Protein stability imposes limits on organism complexity and speed of molecular evolution

Abstract

Classical population genetics a priori assigns fitness to alleles without considering molecular or functional properties of proteins that these alleles encode. Here we study population dynamics in a model where fitness can be inferred from physical properties of proteins under a physiological assumption that loss of stability of any protein encoded by an essential gene confers a lethal phenotype. Accumulation of mutations in organisms containing Gamma genes can then be represented as diffusion within the Gamma-dimensional hypercube with adsorbing boundaries determined, in each dimension, by loss of a protein's stability and, at higher stability, by lack of protein sequences. Solving the diffusion equation whose parameters are derived from the data on point mutations in proteins, we determine a universal distribution of protein stabilities, in agreement with existing data. The theory provides a fundamental relation between mutation rate, maximal genome size, and thermodynamic response of proteins to point mutations. It establishes a universal speed limit on rate of molecular evolution by predicting that populations go extinct (via lethal mutagenesis) when mutation rate exceeds approximately six mutations per essential part of genome per replication for mesophilic organisms and one to two mutations per genome per replication for thermophilic ones. Several RNA viruses function close to the evolutionary speed limit, whereas error correction mechanisms used by DNA viruses and nonmutant strains of bacteria featuring various genome lengths and mutation rates have brought these organisms universally approximately 1,000-fold below the natural speed limit.

Fig. 1.

A schematic representation of the model. (Top) Illustration of the effect of sequence depletion as energy of the native state of a protein decreases. Middle and Bottom show the accessible range of native-state energies within which proteins can mutate. It is limited from below by E_min, where complete sequence depletion occurs. From above, this range is limited by E_max when proteins become unstable, conferring a lethal phenotype to the organism carrying this protein's gene. The range of possible energies is broader for mesophilic organisms and narrows for thermophilic ones.

Fig. 2.

Distribution of stabilities of single-domain proteins and the prediction (smooth line) from analytical equation (6) with parameters h and D derived from mutation data on proteins as explained in the text and in SI Text. The stability data were collected from the ProTherm database (18). The value ΔG_max − ΔG_min is taken to be 20 kcal/mol.

Fig. 3.

The distribution of number of genes per viral genome. The red histogram corresponds to RNA viruses, whereas the black histogram is for dsDNA viruses. The data are taken from National Center for Biotechnology Information Genome database, www.ncbi.nlm.nih.gov/genomes/static/vis.html. The genomes of RNA viruses are much shorter than those of dsDNA viruses.

Fig. 4.

Distribution of the number of genes in 202 prokaryotic genomes for organisms with various optimal growth temperatures. Thermophilic and hyperthermophilic organisms systematically possess shorter genomes than mesophilic ones.

Fig. 5.

Histogram of protein point mutation data obtained from the ProTherm database (15). Two kinds of unfolding methods, ΔΔG and ΔG_H2O, are considered separately, each with 2,804 and 2,418 different point mutations. The two groups of data produce the same shape of ΔΔG distribution. ΔΔG stands for the free energy of unfolding obtained with the Schellman equation (ΔΔG = dT_m/dS) in the case of the thermal denaturation method, whereas ΔΔG_H2O stands for the free energy of unfolding in water, determined by the denaturant (urea, guanidine·HCl, glutathione disulfide/GSH, and guanidine thiocyanate) denaturation of proteins and extrapolation of the data to zero concentration of denaturant; see ref. for more detailed explanations of experimental methods.