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Classical population genetics a priori assigns fitness to alleles withoutconsidering molecular or functional properties of proteins that these allelesencode. Here we study population dynamics in a model where fitness can beinferred from physical properties of proteins under a physiological assumptionthat loss of stability of any protein encoded by an essential gene confers alethal phenotype. Accumulation of mutations in organisms containing Gamma genescan then be represented as diffusion within the Gamma dimensional hypercubewith adsorbing boundaries which are determined, in each dimension, by loss of aprotein stability and, at higher stability, by lack of protein sequences.Solving the diffusion equation whose parameters are derived from the data onpoint mutations in proteins, we determine a universal distribution of proteinstabilities, in agreement with existing data. The theory provides a fundamentalrelation between mutation rate, maximal genome size and thermodynamic responseof proteins to point mutations. It establishes a universal speed limit on rateof molecular evolution by predicting that populations go extinct (via lethalmutagenesis) when mutation rate exceeds approximately 6 mutations per essentialpart of genome per replication for mesophilic organisms and 1 to 2 mutationsper genome per replication for thermophilic ones. Further, our results suggestthat in absence of error correction, modern RNA viruses and primordial genomesmust necessarily be very short. Several RNA viruses function close to theevolutionary speed limit while error correction mechanisms used by DNA virusesand non-mutant strains of bacteria featuring various genome lengths andmutation rates have brought these organisms universally about 1000 fold belowthe natural speed limit.

The Hypercube of Life: How Protein Stability Imposes Limits on Organism Complexity and Speed of Molecular Evolution