arXiv subjects

Marek Cieplak

Publications and source records attributed to Marek Cieplak.

At least 73 records · Page 4Linked to original sources

arXiv2001

Motion of grains, droplets, and bubbles in fluid-filled nano-pores

Molecular dynamics studies of nono-sized rigid grains, droplets and bubbles in nano-sized pores indicate that the drag force may have a hydrodynamic form if the moving object is dense and small compared to the pore diameter. Otherwise, the behavior is non-hydrodynamic. The terminal speed is insensitive to whether the falling droplet is made of liquid or a solid. The velocity profiles within droplets and bubbles that move in the pore are usually non-parabolic and distinct from those corresponding to individual fluids. The density profiles indicate motional shape distortion of the moving objects.

cond-mat.stat-mech↗

arXiv2001

Kinetic non-optimality and vibrational stability of proteins

Scaling of folding times in Go models of proteins and of decoy structures with the Lennard-Jones potentials in the native contacts reveal %robust power law trends when studied under optimal folding conditions. The power law exponent depends on the type of native geometry. Its value indicates lack of kinetic optimality in the model proteins. In proteins, mechanical and thermodynamic stabilities are correlated.

cond-mat.stat-mech↗

arXiv2001

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

cond-mat.stat-mech↗

arXiv2000

Boundary conditions at a fluid - solid interface

We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities, and both simple and chain-molecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.

cond-mat.stat-mech↗

arXiv2000

Amino acid classes and the protein folding problem

We present and implement a distance-based clustering of amino acids within the framework of a statistically derived interaction matrix and show that the resulting groups faithfully reproduce, for well-designed sequences, thermodynamic stability in and kinetic accessibility to the native state. A simple interpretation of the groups is obtained by eigenanalysis of the interaction matrix.

cond-mat.stat-mech↗

arXiv2000

Sequencing of folding events in Go-like proteins

We have studied folding mechanisms of three small globular proteins: crambin (CRN), chymotrypsin inhibitor 2 (CI2) and the fyn Src Homology 3 domain (SH3) which are modelled by a Go-like Hamiltonian with the Lennard-Jones interactions. It is shown that folding is dominated by a well-defined sequencing of events as determined by establishment of particular contacts. The order of events depends primarily on the geometry of the native state. Variations in temperature, coupling strengths and viscosity affect the sequencing scenarios to a rather small extent. The sequencing is strongly correlated with the distance of the contacting aminoacids along the sequence. Thus $α$-helices get established first. Crambin is found to behave like a single-route folder, whereas in CI2 and SH3 the folding trajectories are more diversified. The folding scenarios for CI2 and SH3 are consistent with experimental studies of their transition states.

cond-mat.stat-mech↗

arXiv2000

Molecular dynamics of flows in the Knudsen regime

Novel technological applications often involve fluid flows in the Knudsen regime in which the mean free path is comparable to the system size. We use molecular dynamics simulations to study the transition between the dilute gas and the dense fluid regimes as the fluid density is increased.

cond-mat.stat-mech↗

arXiv2000

Dynamical chaos and power spectra in toy models of heteropolymers and proteins

The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied by molecular dynamics simulations. It is shown that two nearby trajectories quickly diverge from each other if the heteropolymer corresponds to a random sequence. For good folders, on the other hand, two nearby trajectories may initially move apart but eventually they come together. Thus good folders are intrinsically non-chaotic. A choice of a distance of the initial conformation from the native state affects the way in which a separation between the twin trajectories behaves in time. This observation allows one to determine the size of a folding funnel in good folders. We study the energy landscapes of the toy models by determining the power spectra and fractal characteristics of the dependence of the potential energy on time. For good folders, folding and unfolding trajectories have distinctly different correlated behaviors at low frequencies.

cond-mat.stat-mech↗

arXiv2000

Molecular dynamics of folding of secondary structures in Go-type models of proteins

We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic aminoacid-aminoacid potential is Lennard Jones for the native contacts and a soft repulsion for the non-native contacts. The interactions are chosen to make the target secondary structure be the native state of the system. We provide a thorough equilibrium and kinetic characterization of the sequences through the molecular dynamics simulations with the Langevin noise. Models with the steric constraints are found to be better folders and to be more stable, especially in the case of the $β$-structures. Phononic spectra for vibrations around the native states have low frequency gaps that correlate with the thermodynamic stability. Folding of the secondary structures proceeds through a well defined sequence of events. For instance, $α$-helices fold from the ends first. The closer to the native state, the faster establishment of the contacts. Increasing the system size deteriorates the folding characteristics. We study the folding times as a function of viscous friction and find a regime of moderate friction with the linear dependence. We also consider folding when one end of a structure is pinned which imitates instantaneous conditions when a protein is being synthesized. We find that, under such circumstances, folding of helices is faster and of the $β$-sequences slower.

cond-mat.stat-mech↗

arXiv1999

Spin analogs of proteins: scaling of "folding" properties

Reaching a ground state of a spin system is analogous to a protein evolving into its native state. We study the ``folding'' times for various random Ising spin systems and determine characteristic temperatures that relate to the ``folding''. Under optimal kinetic conditions, the ``folding'' times scale with the system size as a power law with a non-universal exponent. This is similar to what happens in model proteins. On the other hand, the scaling behavior of the characteristic temperatures is different than in model proteins. Both in the spin systems and in proteins, the folding properties deteriorate with the system size.

cond-mat.stat-mech↗

arXiv1999

Energy landscapes, supergraphs, and "folding funnels" in spin systems

Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of the system in a unified coarse-grained sense. We give examples of the supergraphs for several two dimensional spin and protein-related systems. We demonstrate that disordered ferromagnets have supergraphs akin to those of model proteins whereas spin glasses behave like random sequences of aminoacids which fold badly.

cond-mat.stat-mech↗

arXiv1999

Delineation of the Native Basin in Continuum Models of Proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.

cond-mat.soft↗

arXiv1999

Folding in two-dimenensional off-lattice models of proteins

Model off-lattice sequences in two dimensions are constructed so that their native states are close to an on-lattice target. The Hamiltonian involves the Lennard-Jones and harmonic interactions. The native states of these sequences are determined with a high degree of certainty through Monte Carlo processes. The sequences are characterized thermodynamically and kinetically. It is shown that the rank-ordering-based scheme of the assignment of contact energies typically fails in off-lattice models even though it generates high stability of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in which the interaction potentials are restricted to the native contacts in a target shape, gives rise to good folding properties. Involving other contacts deteriorates these properties.

cond-mat.soft↗

arXiv1999

Scaling of folding properties in simple models of proteins

Scaling of folding properties of proteins is studied in a toy system -- the lattice Go model with various two- and three- dimensional geometries of the maximally compact native states. Characteristic folding times grow as power laws with the system size. The corresponding exponents are not universal. Scaling of the thermodynamic stability also indicates size-related deterioration of the folding properties.

cond-mat.stat-mech↗

arXiv1999

Simple models of proteins with repulsive non-native contacts

The Go model is extended to the case when the non-native contact energies may be either attractive or repulsive. The folding temperature is found to increase with the energy of non-native contacts. The repulsive non-native contact energies may lead to folding at T=0 for some two-dimensional sequences and to reduction in complexity of disconnectivity graphs for local energy minima.

cond-mat.soft↗

arXiv1999

Master equation approach to protein folding

The dynamics of two 12-monomer heteropolymers on the square lattice is studied exactly within the master equation approach. The time evolution of the occupancy of the native state is determined. At low temperatures, the median folding time follows the Arrhenius law and is governed by the longest relaxation time. For good folders, significant kinetic traps appear in the folding funnel whereas for bad folders, the traps also occur in non-native energy valleys.

cond-mat.stat-mech↗

arXiv1998

Protein folding and models of dynamics on the lattice

We study folding in 16-monomer heteropolymers on the square lattice. For a given sequence, thermodynamic properties and stability of the native state are unique. However, the kinetics of folding depends on the model of dynamics adopted for the time evolution of the system. We consider three such models: Rouse-like dynamics with either single monomer moves or with single and double monomer moves, and the 'slithering snake' dynamics. Usually, the snake dynamics has poorer folding properties compared to the Rouse-like dynamics, but examples of opposite behavior can also be found. This behavior relates to which conformations act as local energy minima when their stability is checked against the moves of a particular dynamics. A characteristic temperature related to the combined probability, $P_L$, to stay in the non-native minima during folding coincides with the temperature of the fastest folding. Studies of $P_L$ yield an easy numerical way to determine conditions of the optimal folding.

cond-mat.stat-mech↗

arXiv1998

Coarse grained description of the protein folding

We consider two- and three-dimensional lattice models of proteins which were characterized previously. We coarse grain their folding dynamics by reducing it to transitions between effective states. We consider two methods of selection of the effective states. The first method is based on the steepest descent mapping of states to underlying local energy minima and the other involves an additional projection to maximally compact conformations. Both methods generate connectivity patterns that allow to distinguish between the good and bad folders. Connectivity graphs corresponding to the folding funnel have few loops and are thus tree-like. The Arrhenius law for the median folding time of a 16-monomer sequence is established and the corresponding barrier is related to easily identifiable kinetic trap states.

cond-mat.stat-mech↗