Structurally constrained protein evolution: results from a lattice simulation

We simulate the evolution of a protein-like sequence subject to point mutations, imposing conservation of the ground state, thermodynamic stability and fast folding. Our model is aimed at describing neutral evolution of natural proteins. We use a cubic lattice model of the protein structure and test the neutrality conditions by extensive Monte Carlo simulations. We observe that sequence space is traversed by neutral networks, i.e. sets of sequences with the same fold connected by point mutations. Typical pairs of sequences on a neutral network are nearly as different as randomly chosen sequences. The fraction of neutral neighbors has strong sequence to sequence variations, which influence the rate of neutral evolution. In this paper we study the thermodynamic stability of different protein sequences. We relate the high variability of the fraction of neutral mutations to the complex energy landscape within a neutral network, arguing that valleys in this landscape are associated to high values of the neutral mutation rate. We find that when a point mutation produces a sequence with a new ground state, this is likely to have a low stability. Thus we tentatively conjecture that neutral networks of different structures are typically well separated in sequence space. This result indicates that changing significantly a protein structure through a biologically acceptable chain of point mutations is a rare, although possible, event. Received 8 July 1999     

A new hierarchy system on the basis of a “Master” Boltzmann equation for microscopic density

It is shown that Boltzmann's equation written in terms of microscopic density (namely the unaveraged Boltzmann function) has a wider range of validity as well as finer resolvability for fluctuations than the conventional Boltzmann equation governing Boltzmann's function. In fact the new Boltzmann equation for ideal gases has implications as a microscopically exact continuity equation like Klimontovich's equation for plasmas, and can be derived without invoking any statistical concepts, e.g., distribution functions, or molecular chaos. The Boltzmann equation in the older formalism is obtained by averaging this equation only under a restricted condition of the molecular chaos. The new Boltzmann equation is seen to contain information comparable with Liouville's equation, and serves as a master kinetic equation. A new hierarchy system is formulated in a certain parallelism to the BBGKY hierarchy. They are shown to yield an identical one-particle equation. The difference between the two hierarchy systems first appears in the two-particle equation. The difference is twofold. First, the present formalism includes thermal fluctuations that are missing in the BBGKY formalism. Second, the former allows us to formulate multi-time correlations as well, whereas the latter is restricted to simultaneous correlation. These two features are favorably utilized in deriving the Landau-Lifshitz fluctuation law in a most straightforward manner. Also, equations describing the nonequilibrium interaction between thermal and fluid-dynamical fluctuations are derived.     

Regulatory networks and connected components of the neutral space

The functioning of a living cell is largely determined by the structure of its regulatory network, comprising non-linear interactions between regulatory genes. An important factor for the stability and evolvability of such regulatory systems is neutrality – typically a large number of alternative network structures give rise to the necessary dynamics. Here we study the discretized regulatory dynamics of the yeast cell cycle [Li et al., PNAS, 2004] and the set of networks capable of reproducing it, which we call functional. Among these, the empirical yeast wildtype network is close to optimal with respect to sparse wiring. Under point mutations, which establish or delete single interactions, the neutral space of functional networks is fragmented into ≈ 4.7 × 10⁸ components. One of the smaller ones contains the wildtype network. On average, functional networks reachable from the wildtype by mutations are sparser, have higher noise resilience and fewer fixed point attractors as compared with networks outside of this wildtype component.     

Current-induced conformational switching in single-molecule junctions

Current-induced conformational switching in single-molecule junctions constitutes a fundamental process in molecular electronics. Motivated by recent experiments on azobenzene derivatives, we study this process for molecules which exhibit two (meta)stable conformations in the neutral state but only a single stable conformation in the ionic state. We derive and analyze appropriate Fokker–Planck equations obtained from a density-matrix formalism starting from a generic model and present comprehensive analytical and numerical results for the switching dynamics in general and the quantum yield in particular.     

Statistical transport theory of reacting two-component fluid: Light scattering from an A⇄B liquid

A theory of light scattering from a simple A?B reacting fluid in which molecular anisotropy has been neglected is presented. The theory is a molecular-statistical one based on Mori's linear response formalism. The time-dependent correlation functions are associated with transport coefficients and the zero time correlation functions are associated with thermodynamic derivatives. The effects of the reaction are observed from both density and concentration fluctuations as well as from cross correlations between density and concentration fluctuations.     

Optimal Control of Trapped Electron Instability by a Modulated Neutral Beam

Equivalent lumped parameter system representation for dissipative trapped electron instability involving many modes is obtained. Optimal control theory in the presence of noise is used to design a stabilizing feedback network, with a modulated neutral beam as a remote suppressor. The optimality criterion is the minimization of the total energy of control and instability fluctuations. It is shown that the control power does not depend on the level of instability fluctuations in the absence of feedback, but on the noise level in plasma.     

Thermo-optical sensitivity analysis in photonic crystal circuits based on semiconducting or metallic metamaterial constituents

We introduce a novel analysis technique for predicting thermo-optical sensitivities in photonic crystal (PC) circuits composed of either dielectric-semiconducting or metallic constituents. The proposed numerical analysis is based on a hybrid formalism of the scattering matrix technique combined with the adjoint network method. The proposed computational scheme can, with modest computational resources, predict with high accuracy, the effect of the temperature fluctuations to the light-wave propagation in PCs. Numerical simulations show that PC circuits based on metallic metamaterial platforms are significantly less sensitive to temperature variations than the usual dielectricor semiconducting PCs.     

Diffusion controlled multiplicative process: typical versus average behaviour

We investigate the dynamics of the number of particles diffusing in a multiplicative medium. We show that the typical behaviour of the growth process is different from the average. We develop a new formalism to study the average growth process and extend it to the calculation of higher moments and finally of the probability distribution. We show that the fluctuations of the growth process increase exponentially with time. We describe the interesting features of the distribution.     

Molecular evolution under fitness fluctuations

Molecular evolution is a stochastic process governed by fitness, mutations, and reproductive fluctuations in a population. Here, we study evolution where fitness itself is stochastic, with random switches in the direction of selection at individual genomic loci. As the correlation time of these fluctuations becomes larger than the diffusion time of mutations within the population, fitness changes from an annealed to a quenched random variable. We show that the rate of evolution has its maximum in the crossover regime, where both time scales are comparable. Adaptive evolution emerges in the quenched fitness regime (evidence for such fitness fluctuations has recently been found in genomic data). The joint statistical theory of reproductive and fitness fluctuations establishes a conceptual connection between evolutionary genetics and statistical physics of disordered systems.     

Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (γ= 2/(3-q)) between the anomalous diffusion exponent γ and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.     

Quantum-mechanical description of the initial stage of fusion reaction

Projectile-nucleus capture by a target nucleus at bombarding energies in the vicinity of the Coulomb barrier is treated on the basis of the reduced-density-matrix formalism. The effect of dissipation and fluctuations on the capture process is taken into account self-consistently within this model. Cross sections for evaporation-residue formation in asymmetric-fusion reactions are found by using the calculated capture probabilities averaged over all orientations of the deformed projectile or target nucleus.     

Constraints on operator ordering from third quantization

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.     

Stochastic dynamics of adaptive evolutionary search

In this paper the stochastic dynamics of adaptive evolutionary search, as performed by the optimization algorithm Population-Based Incremental Learning, is analyzed with physicists' methods for stochastic processes. The master equation of the process is approximated by van Kampen's small fluctuations assumption. It results in an elegant formalism which allows for an understanding of the macroscopic behaviour of the algorithm together with its fluctuations. We consider the search process to be adaptive since the algorithm iteratively reduces its mutation rate while approaching an optimum. On the one hand, it is this feature which allows the algorithm to quickly converge towards an optimum. On the other hand it results in the possibility to get trapped by a local optimum only. To arrive at a detailed understanding we discuss the influence of fluctuations, as caused by mutation, on this behaviour. We study the algorithm for rather small sytem sizes in order to gain an intuitive understanding of the algorithm's performance.     

Newly calculated absolute cross-section for the electron-impact ionization of C2H2 +

New measurements of the cross-section for electron impact ionization of the molecular ion C₂H₂⁺ have been carried out recently. These data differ significantly from earlier data, because cross-sections corresponding to all the possible dissociative ionization processes were determined. The new data in conjunction with the significant discrepancies between the earlier data and the results of various calculations, which disagreed among themselves by a factor of 3, motivated a renewed attempt to apply the semi-classical Deutsch-M?rk (DM) formalism to the calculation of the absolute electron-impact ionization cross-section of this molecular ion. A quantum chemical molecular orbital population analysis for both the neutral molecule and the ion revealed that in the case of C₂H₂⁺ the singly occupied molecular orbital (i.e. the “missing” electron) is highly localized near the site of a C atom in the molecule. This information is explicitly incorporated in our formalism. The results obtained by taking the ionic character directly into account are in excellent agreement with the recent experimental data.     

Kaon condensation in the color–flavor-locked phase of quark matter, the Goldstone theorem, and the 2PI Hartree approximation

At very high densities, QCD is in the color–flavor-locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an O(2)×O(2)-symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the temperature and the chemical potentials. We use the 2-particle irreducible effective action formalism in the Hartree approximation. The renormalization of the gap equations and the effective potential is studied in detail and we show that the counterterms are independent of temperature and chemical potentials. We determine the phase diagram and the medium-dependent quasiparticle masses. It is shown that the Goldstone theorem is satisfied to a very good approximation. The effects of imposing electric charge neutrality is examined as well.     

On the Langevin formalism for nonlinear and nonequilibrium hydrodynamic fluctuations

The Landau-Lifshitz method of fluctuating hydrodynamics is generalized to the cases of nonlinear and nonequilibrium fluctuations. For a simple one-component fluid, the multiplicative random fluxes are constructed by using universal Gaussian variables with variances independent of the specific parameters of a fluid. It is shown that the nonlinear Langevin formalism proposed is equivalent to the approach based on the hydrodynamic Fokker-Planck equation derived earlier by statistical-mechanical methods. Then, the scheme is extended to the case of two-component fluids, where cross effects must be taken into account. In conclusion, the connection of the present formalism with the Keizer approach to nonequilibrium fluctuations is discussed.     

A confirmation of agreement of different approaches for?scalar?gauge-invariant metric perturbations during inflation

We revisit an extension of the well-known formalism for gauge-invariant scalar metric fluctuations to study the spectra for both the inflaton and gauge-invariant (scalar) metric fluctuations in the framework of a single-field inflationary model, in which the quasi-exponential expansion is driven by an inflaton which is minimally coupled to gravity. The proposal here examined is valid also for fluctuations with large amplitudes, but for cosmological scales, where vector and tensor perturbations can be neglected and the fluid is irrotacional.     

Influence of environment and entropy production of a nonequilibrium open system

In the time-dependent projection operator formalism, the influence of environment upon a nonequilibrium open system is analyzed and an entropy equation is derived. The entropy production rate is given in terms of correlation functions of fluctuations of random forces and interacting random forces and cast into the Volterra equation formalism.