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 which are determined, in each dimension, by loss of a protein 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 6 mutations per essential part of genome per replication for mesophilic organisms and 1 to 2 mutations per genome per replication for thermophilic ones. Further, our results suggest that in absence of error correction, modern RNA viruses and primordial genomes must necessarily be very short. Several RNA viruses function close to the evolutionary speed limit while error correction mechanisms used by DNA viruses and non-mutant strains of bacteria featuring various genome lengths and mutation rates have brought these organisms universally about 1000 fold below the natural speed limit.