Search PubMed⌕ Search

Biomedical subjects

Mehran Kardar

Publications and source records attributed to Mehran Kardar.

At least 19 recordsLinked to original sources
PubMed2006

Intricate knots in proteins: Function and evolution.

Our investigation of knotted structures in the Protein Data Bank reveals the most complicated knot discovered to date. We suggest that the occurrence of this knot in a human ubiquitin hydrolase might be related to the role of the enzyme in protein degradation. While knots are usually preserved among homologues, we also identify an exception in a transcarbamylase. This allows us to exemplify the function of knots in proteins and to suggest how they may have been created.

Bacterial Proteins↗
PubMed2006

Untangling influences of hydrophobicity on protein sequences and structures.

We perform a statistical analysis of solvent accessibility and hydrophobicity profiles of a representative set of proteins. The joint probability distribution is well fitted to a multivariable Gaussian, which takes a relatively simple form when expressed in terms of the Fourier transforms of the profiles. This allows us to quantify the asymmetric manner by which these profiles influence each other. For example, the alpha-helix periodicity in sequence hydrophobicity is dictated by the solvent accessibility of structures, and not vice versa, possibly indicating the faster evolution of sequences compared to structures. The decorrelated hydrophobicity and solvent accessibility profiles show distinct behaviors at long periods, where sequence hydrophobicity fluctuates less, while solvent accessibility fluctuates more than average. The correlations between the two profiles can be interpreted as the Boltzmann weight of the solvation energy at room temperature, consistent with earlier observations.

Amino Acid Sequence↗
PubMed2005

Knots in globule and coil phases of a model polyethylene.

We examine the statistics of knots with numerical simulations of a simplified model of polyethylene. We can simulate polymers of up to 1000 monomers (each representing roughly three CH(2) groups), at a range of temperatures spanning coil (good solvent) and globule (bad solvent) phases. We quantify the abundance of knots in the globule phase and in confined polymers, and their rarity in the swollen phase. Since our polymers are open, we consider (and test) various operational definitions for knots, which are rigorously defined only for closed chains. We also associate a typical size with individual knots, which are found to be small (tight and localized) in the swollen phase but large (loose and spread out) in the dense phases.

Journal Article↗
PubMed2005

Symmetry-breaking motility.

Locomotion of bacteria by actin polymerization and in vitro motion of spherical beads coated with a protein catalyzing polymerization are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.

Actins↗
PubMed2005

Apex exponents for polymer-probe interactions.

We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents gamma(1) and gamma(2), characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously with the tip's angle. These apex exponents are calculated analytically by epsilon expansion, and numerically by simulations in three dimensions. We find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.

Biopolymers↗
PubMed2005

Correlation and cross-linking effects in imprinting sites for divalent adsorption in gels.

We examine a method to mimic active sites in proteins by chemical imprinting of p-valent templates in heteropolymer gels. Previous studies have confirmed successful formation of sites by adsorption of targets with p >/= 2 contacts. We investigate the recovery of sites with p = 2 imprinted by lead methacrylate Pb(MAAc)(2) (placing two carboxyl groups in close proximity). The improved binding ability of gels with more cross-links, and the relative insensitivity to changes in gel volume contradict simple theory. We conclude that adsorber pairs are predominantly located on the same polymer chain, posing a challenge to mimicking protein-like function.

Adsorption↗
PubMed2004

Casimir forces, surface fluctuations, and thinning of superfluid film.

Recent experiments on the wetting of 4He have shown that the film becomes thinner at the lambda transition and in the superfluid phase. The difference in thickness above and below the transition has been attributed to a Casimir interaction which is a consequence of a broken continuous symmetry in the bulk superfluid. However, the observed thinning of the film is larger than can be accounted by this Casimir force. We show that surface fluctuations give rise to an additional force, similar in form but larger in magnitude, which may explain the observations.

Journal Article↗
PubMed2004

Information flow through a chaotic channel: prediction and postdiction at finite resolution.

We reconsider the persistence of information under the dynamics of the logistic map in order to discuss communication through a nonlinear channel where the sender can set the initial state of the system with finite resolution, and the recipient measures it with the same accuracy. We separate out the contributions of global phase-space shrinkage and local-phase space contraction and expansion to the uncertainty in predicting and postdicting the state of the system. We determine how the amplification parameter, the time lag, and the resolution influence the possibility for communication. A novel "clockwork" representation for real numbers is introduced that allows for a visualization of the flow of information between scales.

Journal Article↗
PubMed2004

Diffusion in correlated random potentials, with applications to DNA.

Many biological processes involve one-dimensional diffusion over a correlated inhomogeneous energy landscape with a correlation length xi(c). Typical examples are specific protein target location on DNA, nucleosome repositioning, or DNA translocation through a nanopore, in all cases with xi(c) approximately 10 nm. We investigate such transport processes by the mean first passage time (MFPT) formalism, and find diffusion times which exhibit strong sample to sample fluctuations. For a displacement N, the average MFPT is diffusive, while its standard deviation over the ensemble of energy profiles scales as N(3/2) with a large prefactor. Fluctuations are thus dominant for displacements smaller than a characteristic N(c) >> xi(c) : typical values are much less than the mean, and governed by an anomalous diffusion rule. Potential biological consequences of such random walks, composed of rapid scans in the vicinity of favorable energy valleys and occasional jumps to further valleys, is discussed.

Binding Sites↗
PubMed2004

Anomalous dynamics of forced translocation.

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (subdiffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N2 and N1+nu, respectively, where nu is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).

Journal Article↗
PubMed2003

Symmetry considerations and development of pinwheels in visual maps.

Neurons in the visual cortex respond best to rod-like stimuli of given orientation. While the preferred orientation varies continuously across most of the cortex, there are prominent pinwheel centers around which all orientations are present. Oriented segments abound in natural images and tend to be collinear; neurons are also more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. We verify that this requirement extends to cortical maps of monkey and cat by direct statistical analysis. Furthermore, analytical arguments and numerical studies indicate that pinwheels are generically stable in evolving field models that couple orientation and topography.

Animals↗
PubMed2003

Effective membrane model of the immunological synapse.

The immunological synapse is a patterned collection of different types of receptors and ligands that forms in the intercellular junction between T cells and antigen presenting cells during recognition. The synapse is implicated in information transfer between cells, and is characterized by different spatial patterns of receptors at different stages in the life cycle of T cells. We obtain a minimalist model that captures this experimentally observed phenomenology. A functional renormalization group analysis provides further insights.

Antigen-Presenting Cells↗
PubMed2003

Nonlinear stochastic equations with calculable steady states.

We consider generalizations of the Kardar-Parisi-Zhang equation that accommodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and nonperturbative properties. In particular, we derive generalized fluctuation-dissipation conditions on the form of the (nonlinear) equations for the realization of a Gaussian probability density of the fields in the steady state. For the amorphous growth of a single height field in one dimension we give a general class of equations with exactly calculable (Gaussian and more complicated) steady states. In two dimensions, we show that any anisotropic system evolves in long time and length scales either to the usual isotropic strong coupling regime or to a linearlike fixed point associated with a hidden symmetry. Similar results are derived for textural growth equations that couple the height field with additional order parameters which fluctuate on the growing surface. In this context, we propose phenomenological equations for the growth of a crystalline material, where the height field interacts with lattice distortions, and identify two special cases that obtain Gaussian steady states. In the first case compression modes influence growth and are advected by height fluctuations, while in the second case it is the density of dislocations that couples with the height.

Journal Article↗
PubMed2002

Information optimization in coupled audio-visual cortical maps.

Barn owls hunt in the dark by using cues from both sight and sound to locate their prey. This task is facilitated by topographic maps of the external space formed by neurons (e.g., in the optic tectum) that respond to visual or aural signals from a specific direction. Plasticity of these maps has been studied in owls forced to wear prismatic spectacles that shift their visual field. Adaptive behavior in young owls is accompanied by a compensating shift in the response of (mapped) neurons to auditory signals. We model the receptive fields of such neurons by linear filters that sample correlated audio-visual signals and search for filters that maximize the gathered information while subject to the costs of rewiring neurons. Assuming a higher fidelity of visual information, we find that the corresponding receptive fields are robust and unchanged by artificial shifts. The shape of the aural receptive field, however, is controlled by correlations between sight and sound. In response to prismatic glasses, the aural receptive fields shift in the compensating direction, although their shape is modified due to the costs of rewiring.

Acoustic Stimulation↗
PubMed2002

Knots in charged polymers.

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.

Journal Article↗
PubMed2002

Force-extension relations for polymers with sliding links.

Topological entanglements in polymers are mimicked by sliding rings (slip links) that enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip links create additional loops of variable sizes. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation. The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus-de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.

Journal Article↗
PubMed2002

Tightness of slip-linked polymer chains.

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip links) enforce pair contacts between monomers. These slip links divide a closed ring polymer into a number of subloops which can exchange length among each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.

Journal Article↗