Biomedical subjects

U Bastolla

Publications and source records attributed to U Bastolla.

11 recordsLinked to original sources

PubMed2005

Stability constraints and protein evolution: the role of chain length, composition and disulfide bonds.

Stability of the native state is an essential requirement in protein evolution and design. Here we investigated the interplay between chain length and stability constraints using a simple model of protein folding and a statistical study of the Protein Data Bank. We distinguish two types of stability of the native state: with respect to the unfolded state (unfolding stability) and with respect to misfolded configurations (misfolding stability). Several contributions to stability are evaluated and their correlations are disentangled through principal components analysis, with the following main results. (1) We show that longer proteins can fulfil more easily the requirements of unfolding and misfolding stability, because they have a higher number of native interactions per residue. Consistently, in longer proteins native interactions are weaker and they are less optimized with respect to non-native interactions. (2) Stability against misfolding is negatively correlated with the strength of native interactions, which is related to hydrophobicity. Hence there is a trade-off between unfolding and misfolding stability. This trade-off is influenced by protein length: less hydrophobic sequences are observed in very long proteins. (3) The number of disulfide bonds is positively correlated with the deficit of free energy stabilizing the native state. Chain length and the number of disulfide bonds per residue are negatively correlated in proteins with short chains and uncorrelated in proteins with long chains. (4) The number of salt bridges per residue and per native contact increases with chain length. We interpret these observations as an indication that the constraints imposed by unfolding stability are less demanding in long proteins and they are further reduced by the competing requirement for stability against misfolding. In particular, disulfide bonds appear to be positively selected in short proteins, whereas they evolve in an effectively neutral way in long proteins.

Amino Acids↗

PubMed2001

Diversity patterns from ecological models at dynamical equilibrium.

We study a dynamic model of ecosystems where an immigration flux assembles the species community and maintains its biodiversity. This framework is particularly relevant for insular ecosystems. Population dynamics is represented either as an individual-based model or as a set of deterministic equations for population abundances. Local extinctions and immigrations balance at a statistically stationary state where biodiversity fluctuates around a constant mean value. We find a number of scaling laws characterizing this stationary state. In particular, the number of species increases as a power law of the immigration rate. With additional assumptions on the immigration flux, we obtain species-area relationships in agreement with observations for archipelagos. We also find power-law distributions for species abundances and lifetimes.

Animals↗

PubMed2001

How to guarantee optimal stability for most representative structures in the Protein Data Bank.

We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.

Computational Biology↗

PubMed2001

Shape of ecological networks.

We study the statistics of ecosystems with a variable number of coevolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly through successful adaptations and speciations. They are treated as quenched random variables. These interactions determine long-term topological features of the species network, which are found to agree with those of biological systems.

Animals↗

PubMed2001

Exactness of the annealed and the replica symmetric approximations for random heteropolymers.

We study a heteropolymer model with random contact interactions introduced some time ago as a simplified model for proteins. The model consists of self-avoiding walks on the simple cubic lattice, with contact interactions between nearest-neighbor pairs. For each pair, the interaction energy is an independent Gaussian variable with mean value B and variance Delta(2). For this model the annealed approximation is expected to become exact for low disorder, at sufficiently high dimension and in the thermodynamic limit. We show that corrections to the annealed approximation in the three-dimensional high-temperature phase are small, but do not vanish in the thermodynamic limit, and are in good agreement with our replica symmetric calculations. Such corrections derive from the fact that the overlap between two typical chains is nonzero. We explain why previous authors had come to the opposite conclusion, and discuss consequences for the thermodynamics of the model. Numerical results were obtained by simulating chains of length N<or=1400 by means of the recent PERM algorithm, in the coil and molten globular phases, well above the freezing temperature.

Algorithms↗

PubMed2000

A statistical mechanical method to optimize energy functions for protein folding.

We present a method for deriving energy functions for protein folding by maximizing the thermodynamic average of the overlap with the native state. The method has been tested by using the pairwise contact approximation of the energy function and generating alternative structures by threading sequences over a database of 1, 169 structures. With the derived energy function, most native structures: (i) have minimal energy and (ii) are thermodynamically rather stable, and (iii) the corresponding energy landscapes are smooth. Precisely, 92% of the 1,013 x-ray structures are stabilized. Most failures can be attributed to the neglect of interactions between chains forming polychain proteins and of interactions with cofactors. When these are considered, only nine cases remain unexplained. In contrast, 38% of NMR structures are not assigned properly.

Protein Conformation↗

PubMed1999

Neutral evolution of model proteins: diffusion in sequence space and overdispersion.

We stimulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves (1) the structure of the ground state, (2) its thermodynamic stability and (3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space-sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than 1). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with the biological data.

Animals↗

PubMed1998

Testing a new Monte Carlo algorithm for protein folding.

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences.

Algorithms↗

PubMed1997

A numerical study of the critical line of Kauffman networks.

Kauffman networks were introduced in 1969 as a model of genetic regulatory systems. One of the most striking successes of this model is its ability to reproduce, for a critical value of its parameters, the observed scaling laws of the average cell replication time and of the average number of cell types in a given organism vs. the number of genes. Yet, the numerical evidence for such scaling laws in the model is still unsatisfactory, and restricted to a particular critical point, while we expect that the scaling behaviour is universal along the critical line. In this paper we try to sharpen the evidence for the scaling behaviour of critical systems, carrying on a detailed numerical investigation of their properties. We measure the length of the cycles (which in the model represents the period of cell cycles) and their number (which represents the number of cell types) for a point of the critical line different from the only one previously studied. Our results seem to confirm that such quantities scale as radicalN for all critical systems, at least for lengths and numbers small enough. On the other hand, we found that their probability distributions are very broad (power-law like) and become broader with system size. This means that there is an effective scale of the length and of the number of cycles that increases much faster than radicalN, and in the infinite size limit the biological analogy found by Kauffman may be lost. A numerical study of the modular structure of critical networks supports this conclusion. The implications of this fact for the biological interpretation of the model are briefly discussed. Finally, we found that the typical weight of the attraction basins tends to zero as a power law in the infinite size limit, with an exponent which seems to be universal along the whole critical line.

Animals↗

PubMed1994

Collective adaptation in a statistical model of an evolving population.

We simulate asexually and sexually reproducing model populations evolving in a rugged fitness landscape where fit and unfit genotypes are distributed at random, and where all fit genotypes have the same a priori probability of reproduction. Varying the fraction chi of unfit genotypes at a fixed mutation rate we observe a strikingly different behavior for the two reproduction mechanisms. For the asexually reproducing population, the effective mutation rate lambda decreases roughly proportionally to (1-chi), and the fraction delta of sterile individuals--processing an unfit genotype--accordingly increases roughly proportionally to chi. On the other hand, lambda remains approximately constant (and delta increases proportionally to chi) for small values of chi:but, at a critical value chi*, both lambda and delta suddenly drop. This corresponds to the transition to an adaptive regime where the average fitness of the population is enhanced. We show how this transition can be interpreted in terms of an improvement of the collective fitness of the population.

Biological Evolution↗

PubMed1991

[A statistical model of evolution with stabilizing selection].

We consider a population of fixed size and reproducing asexually, evolving in a rugged fitness landscape. Selection takes place only via the elimination of individuals with unfit genomes. Unfit genotypes are distributed at random in genotypic space. The genetic structure of the population and the speed of genetic drift are explicitly computed in the infinite genome limit.

Biological Evolution↗