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...

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Self-assembly of proteins into amyloid fibrils plays a key role in a multitude of human disorders that range from Alzheimer’s disease to type II diabetes. Compact oligomeric species, observed early during amyloid formation, are reported as the molecular entities responsible for the toxic effects of amyloid self-assembly. However, the relation between early-stage oligomeric aggregates and late-stage rigid fibrils, which are the hallmark structure of amyloid plaques, has remained unclear. We show that these different structures occupy well-defined regions in a peculiar phase diagram. Lysozyme amyloid oligomers and their curvilinear fibrils only form after they cross a salt and protein concentration-dependent threshold. We also determine a boundary for the onset of amyloid oligomer precipitation. The oligomeric aggregates are structurally distinct from rigid fibrils and are metastable against nucleation and growth of rigid fibrils. These experimentally determined boundaries match well with colloidal model predictions that account for salt-modulated charge repulsion. The model also incorporates the metastable and kinetic character of oligomer phases. Similarities and differences of amyloid oligomer assembly to metastable liquid–liquid phase separation of proteins and to surfactant aggregation are discussed.

We develop a theory for three states of equilibrium of amyloid peptides: the monomer, oligomer, and fibril. We assume that the oligomeric state is a disordered micellelike collection of a few peptide chains held together loosely by hydrophobic interactions into a spherical hydrophobic core. We assume that fibrillar amyloid chains are aligned and further stabilized by steric zipper interactions-hydrogen bonding, steric packing, and specific hydrophobic side-chain contacts. The model makes a broad set of predictions that are consistent with experimental results: 1), Similar to surfactant micellization, amyloid oligomerization should increase with peptide concentration in solution. 2), The onset of fibrillization limits the concentration of oligomers in the solution. 3), The extent of Aβ fibrillization increases with peptide concentration. 4), The predicted average fibril length versus monomer concentration agrees with data on α-synuclein. 5), Full fibril length distributions agree with data on α-synuclein. 6), Denaturants should melt out fibrils. And finally, 7), added salt should stabilize fibrils by reducing repulsions between amyloid peptide chains. It is of interest that small changes in solvent conditions can tip the equilibrium balance between oligomer and fibril and cause large changes in rates through effects on the transition-state barrier. This model may provide useful insights into the physical processes underlying amyloid diseases.

Antibody solutions are typically much more viscous than solutions of globular proteins at equivalent volume fraction. Here we propose that this is due to molecular entanglements that are caused by the elongated shape and intrinsic flexibility of antibody molecules. We present a simple theory in which the antibodies are modeled as linear polymers that can grow via reversible bonds between the antigen binding domains. This mechanism explains the observation that relatively subtle changes to the interparticle interaction can lead to large changes in the viscosity. The theory explains the presence of distinct power law regimes in the concentration dependence of the viscosity as well as the correlation between the viscosity and the charge on the variable domain in our anti-streptavidin IgG 1 model system.