folding reaction is a process with two consecutive and independent stages, namely the search mechanism and the overall productive stabilization; ($ii$) the folding kinetics results from a mechanism as fast as can be; and ($iii$) at nanoscale dimensions, local thermal fluctuations may have important role on the folding kinetics. Here the first stage of folding process (search mechanism) is focused exclusively. The effects and consequences of local thermal fluctuations on the configurational kinetics, treated here in the context of non extensive statistical mechanics, is analyzed in detail through the dependence of the characteristic time of folding ($\tau$) on the temperature $T$ and on the nonextensive parameter $q$.The model used consists of effective residues forming a chain of 27 beads, which occupy different sites of a $3-$D infinite lattice, representing a single protein chain in solution. The configurational evolution, treated by Monte Carlo simulation, is driven mainly by the change in free energy of transfer between consecutive configurations. ...Comment: 19 pages, 3 figures, 1 tabl

A Multicanonical Molecular Dynamics Study on a Simple Bead-Spring Model for Protein Folding

We have performed a multicanonical molecular dynamics simulation on a simple model protein.We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers.Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker.Comment: 7 pages, 6 postscript figures, To appear in J.Phys.Soc.Jpn. Vol.70 No.

Pathways in Two-State Protein Folding

The thermodynamics of proteins indicate that folding/unfolding takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of the two-state process indicate that folding is guided. We reconcile these two seemingly contradictory observations quantitatively in a schematic model of protein folding. We propose a new dynamical transition temperature which is lower than the thermodynamic one, in qualitative agreement with in vivo measurement of protein stability using E.coli. Finally we demonstrate that our framework is easily generalized to encompass cold unfolding, and make predictions that relate the sharpness of the cold and hot unfolding transitions.Comment: 4 pages RevTeX, 5 Postscript figur

How much of protein sequence space has been explored by life on Earth?

We suggest that the vastness of protein sequence space is actually completely explorable during the populating of the Earth by life by considering upper and lower limits for the number of organisms, genome size, mutation rate and the number of functionally distinct classes of amino acids. We conclude that rather than life having explored only an infinitesimally small part of sequence space in the last 4 Gyr, it is instead quite plausible for all of functional protein sequence space to have been explored and that furthermore, at the molecular level, there is no role for contingency

Reply to Comment on "Criterion that Determines the Foldability of Proteins"

We point out that the correlation between folding times and $\sigma = (T_{\theta } - T_{f})/T_{\theta }$ in protein-like heteropolymer models where $T_{\theta }$ and $T_{f}$ are the collapse and folding transition temperatures was already established in 1993 before the other presumed equivalent criterion (folding times correlating with $T_{f}$ alone) was suggested. We argue that the folding times for these models show no useful correlation with the energy gap even if restricted to the ensemble of compact structures as suggested by Karplus and Shakhnovich (cond-mat/9606037).Comment: 6 pages, Latex, 2 Postscript figures. Plots explicitly showing the lack of correlation between folding time and energy gap are adde

Exploring the Levinthal limit in protein folding

According to the thermodynamic hypothesis, the native state of proteins is uniquely defined by their amino acid sequence. On the other hand, according to Levinthal, the native state is just a local minimum of the free energy and a given amino acid sequence, in the same thermodynamic conditions, can assume many, very different structures that are as thermodynamically stable as the native state. This is the Levinthal limit explored in this work. Using computer simulations, we compare the interactions that stabilize the native state of four different proteins with those that stabilize three non-native states of each protein and find that the nature of the interactions is very similar for all such 16 conformers. Furthermore, an enhancement of the degree of fluctuation of the non-native conformers can be explained by an insufficient relaxation to their local free energy minimum. These results favor Levinthal's hypothesis that protein folding is a kinetic non-equilibrium process.FCT - Foundation for Science and Technology, Portugal [UID/Multi/04326/2013]; Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP); Conselho Nacional de Desenvolvimento Cientia co e Tecnologico (CNPq

Sequence Dependence of Self-Interacting Random Chains

We study the thermodynamic behavior of the random chain model proposed by Iori, Marinari and Parisi, and how this depends on the actual sequence of interactions along the chain. The properties of randomly chosen sequences are compared to those of designed ones, obtained through a simulated annealing procedure in sequence space. We show that the transition to the folded phase takes place at a smaller strength of the quenched disorder for designed sequences. As a result, folding can be relatively fast for these sequences.Comment: 14 pages, uuencoded compressed postscript fil

Folding of small proteins: A matter of geometry?

We review some of our recent results obtained within the scope of simple lattice models and Monte Carlo simulations that illustrate the role of native geometry in the folding kinetics of two state folders.Comment: To appear in Molecular Physic