Marek Cieplak

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 by 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.

Cellular automata studies of mixing in chaotic flows

Abstract Results of cellular automata based studies of mixing in a square cavity are presented. Two periodic models are considered: one in which two walls move in opposite directions one at a time and the other in which they act simultaneously but alternate the directions of motion. Both flows are found to be chaotic and the Poincare sections and Lyapunov exponents are determined. The morphology of mixing is different in the two cases.

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.

Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns

We describe a method based on the principle of entropy maximization to identify the gene interaction network with the highest probability of giving rise to experimentally observed transcript profiles. In its simplest form, the method yields the pairwise gene interaction network, but it can also be extended to deduce higher-order interactions. Analysis of microarray data from genes in Saccharomyces cerevisiae chemostat cultures exhibiting energy metabolic oscillations identifies a gene interaction network that reflects the intracellular communication pathways that adjust cellular metabolic activity and cell division to the limiting nutrient conditions that trigger metabolic oscillations. The success of the present approach in extracting meaningful genetic connections suggests that the maximum entropy principle is a useful concept for understanding living systems, as it is for other complex, nonequilibrium systems.

Molecular origins of friction: the force on adsorbed layers.

Simulations and perturbation theory are used to study the molecular origins of friction in an ideal model system, a layer of adsorbed molecules sliding over a substrate. These calculations reproduce several surprising features of experimental results. In most cases, the frictional force on a solid monolayer has a different form from that observed between macroscopic solids. No threshold force or static friction is needed to initiate sliding; instead, the velocity is proportional to the force. As in experiments, incommensurate solid layers actually slide more readily than fluid layers. A comparison of experiment, simulation, and analytic results shows that dissipation arises from anharmonic coupling between phonon modes and substrate-induced deformations in the adsorbate.

Mechanical stretching of proteins—a theoretical survey of the Protein Data Bank

The mechanical stretching of single proteins has been studied experimentally for about 50 proteins, yielding a variety of force patterns and peak forces. Here we perform a theoretical survey of proteins of known native structure and map out the landscape of possible dynamical behaviours under stretching at constant speed. We consider 7510 proteins comprising not more than 150 amino acids and 239 longer proteins. The model used is constructed based on the native geometry. It is solved by methods of molecular dynamics and validated by comparing the theoretical predictions to experimental results. We characterize the distribution of peak forces and investigate correlations with the system size and with the structure classification as characterized by the CATH scheme. Despite the presence of such correlations, proteins with the same CATH index may belong to different classes of dynamical behaviour. We identify proteins with the biggest forces and show that they belong to few topology classes. We determine which protein segments act as mechanical clamps and show that, in most cases, they correspond to long stretches of parallel β-strands, but other mechanisms are also possible.

Universality Classes in Folding Times of Proteins

Molecular dynamics simulations in simplified models allow one to study the scaling properties of folding times for many proteins together under a controlled setting. We consider three variants of the Go models with different contact potentials and demonstrate scaling described by power laws and no correlation with the relative contact order parameter. We demonstrate existence of at least three kinetic universality classes that are correlated with the types of structure: the alpha-, alpha-beta-, and beta- proteins have the scaling exponents of approximately 1.7, 2.5, and 3.2, respectively. The three classes merge into one when the contact range is truncated at a reasonable value. We elucidate the role of the potential associated with the chirality of a protein.

On the remarkable mechanostability of scaffoldins and the mechanical clamp motif

Protein mechanostability is a fundamental biological property that can only be measured by single-molecule manipulation techniques. Such studies have unveiled a variety of highly mechanostable modules (mainly of the Ig-like, β-sandwich type) in modular proteins subjected to mechanical stress from the cytoskeleton and the metazoan cell–cell interface. Their mechanostability is often attributed to a “mechanical clamp” of secondary structure (a patch of backbone hydrogen bonds) fastening their ends. Here we investigate the nanomechanics of scaffoldins, an important family of scaffolding proteins that assembles a variety of cellulases into the so-called cellulosome, a microbial extracellular nanomachine for cellulose adhesion and degradation. These proteins anchor the microbial cell to cellulose substrates, which makes their connecting region likely to be subjected to mechanical stress. By using single-molecule force spectroscopy based on atomic force microscopy, polyprotein engineering, and computer simulations, here we show that the cohesin I modules from the connecting region of cellulosome scaffoldins are the most robust mechanical proteins studied experimentally or predicted from the entire Protein Data Bank. The mechanostability of the cohesin modules studied correlates well with their mechanical kinetic stability but not with their thermal stability, and it is well predicted by computer simulations, even coarse-grained. This extraordinary mechanical stability is attributed to 2 mechanical clamps in tandem. Our findings provide the current upper limit of protein mechanostability and establish shear mechanical clamps as a general structural/functional motif widespread in proteins putatively subjected to mechanical stress. These data have important implications for the scaffoldin physiology and for protein design in biotechnology and nanotechnology.

Universality Classes of Optimal Channel Networks

Energy minimization of both homogeneous and heterogeneous river networks shows that, over a range of parameter values, there are only three distinct universality classes. The exponents for all three classes of behavior are calculated.

Selection of Optimal Variants of Gō-Like Models of Proteins through Studies of Stretching

The Gō-like models of proteins are constructed based on the knowledge of the native conformation. However, there are many possible choices of a Hamiltonian for which the ground state coincides with the native state. Here, we propose to use experimental data on protein stretching to determine what choices are most adequate physically. This criterion is motivated by the fact that stretching processes usually start with the native structure, in the vicinity of which the Gō-like models should work the best. Our selection procedure is applied to 62 different versions of the Gō model and is based on 28 proteins. We consider different potentials, contact maps, local stiffness energies, and energy scales--uniform and nonuniform. In the latter case, the strength of the nonuniformity was governed either by specificity or by properties related to positioning of the side groups. Among them is the simplest variant: uniform couplings with no i, i + 2 contacts. This choice also leads to good folding properties in most cases. We elucidate relationship between the local stiffness described by a potential which involves local chirality and the one which involves dihedral and bond angles. The latter stiffness improves folding but there is little difference between them when it comes to stretching.