Mapping of mutation-sensitive sites in protein-like chains

In this work we have studied, with the help of a simple on-lattice model, the distribution pattern of sites sensitive to point mutations ('hot' sites) in protein-like chains. It has been found that this pattern depends on the regularity of the matrix that rules the interaction between different kinds of residues. If the interaction matrix is dominated by the hydrophobic effect (Miyazawa Jernigan like matrix), this distribution is very simple - all the 'hot' sites can be found at the positions with maximum number of closest nearest neighbors (bulk). If random or nonlinear corrections are added to such an interaction matrix the distribution pattern changes. The rising of collective effects allows the 'hot' sites to be found in places with smaller number of nearest neighbors (surface) while the general trend of the 'hot' sites to fall into a bulk part of a conformation still holds.Comment: 15 pages, 6 figure

Designability of lattice model heteropolymers

Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the Central Limit Theorem, has a generality which goes beyond the simple model used in its derivation. This expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures, energy difference which constitutes the only parameter controlling designability. Accordingly, the designability of a native conformation is intimately connected to the stability of the sequences folding to them.Comment: in press on Phys. Rev.

Is Heteropolymer Freezing Well Described by the Random Energy Model?

It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over disorder, is violated in different ways for models commonly employed in heteropolymer freezing studies. The implications for proteins are also discussed.Comment: 4 pages, 3 eps figures To appear in Physical Review Letters, May 199

Two-Dimensional Polymers with Random Short-Range Interactions

We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that a polymer undergoes a collapse transition at a temperature $T_{\theta}$, which decreases with increasing imbalance between charges. At the transition point, the dependence of the radius of gyration of the polymer on the number of monomers is characterized by an exponent $\nu_{\theta} = 0.60 \pm 0.02$, which is slightly larger than the similar exponent for homopolymers. We find no evidence of freezing at low temperatures.Comment: 4 two-column pages, 6 eps figures, RevTex, Submitted to Phys. Rev.

Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers

Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary $q \times q$ matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure

Deviations from the mean field predictions for the phase behaviour of random copolymers melts

We investigate the phase behaviour of random copolymers melts via large scale Monte Carlo simulations. We observe macrophase separation into A and B--rich phases as predicted by mean field theory only for systems with a very large correlation lambda of blocks along the polymer chains, far away from the Lifshitz point. For smaller values of lambda, we find that a locally segregated, disordered microemulsion--like structure gradually forms as the temperature decreases. As we increase the number of blocks in the polymers, the region of macrophase separation further shrinks. The results of our Monte Carlo simulation are in agreement with a Ginzburg criterium, which suggests that mean field theory becomes worse as the number of blocks in polymers increases.Comment: 6 pages, 4 figures, Late

Correlated disorder in random block-copolymers

We study the effect of a random Flory-Huggins parameter in a symmetric diblock copolymer melt which is expected to occur in a copolymer where one block is near its structural glass transition. In the clean limit the microphase segregation between the two blocks causes a weak, fluctuation induced first order transition to a lamellar state. Using a renormalization group approach combined with the replica trick to treat the quenched disorder, we show that beyond a critical disorder strength, that depends on the length of the polymer chain, the character of the transition is changed. The system becomes dominated by strong randomness and a glassy rather than an ordered lamellar state occurs. A renormalization of the effective disorder distribution leads to nonlocal disorder correlations that reflect strong compositional fluctuation on the scale of the radius of gyration of the polymer chains. The reason for this behavior is shown to be the chain length dependent role of critical fluctuations, which are less important for shorter chains and become increasingly more relevant as the polymer length increases and the clean first order transition becomes weaker.Comment: 11 pages, 5 figures, submitted to PR

Origin of Native Driving Force in Protein Folding

We derive an expression with four adjustable parameters that reproduces well the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein structures. The numerical values of the parameters can be approximately computed from the surface tension of water, water-screened dipole interactions between residues and water and among residues, and average exposures of residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table

Simple models of protein folding and of non--conventional drug design

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of a protein whose sequence is known. Using insight obtained from simple model simulations of the folding of proteins, in particular of the fact that this phenomenon is essentially controlled by conserved (native) contacts among (few) strongly interacting ("hot"), as a rule hydrophobic, amino acids, which also stabilize local elementary structures (LES, hidden, incipient secondary structures like $\alpha$--helices and $\beta$--sheets) formed early in the folding process and leading to the postcritical folding nucleus (i.e., the minimum set of native contacts which bring the system pass beyond the highest free--energy barrier found in the whole folding process) it is possible to work out a succesful strategy for reading the native structure of designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids. Because LES have undergone millions of years of evolution to selectively dock to their complementary structures, small peptides made out of the same amino acids as the LES are expected to selectively attach to the newly expressed (unfolded) protein and inhibit its folding, or to the native (fluctuating) native conformation and denaturate it. These peptides, or their mimetic molecules, can thus be used as effective non--conventional drugs to those already existing (and directed at neutralizing the active site of enzymes), displaying the advantage of not suffering from the uprise of resistance