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Thomas A. Vilgis

Publications and source records attributed to Thomas A. Vilgis.

At least 19 recordsLinked to original sources

Identifying sequential residue patterns in bitter and umami peptides

The primary structures of peptides, originating from food proteins, affect their taste. Connecting primary structure to taste, however, is difficult because the size of the peptide sequence space increases exponentially with increasing peptide length, while experimentally-labeled data on peptides' tastes remain scarce. We propose a method that coarse-grains the sequence space to reduce its size and systematically identifies the most common coarse-grained residue patterns found in known bitter and umami peptides. We select the optimal patterns by performing extensive out-of-sample tests. The optimal patterns better represent the bitter and umami peptides when compared against baseline peptides, bitter peptides with all hydrophobic residues and umami peptides with all negatively charged residues, and peptides with randomly-chosen residues. Our method complements quantitative structure--activity relationship methods by offering generic, coarse-grained bitter and umami residue patterns that can aid in locating short bitter or umami segments in a protein and in designing new umami peptides.

physics.chem-ph↗

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time $<τ>$ decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 ÷4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time $<τ>$ declines with growing contour length $L$ as $<τ>\propto L^{-0.17}$, and with side chain length as $<τ>\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.

cond-mat.soft↗

Dynamics of a three-dimensional inextensible chain

In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the $z-$axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is similar to the reduction of the statistical mechanics of a directed polymer to the random walk of a two-dimensional particle.

cond-mat.stat-mech↗

A path integral approach to the dynamics of a random chain with rigid constraints

In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.

cond-mat.stat-mech↗

Adsorption of Multi-block and Random Copolymer on a Solid Surface: Critical Behavior and Phase Diagram

The adsorption of a single multi-block $AB$-copolymer on a solid planar substrate is investigated by means of computer simulations and scaling analysis. It is shown that the problem can be mapped onto an effective homopolymer adsorption problem. In particular we discuss how the critical adsorption energy and the fraction of adsorbed monomers depend on the block length $M$ of sticking monomers $A$, and on the total length $N$ of the polymer chains. Also the adsorption of the random copolymers is considered and found to be well described within the framework of the annealed approximation. For a better test of our theoretical prediction, two different Monte Carlo (MC) simulation methods were employed: a) off-lattice dynamic bead-spring model, based on the standard Metropolis algorithm (MA), and b) coarse-grained lattice model using the Pruned-enriched Rosenbluth method (PERM) which enables tests for very long chains. The findings of both methods are fully consistent and in good agreement with theoretical predictions.

cond-mat.soft↗

Globular Structures of a Helix-Coil Copolymer: Self-Consistent Treatment

A self-consistent field theory was developed in the grand-canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths correspondingly. The resulting field-theory takes, in addition to the conventional Zimm-Bragg (B.H. Zimm, I.K. Bragg, J. Chem. Phys. 31, 526 (1959)) parameters, also three-dimensional interaction terms into account. The appropriate differential equations which determine the self-consistent fields were solved numerically with finite element method. Three different phase states are found: open chain, amorphous globule and nematic liquid-crystalline (LC) globule. The LC-globule formation is driven by the interplay between the hydrophobic helical segments attraction and the anisotropic globule surface energy of an entropic nature. The full phase diagram of the helix-coil copolymer was calculated and thoroughly discussed. The suggested theory shows a clear interplay between secondary and tertiary structures in globular homopolypeptides.

cond-mat.soft↗

Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment

We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with chain length $N$ and block length $M$ as $τ_{\perp} \propto M^{1+2ν}$ (here $ν\approx 0.6$ is the Flory exponent) and as $τ_{\parallel} \propto N^2$, although initially the rate of coil flattening is expected to decrease with block size as $\propto M^{-1}$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface. We also demonstrate that these scaling predictions agree well with the results of extensive Monte Carlo simulations of the localization dynamics.

cond-mat.soft↗

Entropically driven transition to a liquid-crystalline polymer globule

A self-consistent-field theory (SCFT) in the grand canonical ensemble formulation is used to study transitions in a helix-coil multiblock copolymer globule. The helices are modeled as stiff rods. In addition to the established coil-globule transition we show for the first time that, even without explicit rod-rod alignment interaction, the system undergoes a transition to a nematic liquid-crystalline (LC) globular state. The LC-globule formation is driven by the hydrophobic helical segment attraction and the anisotropy of the globule surface energy. The full phase diagram of the copolymer was calculated. It discriminates between an open chain, amorphous globule and LC-globule. This model provides a relatively simple example of the interplay between secondary and tertiary structures in homopolypeptides. Moreover, it gives a simple explanation for the formation of helix bundles in certain globular proteins.

cond-mat.soft↗

Self-consistent variational theory for globules

A self-consistent variational theory for globules based on the uniform expansion method is presented. This method, first introduced by Edwards and Singh to estimate the size of a self-avoiding chain, is restricted to a good solvent regime, where two-body repulsion leads to chain swelling. We extend the variational method to a poor solvent regime where the balance between the two-body attractive and the three-body repulsive interactions leads to contraction of the chain to form a globule. By employing the Ginzburg criterion, we recover the correct scaling for the $θ$-temperature. The introduction of the three-body interaction term in the variational scheme recovers the correct scaling for the two important length scales in the globule - its overall size $R$, and the thermal blob size $ξ_{T}$. Since these two length scales follow very different statistics - Gaussian on length scales $ξ_{T}$, and space filling on length scale $R$ - our approach extends the validity of the uniform expansion method to non-uniform contraction rendering it applicable to polymeric systems with attractive interactions. We present one such application by studying the Rayleigh instability of polyelectrolyte globules in poor solvents. At a critical fraction of charged monomers, $f_c$, along the chain backbone, we observe a clear indication of a first-order transition from a globular state at small $f$, to a stretched state at large $f$; in the intermediate regime the bistable equilibrium between these two states shows the existence of a pearl-necklace structure.

cond-mat.soft↗

Directed Polymers with Constrained Winding Angle

In this article we study from a non-perturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac $δ-$function potential. An exact formula of the so-called second moment of the winding angle is derived. This result is used to provide a thorough analysis of entanglement phenomena in the classical system of two polymers subjected to repulsive interactions and related problems. No approximation is made in treating the constraint on the winding angle and the repulsive forces. In particular, we investigate how repulsive forces influence the entanglement degree of the two-polymer system. In the limit of ideal polymers, in which the interactions are switched off, we show that our results are in agreement with those of previous works.

cond-mat.soft↗

Localization of a multiblock copolymer at a selective interface: Scaling predictions and Monte Carlo verification

We investigate the localization of a hydrophobic - polar (HP) - regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length $M$ on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter χ. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D is also derived. We implement a dynamic off-lattice Monte - Carlo model to verify these scaling predictions. For chain lengths in a wide range (32 < N < 512) we find good agreement with the scaling predictions.

cond-mat.soft↗

Constrained dynamics of a polymer ring enclosing a constant area

The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the Lagrange multiplier function which is time dependent. The time dependence of the Lagrange multiplier is evaluated in a closed form both at short and long times. At long times, the time dependence is weak, and is mainly governed by the inverse of the first mode of the area. The presence of the constraint changes the nature of the relaxation of the internal modes. The time correlation of the position vectors of the ring is found to be dominated by the first Rouse mode which does not relax even at very long times. The mean square displacement of the radius vector is found to be diffusive, which is associated with the rotational diffusion of the ring.

cond-mat.soft↗

Semiflexible polymers in a random environment

We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degrees of flexibility and allows us to propose a phase diagram for the highly folded (localized) states of semiflexible polymers as a function of the disorder strength and chain rigidity.

cond-mat.soft↗

Localization and freezing of a Gaussian chain in a quenched random potential

The Gaussian chain in a quenched random potential (which is characterized by the disorder strength $Δ$) is investigated in the $d$ - dimensional space by the replicated variational method. The general expression for the free energy within so called one - step - replica symmetry breaking (1 - RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of this expression can describe the chain center of mass localization and collapse. The critical disorder when the chain becomes localized scales as $Δ_c \simeq b^d N^{-2 + d/2}$ (where $b$ is the length of the Kuhn segment length and $N$ is the chain length) whereas the chain gyration radius $R_{\rm g} \simeq b (b^d/Δ)^{1/(4 - d)}$. The freezing of the internal degrees of freedom follows to the 1-RSB - scenario and is characterized by the beads localization length $\bar{{\cal D}^2}$. It was demonstrated that the solution for $\bar{{\cal D}^2}$ appears as a metastable state at $Δ= Δ_A$ and behaves similarly to the corresponding frozen states in heteropolymers or in $p$ - spin random spherical model.

cond-mat.soft↗

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, $(Δ/b^d) N^{2 - νd} \ge 1$, where $Δ$ is a disorder strength, $b$ is a Kuhnian segment length, $N$ is a chain length and $ν$ is the Flory exponent. We have derived the general equation for the non - ergodicity function $f(p)$ which characterizes the amplitude of frozen Rouse modes with an index $p = 2πj/N$. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength $Δ_c \sim N^{-γ}$ where the exponent $γ\approx 0.25$ and does not depend from the solvent quality.

cond-mat.stat-mech↗

Single Chain Force Spectroscopy: Sequence Dependence

We study the elastic properties of a single A/B copolymer chain with a specific sequence. We predict a rich structure in the force extension relations which can be addressed to the sequence. The variational method is introduced to probe local minima on the path of stretching and releasing. At given force, we find multiple configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which unravel cooperatively. Upon stretching, unfolding path shows stepwise pattern corresponding to the unfolding of each domain. While releasing, several cores can be created simultaneously in the middle of the chain resulting in a different path of collapse.

cond-mat.soft↗