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Sorption in disordered porous media
The lattice-gas model of sorption in disordered porous media is studied for a variety of
settings, using existing, updated and newly developed numerical techniques. Firstly, we
construct an efficient algorithm to calculate the exact partition function for small lattice-gas
systems. The exact partition function is used for detailed analysis of the core features exhibited
by such systems. We proceed to develop an interactive Monte Carlo (MC) simulation
engine, that simulates sorption in a porous media sample and provides real-time visual
data of the state space projection and the 3d view of the sample among other parameters
of interest, as the external fields are manipulated. The use of such tool provides a more
intuitive understanding of the system behaviour. The MC simulations are employed to study
sorption in several porous solids: silica aerogel, Vycor glass and soil. We investigate how the
phenomena depend on the microstructure of the original samples, how the behaviour varies
with the external conditions, and how it is reflected in the paths that the system takes across
its state space. Secondly, we develop two methods for estimation of the relative degeneracy
(the number of microstates that have the same value of some macroscopic variables) in the
systems that are too large to be handled exactly. The methods, based on a restricted infinite
temperature sampling, obtain equidegenerate surfaces and the degeneracy gradient across the
state space. Combined with the knowledge of an internal energy of a microstate, it enables
us to construct the free energy map and thus the equilibrium probability distribution for the
studied projection of the state space. Thirdly, the jump-walking Monte-Carlo algorithm is revisited
and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity.
It is designed for a single processing thread as opposed to currently predominant algorithms
for large parallel processing systems. The updated algorithm is tested on the Ising model and
applied to the lattice-gas model for sorption in aerogel and Vycor glass at low temperatures,
when dynamics of the system is significantly slowed down. It is demonstrated that the
updated jump-walking simulations are able to produce equilibrium isotherms which are
typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.
As a result, we answer the long standing question about the existence of the first-order phase
transitions in Vycor. Finally, we investigate sorption in several distinct topology network
representations of soil and aerogel samples and demonstrate that the recently developed
analytical techniques for random networks can be used to achieve a qualitative understanding
of the phenomena in real materials.EPSR
Protein Biophysics Explains Why Highly Abundant Proteins Evolve Slowly
The consistent observation across all kingdoms of life that highly abundant proteins evolve slowly demonstrates that cellular abundance is a key determinant of protein evolutionary rate. However, other empirical findings, such as the broad distribution of evolutionary rates, suggest that additional variables determine the rate of protein evolution. Here, we report that under the global selection against the cytotoxic effects of misfolded proteins, folding stability (ΔG), simultaneous with abundance, is a causal variable of evolutionary rate. Using both theoretical analysis and multiscale simulations, we demonstrate that the anticorrelation between the premutation ΔG and the arising mutational effect (ΔΔG), purely biophysical in origin, is a necessary requirement for abundance–evolutionary rate covariation. Additionally, we predict and demonstrate in bacteria that the strength of abundance–evolutionary rate correlation depends on the divergence time separating reference genomes. Altogether, these results highlight the intrinsic role of protein biophysics in the emerging universal patterns of molecular evolution