An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

Folding and Aggregation of Designed Proteins

Studies of how protein fold have shown that the way protein clumps form in the test tube is similar to how proteins form the so-called ``amyloid'' deposits that are the pathological signal of a variety of diseases, among them the memory disorder Alzheimer's. Protein aggregation have traditionally been connected to either unfolded or native states. Inclusion body formation (disordered aggregation) has been assumed to arise from hydrophobic aggregation of the unfolded or denaturated states, while the amyloid fibrils (ordered aggregation) have been assumed to arise from native-like conformations in a process analogous to the polymerization of hemoglobin S. Making use of lattice-model simulations we find that both ordered and disordered aggregation arise from elementary structures which eventually build the folding nucleus of the heteropolymers, and takes place when some of the most strongly interacting amino acids establish their contacts leading to the formation of a specific subset of the native structure. These elementary structures can be viewed as the partially folded intermediates suggested to be involved in the aggregation of a number of proteins. These results have evolutionary implications, as the elementary structures forming the folding core of designed proteins contain the residues which are conserved among the members of homologous sequences.Comment: 10 pages, 2 colour ps figures and 1 b/w ps figur

Soluble oligomerization provides a beneficial fitness effect on destabilizing mutations.

Protein stability is widely recognized as a major evolutionary constraint. However, the relation between mutation-induced perturbations of protein stability and biological fitness has remained elusive. Here we explore this relation by introducing a selected set of mostly destabilizing mutations into an essential chromosomal gene of E.coli encoding dihydrofolate reductase (DHFR) to determine how changes in protein stability, activity and abundance affect fitness. Several mutant strains showed no growth while many exhibited fitness higher than wild type. Overexpression of chaperonins (GroEL/ES) buffered the effect of mutations by rescuing the lethal phenotypes and worsening better-fit strains. Changes in stability affect fitness by mediating the abundance of active and soluble proteins; DHFR of lethal strains aggregates, while destabilized DHFR of high fitness strains remains monomeric and soluble at 30oC and forms soluble oligomers at 42oC. These results suggest an evolutionary path where mutational destabilization is counterbalanced by specific oligomerization protecting proteins from aggregation

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