Stationary states of an active Brownian particle in a harmonic trap.

We study the stationary states of an overdamped active Brownian particle (ABP) in a harmonic trap in two dimensions via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with a certain velocity, whose magnitude is constant, but its direction is subject to Brownian rotation. In the limit where translational diffusion is negligible, the stationary distribution of the particle's position shows a transition between two different shapes, one with maximum and the other with minimum density at the center, as the trap stiffness is increased.

Force-velocity relation and load-sharing in the linear polymerization ratchet revisited: the effects of barrier diffusion.

We study the velocity-force (V-F) relation for a Brownian ratchet consisting of a linear rigid polymer growing against a diffusing barrier, acted upon by a opposing constant force (F). Using a careful mathematical analysis, we derive the V-F relations in the extreme limits of fast and slow barrier diffusion. In the first case, V depends exponentially on the load F, in agreement with the well-known formula proposed by Peskin, Odell and Oster (1993), while the relationship becomes linear in the second case.

Microtubule catastrophe under force: mathematical and computational results from a Brownian ratchet model.

In the intracellular environment, the intrinsic dynamics of microtubule filaments is often hindered by the presence of barriers of various kind, such as kinetochore complexes and cell cortex, which impact their polymerisation force and dynamical properties such as catastrophe frequency. We present a theoretical study of the effect of a forced barrier, also subjected to thermal noise, on the statistics of catastrophe events in a single microtubule as well as a 'bundle' of two parallel microtubules. For microtubule dynamics, which includes growth, detachment, hydrolysis and the consequent dynamic instability, we employ a one-dimensional discrete stochastic model.

Detection of sub-degree angular fluctuations of the local cell membrane slope using optical tweezers.

Normal thermal fluctuations of the cell membrane have been studied extensively using high resolution microscopy and focused light, particularly at the peripheral regions of a cell. We use a single probe particle attached non-specifically to the cell-membrane to determine that the power spectral density is proportional to (frequency)-5/3 in the range of 5 Hz to 1 kHz. We also use a new technique to simultaneously ascertain the slope fluctuations of the membrane by relying upon the determination of pitch motion of the birefringent probe particle trapped in linearly polarized optical tweezers.

Spatio-temporal correlations between catastrophe events in a microtubule bundle: a computational study.

We explore correlations between dynamics of different microtubules in a bundle, via numerical simulations, using a one-dimensional stochastic model of a microtubule. The guanosine triphosphate (GTP)-bound tubulins undergo diffusion-limited binding to the tip. Random hydrolysis events take place along the microtubule and converts the bound GTP in tubulin to guanosine diphosphate (GDP).

Temporal cooperativity of motor proteins under constant force: insights from Kramers' escape problem.

The microtubule-bound motors kinesin and dynein differ in many respects, a striking difference being that while kinesin is known to function mostly alone, dynein operates in large groups, much like myosinV in actin. Optical tweezer experiments in vitro have shown that the mean detachment time of a bead attached to [Formula: see text] kinesins under stall conditions is a slowly decreasing function of [Formula: see text], while for dyneins, the time increases almost linearly with [Formula: see text]. This makes dynein a team worker, capable of producing and sustaining a large collective force without detaching.

Pyopericardium progressing to tamponade in a patient with immune thrombocytopenia.

Pericardial effusion can develop during any stage of pericarditis, and small effusions that appear rapidly can cause cardiac tamponade. Pyopericardium is a rare aetiology for tamponade. This is a case of an elderly diabetic lady, on steroid therapy for immune thrombocytopenia, who presented with fever and acute dyspnoea.

Polymerisation force of a rigid filament bundle: diffusive interaction leads to sublinear force-number scaling.

Polymerising filaments generate force against an obstacle, as in, e.g., microtubule-kinetochore interactions in the eukaryotic cell.

Ultrasensitivity and fluctuations in the Barkai-Leibler model of chemotaxis receptors in Escherichia coli.

A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is studied here with the goal of elucidating the effects of intrinsic network noise in their conformational dynamics. The model was originally proposed to explain the robust and near-perfect adaptation of E. coli observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations.

Transport of organelles by elastically coupled motor proteins.

Motor-driven intracellular transport is a complex phenomenon where multiple motor proteins simultaneously attached on to a cargo engage in pulling activity, often leading to tug-of-war, displaying bidirectional motion. However, most mathematical and computational models ignore the details of the motor-cargo interaction. A few studies have focused on more realistic models of cargo transport by including elastic motor-cargo coupling, but either restrict the number of motors and/or use purely phenomenological forms for force-dependent hopping rates.

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population.

Several independent observations have suggested that the catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al. [M.

Zero-order ultrasensitivity: a study of criticality and fluctuations under the total quasi-steady state approximation in the linear noise regime.

Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a 'push-pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking.

Memory, bias, and correlations in bidirectional transport of molecular-motor-driven cargoes.

Molecular motors are specialized proteins that perform active, directed transport of cellular cargoes on cytoskeletal filaments. In many cases, cargo motion powered by motor proteins is found to be bidirectional, and may be viewed as a biased random walk with fast unidirectional runs interspersed with slow tug-of-war states. The statistical properties of this walk are not known in detail, and here, we study memory and bias, as well as directional correlations between successive runs in bidirectional transport.

Microtubule catastrophe from protofilament dynamics.

The disappearance of the guanosine triphosphate- (GTP) tubulin cap is widely believed to be the forerunner event for the growth-shrinkage transition ("catastrophe") in microtubule filaments in eukaryotic cells. We study a discrete version of a stochastic model of the GTP cap dynamics, originally proposed by Flyvbjerg, Holy, and Leibler [Phys. Rev.

Effectiveness of a dynein team in a tug of war helped by reduced load sensitivity of detachment: evidence from the study of bidirectional endosome transport in D. discoideum.

Bidirectional cargo transport by molecular motors in cells is a complex phenomenon in which the cargo (usually a vesicle) alternately moves in retrograde and anterograde directions. In this case, teams of oppositely pulling motors (e.g.

A first-passage-time theory for search and capture of chromosomes by microtubules in mitosis.

The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work toward the formation of the spindle, one of which is the 'capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour.

Theoretical results for chemotactic response and drift of E. coli in a weak attractant gradient.

The bacterium Escherichia coli (E. coli) moves in its natural environment in a series of straight runs, interrupted by tumbles which cause change of direction. It performs chemotaxis towards chemo-attractants by extending the duration of runs in the direction of the source.

A catalytic role of heparin within the extracellular matrix.

We investigated the mechanism by which heparin enhances the binding of vascular endothelial growth factor (VEGF) to the extracellular matrix protein fibronectin. In contrast to other systems, where heparin acts as a protein scaffold, we found that heparin functions catalytically to modulate VEGF binding site availability on fibronectin. By measuring the binding of VEGF and heparin to surface-immobilized fibronectin, we show that substoichiometric amounts of heparin exposed cryptic VEGF binding sites within fibronectin that remain available after heparin removal.

Self-consistent theory of reversible ligand binding to a spherical cell.

Ligand binding to receptors is the initial event in many signaling processes, and a quantitative understanding of this interaction is important for modeling cell behavior. In this paper, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner.

Response and fluctuations of a two-state signaling module with feedback.

We study the stochastic kinetics of a signaling module consisting of a two-state stochastic point process with negative feedback. In the active state, a product is synthesized which increases the active-to-inactive transition rate of the process. We analyze this simple autoregulatory module using a path-integral technique based on the temporal statistics of state flips of the process.

Effects of receptor clustering on ligand dissociation kinetics: theory and simulations.

Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans (HSPGs), co-receptors for FGF-2.

Ligand rebinding: self-consistent mean-field theory and numerical simulations applied to surface plasmon resonance studies.

Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that the dissociation, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction.

Dynamics of a passive sliding particle on a randomly fluctuating surface.

We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square displacement of the sliding particle shows distinct dynamic scaling behavior, depending on whether the surface fluctuates faster or slower than the motion of the particle. When the surface fluctuations occur on a time scale much smaller than the particle motion, we find that the characteristic length scale shows anomalous diffusion with xi(t) approximately t(2phi), where phi approximately 0.

Ligand-induced coupling versus receptor pre-association: cellular automaton simulations of FGF-2 binding.

The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subsequent signal transduction is known to be enhanced by heparan sulfate proteoglycans (HSPGs). HSPGs bind FGF-2 with low affinity and likely impact CSR-mediated signaling via stabilization of FGF-2-CSR complexes via association with both the ligand and the receptor. What is unknown is whether HSPG associates with CSR in the absence of FGF-2.