Kingshuk Ghosh

Physical limits of cells and proteomes

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 P(N) 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.

Polyelectrolyte solutions with added salt: A simulation study

Using Langevin dynamics simulations, we have investigated the distribution of counterions around a flexible polyelectrolyte chain as a function of polymer concentration (Cp), salt concentration (Cs), and valency of the counterion from the added salt. In the present simulations, the aqueous solutions are at room temperatures and polymer concentrations are either below or comparable to overlap concentrations. The net polymer charge and the radius of gyration (Rg) of a labeled chain are found to decrease with an increase in either Cp or Cs. We present details of the distribution of monovalent and divalent counterions inside the counterion worm surrounding a polymer chain, when a salt-free solution of polyelectrolytes with monovalent counterions is challenged by a salt with divalent counterions. The simulation results for the dependence of Rg on chain length (N), Cp and Cs are compared with the theory of Muthukumar [J. Chem. Phys. 86, 7230 (1987); 105, 5183 (1996)] which contains two parameters, viz., degree ...

What Drives Amyloid Molecules To Assemble into Oligomers and Fibrils

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.

Computing protein stabilities from their chain lengths

New amino acid sequences of proteins are being learned at a rapid rate, thanks to modern genomics. The native structures and functions of those proteins can often be inferred using bioinformatics methods. We show here that it is also possible to infer the stabilities and thermal folding properties of proteins, given only simple genomics information: the chain length and the numbers of charged side chains. In particular, our model predicts ΔH(T), ΔS(T), ΔCp, and ΔF(T) —the folding enthalpy, entropy, heat capacity, and free energy—as functions of temperature T; the denaturant m values in guanidine and urea; the pH-temperature-salt phase diagrams, and the energy of confinement F(s) of the protein inside a cavity of radius s. All combinations of these phase equilibria can also then be computed from that information. As one illustration, we compute the pH and salt conditions that would denature a protein inside a small confined cavity. Because the model is analytical, it is computationally efficient enough that it could be used to automatically annotate whole proteomes with protein stability information.

How Do Thermophilic Proteins and Proteomes Withstand High Temperature

We attempt to understand the origin of enhanced stability in thermophilic proteins by analyzing thermodynamic data for 116 proteins, the largest data set achieved to date. We compute changes in entropy and enthalpy at the convergence temperature where different driving forces are maximally decoupled, in contrast to the majority of previous studies that were performed at the melting temperature. We find, on average, that the gain in enthalpy upon folding is lower in thermophiles than in mesophiles, whereas the loss in entropy upon folding is higher in mesophiles than in thermophiles. This implies that entropic stabilization may be responsible for the high melting temperature, and hints at residual structure or compactness of the denatured state in thermophiles. We find a similar trend by analyzing a homologous set of proteins classified based only on the optimum growth temperature of the organisms from which they were extracted. We find that the folding free energy at the temperature of maximal stability is significantly more favorable in thermophiles than in mesophiles, whereas the maximal stability temperature itself is similar between these two classes. Furthermore, we extend the thermodynamic analysis to model the entire proteome. The results explain the high optimal growth temperature in thermophilic organisms and are in excellent quantitative agreement with full thermal growth rate data obtained in a dozen thermophilic and mesophilic organisms.

Cellular Proteomes Have Broad Distributions of Protein Stability

Biological cells are extremely sensitive to temperature. What is the mechanism? We compute the thermal stabilities of the whole proteomes of Escherichia coli, yeast, and Caenorhabditis elegans using an analytical model and an extensive database of stabilities of individual proteins. Our results support the hypothesis that a cells thermal sensitivities arise from the collective instability of its proteins. This model shows a denaturation catastrophe at temperatures of 49-55°C, roughly the thermal death point of mesophiles. Cells live on the edge of a proteostasis catastrophe. According to the model, it is not that the average protein is problematic; it is the tail of the distribution. About 650 of E. colis 4300 proteins are less than 4 kcal mol(-1) stable to denaturation. And upshifting by only 4° from 37° to 41°C is estimated to destabilize an average protein by nearly 20%. This model also treats effects of denaturants, osmolytes, and other physical stressors. In addition, it predicts the dependence of cellular growth rates on temperature. This approach may be useful for studying physical forces in biological evolution and the role of climate change on biology.

Maximum Caliber: A variational approach applied to two-state dynamics

We show how to apply a general theoretical approach to nonequilibrium statistical mechanics, called Maximum Caliber, originally suggested by E. T. Jaynes [Annu. Rev. Phys. Chem. 31, 579 (1980)], to a problem of two-state dynamics. Maximum Caliber is a variational principle for dynamics in the same spirit that Maximum Entropy is a variational principle for equilibrium statistical mechanics. The central idea is to compute a dynamical partition function, a sum of weights over all microscopic paths, rather than over microstates. We illustrate the method on the simple problem of two-state dynamics, A<-->B, first for a single particle, then for M particles. Maximum Caliber gives a unified framework for deriving all the relevant dynamical properties, including the microtrajectories and all the moments of the time-dependent probability density. While it can readily be used to derive the traditional master equation and the Langevin results, it goes beyond them in also giving trajectory information. For example, we derive the Langevin noise distribution rather than assuming it. As a general approach to solving nonequilibrium statistical mechanics dynamical problems, Maximum Caliber has some advantages: (1) It is partition-function-based, so we can draw insights from similarities to equilibrium statistical mechanics. (2) It is trajectory-based, so it gives more dynamical information than population-based approaches like master equations; this is particularly important for few-particle and single-molecule systems. (3) It gives an unambiguous way to relate flows to forces, which has traditionally posed challenges. (4) Like Maximum Entropy, it may be useful for data analysis, specifically for time-dependent phenomena.

Evidence of multiple folding pathways for the villin headpiece subdomain.

The defining property of two-state models of protein folding is that the measured relaxation rates are independent of the starting conditions and only depend on the final conditions. In this work we compare the kinetics of the very fast folding villin subdomain measured after a large change in denaturant concentration using an ultrarapid microfluidic mixer with the kinetics measured after a small temperature change in a laser T-jump experiment and find a significant difference in the observed folding kinetics. The final conditions of temperature and denaturant concentration and the use of tryptophan fluorescence as a probe are the same in both experiments, while the initial conditions are very different. The slower mixing kinetics show no evidence of the faster phase in T-jump experiments, which would support models of on- or off-pathway intermediates. Rather we interpret the combined mixer and T-jump experiments as evidence of an ensemble of unfolded states, some of which are traps. The ensemble after dilution from high denaturant is more expanded than the ensemble after an increase in temperature and, on average, takes longer to reach the native state.

Configurational properties of a single semiflexible polyelectrolyte

Using a variational calculation, we have considered the effect of chain length, intrinsic backbone stiffness, solvent quality, and salt concentration on the behavior of a single semiflexible polyelectrolyte in dilute solution. Explicitly, we have calculated the radius of gyration (Rg) and effective persistence length for different solvent qualities and salt concentrations. For an isolated semiflexible polyelectrolyte with increasing molecular weight, there can be five regimes with effective exponent ν (defining the molecular weight dependence of Rg) being 1, 1/2, 1, 2/5, and 1/2 in the absence of nonelectrostatic excluded volume interaction. This suggests a double crossover behavior from rodlike to Gaussian and then to Gaussian again as the chain length is increased. During the second crossover, ν can be as high as 1, although the actual value of Rg is order of magnitude smaller than the rodlike value. There can be another regime in this second crossover where the apparent exponent is 2/5 due to additiona...

Particle-hopping models of vehicular traffic: Distributions of distance headways and distance between jams

We calculate the distribution of the distance headways (i.e., the instantaneous gap between successive vehicles) as well as the distribution of instantaneous distance between successive jams in the Nagel-Schreckenberg (NS) model of vehicular traffic. When the maximum allowed speed, Vmax, of the vehicles is larger than unity, over an intermediate range of densities of vehicles, our Monte Carlo (MC) data for the distance headway distribution exhibit two peaks, which indicate the coexistence of “free-flowing” traffic and traffic jams. Our analytical arguments clearly rule out the possibility of occurrence of more than one peak in the distribution of distance headways in the NS model when Vmax=1 as well as in the asymmetric simple exclusion process. Modifying and extending an earlier analytical approach for the NS model with Vmax=1, and introducing a novel transfer matrix technique, we also calculate the exact analytical expression for the distribution of distance between the jams in this model; the corresponding distributions for Vmax > 1 have been computed numerically through MC simulation.