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Single-point mutations in the transmembrane (TM) region of receptor tyrosine kinases (RTKs) can lead to abnormal ligand-independent activation. We use a combination of computational modeling, NMR spectroscopy and cell experiments to analyze in detail the mechanism of how TM domains contribute to the activation of wild-type (WT) PDGFRA and its oncogenic V536E mutant. Using a computational framework, we scan all positions in PDGFRA TM helix for identification of potential functional mutations for the WT and the mutant and reveal the relationship between the receptor activity and TM dimerization via different interfaces. This strategy also allows us design a novel activating mutation in the WT (I537D) and a compensatory mutation in the V536E background eliminating its constitutive activity (S541G). We show both computationally and experimentally that single-point mutations in the TM region reshape the TM dimer ensemble and delineate the structural and dynamic determinants of spontaneous activation of PDGFRA via its TM domain. Our atomistic picture of the coupling between TM dimerization and PDGFRA activation corroborates the data obtained for other RTKs and provides a foundation for developing novel modulators of the pathological activity of PDGFRA.
We study the stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service times of a given customer are independent at the occupied servers. The service time has an exponential, phase-type or hyper-exponential distribution. We define an auxiliary service process that is the number of completed services by all m servers under the assumption that there are always customers in the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. It allows us to deduce the stability criterion of the model under consideration. It turns out that the stability condition does not depend on the structure of the input flow, only the rate of this process plays a role. Nevertheless the distribution of the service time is a very important factor. We give examples which show that the stability condition can not be expressed in terms of the mean of the service time.
model for deep bed filtration of a monodisperse suspension in a porous medium with multiple geometric
particle capture mechanisms is considered. It is assumed that identical suspended particles can block pores of
different sizes. The pores smaller than the particle size are clogged by single particles; if the pore size exceeds
the diameter of the particles, it can be blocked by bridging— several particles forming various stable structures.
An exact solution is obtained for constant filtration coefficients. Exact solutions for non-constant filtration
functions are obtained on the concentrations front of the suspended and retained particles and at the porous
medium inlet. Asymptotic solutions are constructed near these lines. For small and close to constant filtration
functions, global asymptotic solutions are obtained.
A basic model with two mechanisms of particle capture is studied in detail. Asymptotic solutions are compared
to the results of numerical simulation. The applicability of various types of asymptotics is analyzed.
The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion.
The counterion is assumed to freelymove around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume
contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in lowpolar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results ofMD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.
The anomalous magnetic moment (AMM) for excited states of an electron in a constant magnetic field has been calculated within the framework of two-dimensional electrodynamics. The analytical results for the interaction energy of the anomalous magnetic moment with the external magnetic field are obtained in two limiting cases of nonrelativistic and relativistic energy values in a comparatively weak magnetic field. It is shown that the interaction energy of the spin with the external field does not contain infrared divergence and tends to zero as magnetic field decreases, while the electron’s AMM increases logarithmically.
We study properties of generalized $K$-functionals and generalized moduli of smoothness in $L_p(\R)$ spaces with $1 \le p \le +\infty$. We obtain the direct Jackson type estimate and the inverse Bernstein type estimate for them. We state equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support generalized $K$-functionals generated by homogeneous function and generalized moduli of smoothness generated by $2\pi$-periodic generator subject to equivalence of their generators. We show that generalized $K$-functionals and generalized moduli of smoothness contain, as their special cases many well-known constructions of $K$-functionals and moduli of smoothness with an appropriate choice of the generators.
A procedure has been proposed for calculating limited orbits around the L2 libration points of the Sun–Earth system. The motion of a spacecraft in the vicinity of the libration point has been considered a superposition of three components, i.e., decreasing (stable), increasing (unstable), and limited. The proposed procedure makes it possible to correct the state vector of the spacecraft so as to neutralize the unstable component of the motion. Using this procedure, the calculation of orbits around various types of libration points has been carried out and the dependence on the orbit type on the initial conditions has been studied.
The filtration problem in a porous medium is an important part of underground hydromechanics. Filtration of suspensions and colloids determines the processes of strengthening the soil and creating waterproof walls in the ground while building the foundations of buildings and underground structures. It is assumed that the formation of a deposit is dominated by the size-exclusion mechanism of pore blocking: solid particles pass freely through large pores and get stuck at the inlet of pores smaller than the diameter of the particles. A one-dimensional mathematical model for the filtration of a monodisperse suspension includes the equation for the mass balance of suspended and retained particles and the kinetic equation for the growth of the deposit. For the blocking filtration coefficient with a double root, the exact solution is given implicitly. The asymptotics of the filtration problem is constructed for large time. The numerical calculation of the problem is carried out by the finite differences method. It is shown that asymptotic approximations rapidly converge to a solution with the increase of the expansion order.
Control of Discrete-Time Descriptor Systems takes an anisotropy-based approach to the explanation of random input disturbance with an information-theoretic representation. It describes the random input signal more precisely, and the anisotropic norm minimization included in the book enables readers to tune their controllers better through the mathematical methods provided. The book contains numerous examples of practical applications of descriptor systems in various fields, from robotics to economics, and presents an information-theoretic approach to the mathematical description of coloured noise. Anisotropy-based analysis and design for descriptor systems is supplied along with proofs of basic statements, which help readers to understand the algorithms proposed, and to undertake their own numerical simulations. This book serves as a source of ideas for academic researchers and postgraduate students working in the control of discrete-time systems. The control design procedures outlined are numerically effective and easily implementable in MATLAB®
We propose new deterministic and stochastic models for synchronization of clocks in nodes of distributed networks. An external accurate time server is used to ensure convergence of the node clocks to the exact time. These systems have much in common with mathematical models of opinion formation in multiagent systems. There is a direct analogy between the time server/node clocks pair in asynchronous networks and the leader/follower pair in the context of social network models.
We consider the problem of flow of a viscous compressible subsonic fluid along a flat plate with small localized (hump-type) irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of the flow in the thin boundary layer (i.e., in the near-boundary region).
We investigate critical properties of a spatial evolutionary game based on the Prisoner’s Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases
In this paper, we describe the Desmos cluster that consists of 32 hybrid nodes connected by a low-latency high-bandwidth torus interconnect. This cluster is aimed at cost-effective classical molecular dynamics calculations. We present strong scaling benchmarks for GROMACS, LAMMPS and VASP and compare the results with other HPC systems. This cluster serves as a test bed for the Angara interconnect that supports 3D and 4D torus network topologies, and verifies its ability to unite MPP systems speeding-up effectively MPI-based applications. We describe the interconnect presenting typical MPI benchmarks.
Here, we present a new model of adsorption-induced deformation of mesoporous solids. The model is based on a simplified version of local density functional theory in the framework of solvation free energy. Instead of density, which is treated as constant here, we used film thickness and pore radius as order parameters. This allows us to obtain a self-consistent system of equations describing simultaneously the processes of gas adsorption and adsorbent deformation, as well as conditions for capillary condensation and evaporation. In the limit of infinitely rigid pore walls, when the film becomes several monolayers thick, the model reduces to the well-known Derjaguin–Broekhoff–de Boer theory for pores with cylindrical geometry. We have investigated the effects of enhanced flexibility of the solid as well as the influence of pore size distribution on the adsorption/deformation process. The formulation of the theory allows to determine the average pore size and its width from the desorption branch of the strain isotherm only. The model reproduces the nonmonotonic behavior of the strain isotherm at low relative pressure. Furthermore, we discuss the effect of rigidity of the adsorbent on the pore size distribution, showing qualitatively different results of the adsorption isotherms for rigid and highly flexible materials, in particular, the shift of evaporation pressure to lower values and the absence of a limiting value of the loading at high relative pressure. We also discuss the results of the theory with respect to experimental data obtained from the literature.
Depending on the scales of periodic irregularities in the problem under study, a solution arises which describes two (“double-deck”) or three (“triple-deck”) boundary layers on the plate. Mainly, we study the equations describing the velocity oscillations in the boundary layers arising because of periodic irregularities and show their command nature.
We study the Chandler wobble (CW) of the pole from 1846 to 2017 extracted by the Panteleev ltering. The CW has period of 433 days, average amplitude of 0.13 milliarcseconds (mas) which is changing, and phase jump by pi in 1930-th. The CW amplitude strongly (almost to zero) decreases in 1930-th and 2010-th with the phase jump in 1930th. The envelope model contains 83- and 42-years quasi-periodicities. We think the rst one can be represented by the 166-years changes of the envelope, crossing zero in 1930th. We reconstruct Chandler input excitation based on the Euler-Liouville equation. Its amplitude has 20-years variations. We explain this based on simple model and prove, that they appear in consequence of 42-years modulation of CW. The excitation ampli es the amplitude of CW for 20 years then damps it for another 20 years. The analysis of the modulated CW signal in a sliding window demonstrates the specific effect, we called the "escargot effect", when instantaneous "virtual" retrograde component appears in the purely prograde (at long-time interval) signal. Chandler excitation envelope shape is similar to this instantaneous retrograde component, which re ects the changes of ellipticity of the approximation ellipse.
A Euclidean distance matrix D(α) is defined by D_ij=(α_i−α_j)^2, where α=(α_1,…,α_n) is a real vector. We prove that D(α) cannot be written as a sum of [2sqrt(n)−2] nonnegative rank-one matrices, provided that the coordinates of α are algebraically independent. As a corollary, we provide an asymptotically optimal separation between the complexities of quantum and classical communication protocols computing a given matrix in expectation.
In this Review, we present a critical analysis of various applications of the Flory-type theories to a theoretical description of the conformational behavior of single polymer chains in dilute polymer solutions under a few external stimuli. Different theoretical models of flexible polymer chains in the supercritical fluid are discussed and analysed. Different points of view on the conformational behavior of the polymer chain near the liquid–gas transition critical point of the solvent are presented. A theoretical description of the co-solvent-induced coilglobule transitions within the implicit-solvent-explicit-co-solvent models is discussed. Several explicit-solvent-explicit-co-solvent theoretical models of the coil-to-globule-to-coil transition of the polymer chain in a mixture of good solvents (co-nonsolvency) are analysed and compared with each other. Finally, a new theoretical model of the conformational behavior of the dielectric polymer chain under the external constant electric field in the dilute polymer solution with an explicit account for the many-body dipole correlations is discussed. The polymer chain collapse induced by many-body dipole correlations of monomers in the context of statistical thermodynamics of dielectric polymers is analysed.