arXiv subjects

Manoj Gopalakrishnan

Publications and source records attributed to Manoj Gopalakrishnan.

At least 19 recordsLinked to original sources

arXiv2026

Origin of Persistent Boundary Motion in Confined Active Matter

Active matter systems under confinement display persistent surface motion and a strong boundary affinity. However, despite extensive studies of their positional dynamics, much less attention has been given to the corresponding orientational behavior. Here, using molecular simulations of an active Brownian particle confined within a hard circular boundary and the Fokker-Planck equation, we show that the positional distribution of the particle is directly coupled to orientational fluctuations, as characterized by the conditional orientational distribution. Confinement generates two preferred tangential orientational states connected by stochastic flipping pathways: rapid boundary-localized switching and slower bulk-mediated excursions. Further, the positional distribution exhibits a nontrivial power-law decay with distance from the boundary that is closely linked to curvature-induced bistable orientational states and the variance of the associated conditional distribution. The mean waiting time between flips exhibits power-law dependence on the confinement strength. Our results establish that the interplay between orientational fluctuations, bistability, positional accumulation, and stochastic switching governs the observed dynamics of active particles under confinement, providing a framework for understanding transport, exploration, and escape processes in confined active systems.

cond-mat.soft↗

arXiv2025

Active particles in power-law potentials: steady state distributions and shape transitions

We study the stationary states of an active Brownian particle (ABP) and run-and-tumble particle (RTP) in two dimensional power-law potentials, in the limit where translational diffusion is negligible. The potential energy of the particle has the form $U(r)\propto r^{n}$, where $n\geq 2$ and even. In two dimensions, we derive the exact equations for the positional probability distribution $\phi({\bf r})$ of ABP ($n\geq 2)$ and RTP ($n=2$), whose solutions are obtained under the assumption that the particle's orientation angle is Gaussian. Both analytical and numerical results show that, in all cases, $\phi({\bf r})$ has compact support and undergoes a phase transition-like shape change as a function of the trap strength. For ABP, our theory predicts a continuous transition in shape for $n=2$ and a discontinuous transition for $n>2$, both of which agree with the simulation results. Simulations suggest the existence of both types of shape transition in the case of RTP as well. For ABP, in the strongly active regime, the orientational probability distribution is unimodal near the outer boundary but becomes bimodal towards the interior, signifying a transition from predominantly radial orientation to orbiting motion. In RTP, the analogous shape transition in the orientational distribution is almost absent.

cond-mat.soft↗

arXiv2024

Curvature dependent dynamics of a bacterium confined in a giant unilamellar vesicle

We investigate the positional behavior of a single bacterium confined within a vesicle by measuring the probability of locating the bacterium at a certain distance from the vesicle boundary. We observe that the distribution is bi-exponential in nature. Near the boundary, the distribution exhibits rapid exponential decay, transitioning to a slower exponential decay, and eventually becoming uniform further away from the boundary. The length scales associated with the decay are found to depend on the confinement radius. We interpret these observations using molecular simulations and analytical calculations based on the Fokker-Planck equation for an Active Brownian Particle model. Our findings reveal that the small length scale is strongly influenced by the translational diffusion coefficient, while the larger length scale is governed by rotational diffusivity and self-propulsion. These results are explained in terms of two dimensionless parameters that explicitly include the confinement radius. The scaling behavior predicted analytically for the observed length scales is confirmed through simulations.

cond-mat.soft↗

arXiv2023

Stationary states of an active Brownian particle in a harmonic trap

We study the stationary states of an over-damped 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 centre, as the trap stiffness is increased. We show that this non-intuitive behaviour is captured by the relevant Fokker-Planck equation, which, under minimal assumptions, predicts a continuous ``phase transition" between the two different shapes. As the translational diffusion coefficient is increased, both these distributions converge into the equilibrium, Boltzmann form. Our simulations support the analytical predictions, and also show that the probability distribution of the orientation angle of the self-propulsion velocity undergoes a transition from unimodal to bimodal forms in this limit. We also extend our simulations to a three dimensional trap, and find similar behaviour.

cond-mat.stat-mech↗

arXiv2020

Detection of sub-degree fluctuations of the local cellmembrane 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)^(-1.66) 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. In the process, we also develop the technique to identify pitch rotation to a high resolu-tion using optical tweezers. We find that the power spectrum of slope fluctuations is proportional to 1/(frequency), which we also explain theoretically. We find that we can extract parameters like bending rigidity directly from the coefficient of the power spectrum particularly at high frequencies,instead of being convoluted with other parameters, thereby improving the accuracy of estimation.We anticipate this technique for determination of the pitch angle in spherical particles to high resolution as a starting point for many interesting studies using the optical tweezers

physics.bio-ph↗

arXiv2018

A path-integral formulation of the run and tumble motion and chemotaxis in Escherichia coli

Bacteria such as Escherichia coli move about in a series of runs and tumbles: while a run state (straight motion) entails all the flagellar motors spinning in counterclockwise mode, a tumble is caused by a shift in the state of one or more motors to clockwise spinning mode. In the presence of an attractant gradient in the environment, runs in the favourable direction are extended, and this results in a net drift of the organism in the direction of the gradient. The underlying signal transduction mechanism produces directed motion through a bi-lobed response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration. The two lobes (positive and negative) of the response function are separated by a time interval of $\sim 1$s, such that the bacterium effectively compares the concentration at two different positions in space and responds accordingly. We present here a novel path-integral method which allows us to address this problem in the most general way possible, including multi-step CW-CCW transitions, directional persistence and power-law waiting time distributions. The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, in a power series expansion in the attractant gradient. Explicit results in the lowest order in the expansion are presented for specific models, which, wherever applicable, agree with the known results. New results for gamma-distributed run interval distributions are also presented.

q-bio.QM↗

arXiv2017

Ultrasensitivity and Fluctuations in the Barkai-Leibler Model of Chemotaxis Receptors in {\it Escherichia coli}

A stochastic version of the Barkai-Leibler model of chemotaxis receptors in {\it E. coli} is studied here to elucidate the effects of intrinsic network noise in their conformational dynamics. It was originally proposed to explain the robust and near-perfect adaptation of {\it E. coli} observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations. A receptor is either active or inactive and can stochastically switch between the two states. Enzyme CheR methylates inactive receptors while CheB demethylates active ones and the probability for it to be active depends on its level of methylation and ligandation. A simple version of the model with two methylation sites per receptor (M=2) shows zero-order ultrasensitivity (ZOU) akin to the classical 2-state model of covalent modification studied by Goldbeter and Koshland (GK). For extremely small and large ligand concentrations, the system reduces to two 2-state GK modules. A quantitative measure of the spontaneous fluctuations in activity (variance) estimated mathematically under linear noise approximation (LNA) is found to peak near the ZOU transition. The variance is a weak, non-monotonic and decreasing functions of ligand and receptor concentrations. Gillespie simulations for M=2 show excellent agreement with analytical results obtained under LNA. Numerical results for M=2, 3 and 4 show ZOU in mean activity; the variance is found to be smaller for larger M. The magnitude of receptor noise deduced from available experimental data is consistent with our predictions. A simple analysis of the downstream signaling pathway shows that this noise is large enough to have a beneficial effect on the motility of the organism. The response of mean receptor activity to small time-dependent changes in the external ligand concentration, computed within linear response theory, is found to have a bilobe form.

physics.bio-ph↗

arXiv2017

Stall force of a cargo driven by N interacting motor proteins

We study a generic one-dimensional model for an intracellular cargo driven by N motor proteins against an external applied force. The model includes motor-cargo and motor-motor interactions. The cargo motion is described by an over-damped Langevin equation, while motor dynamics is specified by hopping rates which follow a local detailed balance condition with respect to change in energy per hopping event. Based on this model, we show that the stall force, the mean external force corresponding to zero mean cargo velocity, is completely independent of the details of the interactions and is, therefore, always equal to the sum of the stall forces of the individual motors. This exact result is arrived on the basis of a simple assumption: the (macroscopic) state of stall of the cargo is analogous to a state of thermodynamic equilibrium, and is characterized by vanishing net probability current between any two microstates, with the latter specified by motor positions relative to the cargo. The corresponding probability distribution of the microstates under stall is also determined. These predictions are in complete agreement with numerical simulations, carried out using specific forms of interaction potentials.

physics.bio-ph↗

arXiv2016

Transport of organelles by elastically coupled motor proteins

Motor-driven cargo transport is a complex phenomenon where multiple motor proteins 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. Here, we study a generic model in which N motors are elastically coupled to a cargo, which itself is subjected to thermal noise in the cytoplasm and to an additional external applied force. The motor-hopping rates are chosen to satisfy detailed balance with respect to the energy of elastic stretching. With these assumptions, an (N+1)-variable master equation is constructed for dynamics of the motor-cargo complex. By expanding the hopping rates to linear order in fluctuations in motor positions, we obtain a linear Fokker-Planck equation. The deterministic equations governing the average quantities are separated out and explicit analytical expressions are obtained for the mean velocity and diffusion coefficient of the cargo. We also study the statistical features of the force experienced by an individual motor and quantitatively characterize the load-sharing among the cargo-bound motors. The mean cargo velocity and the effective diffusion coefficient are found to be decreasing functions of the stiffness. While increase in the number of motors N does not increase the velocity substantially, it decreases the effective diffusion coefficient which falls as 1/N asymptotically. We further show that the cargo-bound motors share the force exerted on the cargo equally only in the limit of vanishing elastic stiffness; as stiffness is increased, deviations from equal load sharing are observed. Numerical simulations agree with our analytical results where expected. Interestingly, we find in simulations that the stall force of a cargo elastically coupled to motors is independent of the stiffness.

physics.bio-ph↗

arXiv2015

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

Several independent observations have suggested that catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent {\it in vitro} observations by Gardner et al.[ M. K. Gardner et al., Cell {\bf147}, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here, we investigate, via numerical simulations and mathematical calculations, some of the consequences of age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically and purely linear growth. The boundary demarcating the steady state and non-steady state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to non-exponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

q-bio.SC↗

arXiv2013

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. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a "critical point" for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.

q-bio.MN↗

arXiv2013

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 (Flyvbjerg, Holy and Leibler, Phys. Rev. Lett. 73, 2372, 1994). Our model includes both spontaneous and vectorial hydrolysis, as well as dissociation of a non-hydrolyzed dimer from the filament after incorporation. In the first part of the paper, we apply this model to a single protofilament of a microtubule. A catastrophe transition is defined for each protofilament, similar to the earlier one-dimensional models, the frequency of occurrence of which is then calculated under various conditions, but without explicit assumption of steady state conditions. Using a perturbative approach, we show that the leading asymptotic behavior of the protofilament catastrophe in the limit of large growth velocities is remarkably similar across different models. In the second part of the paper, we extend our analysis to the entire filament by making a conjecture that a minimum number of such transitions are required to occur for the onset of microtubule catastrophe. The frequency of microtubule catastrophe is then determined using numerical simulations, and compared with analytical/semi-analytical estimates made under steady state/quasi-steady state assumptions respectively for the protofilament dynamics. A few relevant experimental results are analyzed in detail, and compared with predictions from the model. Our results indicate that loss of GTP cap in 2-3 protofilaments is necessary to trigger catastrophe in a microtubule.

q-bio.SC↗

arXiv2013

Memory, Bias and Correlations in Bidirectional Transport of Molecular Motor-driven Cargoes

Molecular motors are specialized proteins which 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. We show, based on a study of the direction reversal probabilities of the cargo using a purely stochastic (tug-of-war) model, that bidirectional motion of cellular cargoes is, in general, a correlated random walk. In particular, while the motion of a cargo driven by two oppositely pulling motors is a Markovian random walk, memory of direction appears when multiple motors haul the cargo in one or both directions. In the latter case, the Markovian nature of the underlying single motor processes is hidden by internal transitions between degenerate run and pause states of the cargo. Interestingly, memory is found to be a non-monotonic function of the number of motors. Stochastic numerical simulations of the tug-of-war model support our mathematical results and extend them to biologically relevant situations.

q-bio.SC↗

arXiv2012

Effectiveness of a dynein team in tug-of-war helped by reduced load-sensitivity of detachment: evidence from study of bidirectional endosome transport in Dictyostelium 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 (eg., kinesin and dynein) bind to the cargo simultaneously, and `coordinate' their activity such that the motion consists of spells of positively and negatively directed segments, separated by pauses of varying duration. A set of recent experiments have analyzed the bidirectional motion of endosomes in the amoeba D. discoideum in detail. It was found that in between directional switches, a team of 5-6 dyneins stall a cargo against a stronger kinesin in tug of war, which lasts for almost a second. As the mean detachment time of a kinesin under its stall load was also observed to be ~ 1s, we infer that the collective detachment time of the dynein assembly must also be similar. Here, we analyze this inference from a modeling perspective, using experimentally measured single-molecule parameters as inputs. We find that the commonly assumed exponential load-dependent detachment rate is inconsistent with observations, as it predicts that a 5-dynein assembly will detach under its combined stall load in less than a hundredth of a second. A modified model where the load-dependent unbinding rate is assumed to saturate at stall-force level for super-stall loads gives results which are in agreement with experimental data. Our analysis suggests that the load-dependent detachment of a dynein in a team is qualitatively different at sub-stall and super-stall loads, a conclusion which is likely to have implications in other situations involving collective effects of many motors.

q-bio.SC↗

arXiv2011

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 towards 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. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In {\it Xenopus} extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase.

q-bio.SC↗

arXiv2010

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. When there is a spatial gradient in the attractant concentration, this bias produces a drift velocity directed towards its source, whereas in a uniform concentration, E.coli adapts, almost perfectly in case of methyl aspartate. Recently, microfluidic experiments have measured the drift velocity of E.coli in precisely controlled attractant gradients, but no general theoretical expression for the same exists. With this motivation, we study an analytically soluble model here, based on the Barkai-Leibler model, originally introduced to explain the perfect adaptation. Rigorous mathematical expressions are obtained for the chemotactic response function and the drift velocity in the limit of weak gradients and under the assumption of completely random tumbles. The theoretical predictions compare favorably with experimental results, especially at high concentrations. We further show that the signal transduction network weakens the dependence of the drift on concentration, thus enhancing the range of sensitivity.

q-bio.QM↗

arXiv2008

From random to directed motion: Understanding chemotaxis in E. Coli within a simplified model

The bacterium E.Coli swims in a zig-zag manner, in a series of straight runs and tumbles occurring alternately, with the run-durations dependent on the local spatial gradient of chemo-attractants/repellants. This enables the organism to move towards nutrient sources and move away from toxins. The signal transduction network of E.Coli has been well-characterized, and theoretical modeling has been used, with some success, in understanding its many remarkable features, including the near-perfect adaptation to spatially uniform stimulus. We study a reduced form of this network, with 3 methylation states for the receptor instead of 5. We derive an analytical form of the response function of the tumbling rate and use it to compute the drift velocity of the bacterium in the presence of a weak spatial attractant gradient.

q-bio.CB↗

arXiv2008

Length control of microtubules by depolymerizing motor proteins

In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.

physics.bio-ph↗