What are the physical limits to cell behavior? Often, the physical limitations can be dominated by the proteome, the cell's complement of proteins. We combine known protein sizes, stabilities, and rates of folding and diffusion, with the known protein-length distributions PðNÞ of proteomes (Escherichia coli, yeast, and worm), to formulate distributions and scaling relationships in order to address questions of cell physics. Why do mesophilic cells die around 50°C? How can the maximal growth-rate temperature (around 37°C) occur so close to the cell-death temperature? The model shows that the cell's death temperature coincides with a denaturation catastrophe of its proteome. The reason cells can function so well just a few degrees below their death temperature is because proteome denaturation is so cooperative. Why are cells so dense-packed with protein molecules (about 20% by volume)? Cells are packed at a density that maximizes biochemical reaction rates. At lower densities, proteins collide too rarely. At higher densities, proteins diffuse too slowly through the crowded cell. What limits cell sizes and growth rates? Cell growth is limited by rates of protein synthesis, by the folding rates of its slowest proteins, and-for large cells-by the rates of its protein diffusion. Useful insights into cell physics may be obtainable from scaling laws that encapsulate information from protein knowledge bases. . So, some behaviors of cells are likely to be dominated by the physical properties of its proteomethe collection of its thousands of different types of proteins. We develop here some biophysical scaling relationships of proteomes, and we use those relationships to make estimates of the physical limits of cell behavior. Our scaling relationships come from combining current databases of the properties of proteins that have been measured in vitro, with PðNÞ, the length distributions of proteins that are known for several proteomes. Some of the hypotheses we explore are not new; what is previously undescribed is the use of modern databases to make quantitative estimates of physical limits. A key point, previously also made by Thirumalai (4), is that many physical properties of proteins just depend on N, the number of amino acids in the protein. We estimate the folding stabilities for mesophiles and thermophiles, the folding rates, and the diffusion coefficients of whole proteomes, and we compare these various rates at the end. We first consider the folding stabilities of proteomes.
Proteomes Are Marginally Stable to DenaturationFor at least 116 monomeric, two-state and reversible folding proteins there are calorimetric measurements of the folding stability, ΔG ¼ G unfolded − G folded , enthalpy ΔH, entropy ΔS, and heat capacity, ΔC p . Data are now available for both mesophilic and thermophilic proteins. Taken over the full set of proteins, these thermal quantities depend, remarkably, mainly just on the number, N, of amino acids in the chain. The relationship is simply linear. For both enthalpy and entropy the correlati...