Lethal Mutagenesis in Viruses and Bacteria

Here we study how mutations which change physical properties of cell proteins (stability) impact population survival and growth. In our model the genotype is presented as a set of N numbers, folding free energies of cells N proteins. Mutations occur upon replications so that stabilities of some proteins in daughter cells differ from those in parent cell by random amounts drawn from experimental distribution of mutational effects on protein stability. The genotype-phenotype relationship posits that unstable proteins confer lethal phenotype to a cell and in addition the cells fitness (duplication rate) is proportional to the concentration of its folded proteins. Simulations reveal that lethal mutagenesis occurs at mutation rates close to 7 mutations per genome per replications for RNA viruses and about half of that for DNA based organisms, in accord with earlier predictions from analytical theory and experiment. This number appears somewhat dependent on the number of genes in the organisms and natural death rate. Further, our model reproduces the distribution of stabilities of natural proteins in excellent agreement with experiment. Our model predicts that species with high mutation rates, tend to have less stable proteins compared to species with low mutation rate

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure

Statistical properties of neutral evolution

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered, and fluctuates strongly from one branch of the evolutionary tree to another, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are also due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results could improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences.Comment: 17 pages, 11 figure

Chance and Necessity in Evolution: Lessons from RNA

The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are realized much more frequently than others), (2) the notion of shape space covering (that all typical shapes are realized in a small neighborhood of any random sequence), and (3) the notion of a neutral network (that sequences folding into the same typical shape form networks that percolate through sequence space). Neutral networks loosen the requirements on the mutation rate for selection to remain effective. The original (genotypic) error threshold has to be reformulated in terms of a phenotypic error threshold. With regard to adaptation, neutrality has two seemingly contradictory effects: It acts as a buffer against mutations ensuring that a phenotype is preserved. Yet it is deeply enabling, because it permits evolutionary change to occur by allowing the sequence context to vary silently until a single point mutation can become phenotypically consequential. Neutrality also influences predictability of adaptive trajectories in seemingly contradictory ways. On the one hand it increases the uncertainty of their genotypic trace. At the same time neutrality structures the access from one shape to another, thereby inducing a topology among RNA shapes which permits a distinction between continuous and discontinuous shape transformations. To the extent that adaptive trajectories must undergo such transformations, their phenotypic trace becomes more predictable.Comment: 37 pages, 14 figures; 1998 CNLS conference; high quality figures at http://www.santafe.edu/~walte

Molecular Mechanics Study of Protein Folding and Protein-Ligand Binding

In this dissertation, molecular dynamics (MD) simulations were applied to study the effect of single point mutations on protein folding free energy and the protein-ligand binding in the bifunctional protein dihydrofolate reductase-thymidylate synthase (TS-DHFR) in plasmodium falciparum (pf). The main goal of current computational studies is to have a deeper understanding of factors related to protein folding stability and protein-ligand binding. Chapter two aims to seek solutions for improving the accuracy of predicting changes of folding free energy upon single point mutations in proteins. While the importance of conformational sampling was adequately addressed, the diverse dielectric properties of proteins were also taken into consideration in this study. Through developing a three-dielectric-constant model and broadening conformational sampling, a method for predicting the effect of point mutations on protein folding free energy is described, and factors of affecting the prediction accuracy are addressed in this chapter. The following two chapters focus on the binding process and domain-domain interactions in the bifunctional protein pfDHFR-TS. This protein usually plays as the target of antimalarial drugs, but the drug resistance in this protein has caused lots of problems. In chapter three, the mechanism of the development of drug resistance was investigated. This study indicated that the accumulation of mutations in pfDHFR caused obvious changes of conformation and interactions among residues in the binding pocket, which further weakened the binding affinity between pfDHFR and the inhibitor drug. Furthermore, the high rigidity and significantly weakened communications among key residues in the protein binding pocket were exhibited in the pfDHFR quadruple mutant. The rigid binding site was associated with the failure of conformational reorganization upon the binding of pyrimethamine in the quadruple mutant. Chapter four investigated the effect of the N-terminus in pfDHFR-TS on enzyme activity and domain-domain communications. This is the first computational study that focuses on the full-length pfDHFR-TS dimer. This study provided computational evidence to support that remote mutations could disturb the interactions and conformations of the binding site through disrupting dynamic motions in pfDHFR-TS

The Role of Mutations in Protein Structural Dynamics and Function: A Multi-scale Computational Approach

abstract: Proteins are a fundamental unit in biology. Although proteins have been extensively studied, there is still much to investigate. The mechanism by which proteins fold into their native state, how evolution shapes structural dynamics, and the dynamic mechanisms of many diseases are not well understood. In this thesis, protein folding is explored using a multi-scale modeling method including (i) geometric constraint based simulations that efficiently search for native like topologies and (ii) reservoir replica exchange molecular dynamics, which identify the low free energy structures and refines these structures toward the native conformation. A test set of eight proteins and three ancestral steroid receptor proteins are folded to 2.7Å all-atom RMSD from their experimental crystal structures. Protein evolution and disease associated mutations (DAMs) are most commonly studied by in silico multiple sequence alignment methods. Here, however, the structural dynamics are incorporated to give insight into the evolution of three ancestral proteins and the mechanism of several diseases in human ferritin protein. The differences in conformational dynamics of these evolutionary related, functionally diverged ancestral steroid receptor proteins are investigated by obtaining the most collective motion through essential dynamics. Strikingly, this analysis shows that evolutionary diverged proteins of the same family do not share the same dynamic subspace. Rather, those sharing the same function are simultaneously clustered together and distant from those functionally diverged homologs. This dynamics analysis also identifies 77% of mutations (functional and permissive) necessary to evolve new function. In silico methods for prediction of DAMs rely on differences in evolution rate due to purifying selection and therefore the accuracy of DAM prediction decreases at fast and slow evolvable sites. Here, we investigate structural dynamics through computing the contribution of each residue to the biologically relevant fluctuations and from this define a metric: the dynamic stability index (DSI). Using DSI we study the mechanism for three diseases observed in the human ferritin protein. The T30I and R40G DAMs show a loss of dynamic stability at the C-terminus helix and nearby regulatory loop, agreeing with experimental results implicating the same regulatory loop as a cause in cataracts syndrome.Dissertation/ThesisPh.D. Physics 201

Computational and Experimental Approaches to Reveal the Effects of Single Nucleotide Polymorphisms with Respect to Disease Diagnostics

DNA mutations are the cause of many human diseases and they are the reason for natural differences among individuals by affecting the structure, function, interactions, and other properties of DNA and expressed proteins. The ability to predict whether a given mutation is disease-causing or harmless is of great importance for the early detection of patients with a high risk of developing a particular disease and would pave the way for personalized medicine and diagnostics. Here we review existing methods and techniques to study and predict the effects of DNA mutations from three different perspectives: in silico, in vitro and in vivo. It is emphasized that the problem is complicated and successful detection of a pathogenic mutation frequently requires a combination of several methods and a knowledge of the biological phenomena associated with the corresponding macromolecules