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

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.Comment: Accepted in Europhysics Letter

Non-equilibrium dynamics of the piston in the Szilard engine

We consider a Szilard engine in one dimension, consisting of a single particle of mass $m$, moving between a piston of mass $M$, and a heat reservoir at temperature $T$. In addition to an external force, the piston experiences repeated elastic collisions with the particle. We find that the motion of a heavy piston ($M \gg m$), can be described effectively by a Langevin equation. Various numerical evidences suggest that the frictional coefficient in the Langevin equation is given by $\gamma = (1/X)\sqrt{8 \pi m k_BT}$, where $X$ is the position of the piston measured from the thermal wall. Starting from the exact master equation for the full system and using a perturbation expansion in $\epsilon= \sqrt{m/M}$, we integrate out the degrees of freedom of the particle to obtain the effective Fokker-Planck equation for the piston albeit with a different frictional coefficient. Our microscopic study shows that the piston is never in equilibrium during the expansion step, contrary to the assumption made in the usual Szilard engine analysis --- nevertheless the conclusions of Szilard remain valid

Deposition of alumina films by inverted cylindrical magnetron sputtering assisted by optical emission spectroscopy

Alumina coatings have been deposited on glass substrates by reactive ac (41 kHz) magnetron sputtering of two hollow aluminum targets in argon-oxygen plasma at 5 kW sputtering power in the poisoned mode and in the unstable region of hysteresis loop of reactive sputtering. The poisoned mode produces nanocrystalline films of and alumina at a low deposition rate of 0.06 nm·s-1. Amorphous alumina films have been grown at a higher deposition rate of 0.2 nm·s-1 with the aid of optical emission spectroscopy in which the feedback signal of Al emission spectral line at 396 nm monitored Al concentration in the plasma discharge and accomplished the controlled oxidation of targets during reactive sputtering. Dynamic secondary ion mass spectroscopy studies confirm that alumina films grown in the unstable region of the hysteresis loop of reactive sputtering are highly stoichiometric and of uniform composition with film thickness. Our study demonstrates the successful coupling of optical emission spectroscopy with hollow cylindrical magnetrons for deposition of alumina films

Genome replication in asynchronously growing microbial populations

Biological cells adopt specific programs to replicate their genomes. Information about the replication program of an organism can be obtained by sequencing an exponentially growing cell culture and studying the frequency of DNA fragments as a function of genomic position. However, a quantitative interpretation of this data has been challenging for asynchronously growing cultures. In this paper, we introduce a general theory to predict the abundance of DNA fragments in asynchronously growing cultures from any given stochastic model of the DNA replication program. As key examples, we present stochastic models of DNA replication in Escherichia coli and in budding yeast. In both cases, our approach leads to analytical predictions that are in excellent agreement with experimental data and permit to infer biophysically relevant parameters. In particular, our method is able to infer the locations of known replication origins in budding yeast with high accuracy. These examples demonstrate that our method can provide insight into a broad range of organisms, from bacteria to eukaryotes.Comment: 18 pages, 8 figure

Search and localization dynamics of the CRISPR/Cas9 system

The CRISPR/Cas9 system acts as the prokaryotic immune system and has important applications in gene editing. The protein Cas9 is one of its crucial components. The role of Cas9 is to search for specific target sequences on the DNA and cleave them. In this Letter, we introduce a model of facilitated diffusion for Cas9 and fit its parameters to single-molecule experiments. Our model confirms that Cas9 search for targets by sliding, but shows that its sliding length is rather short. We then investigate how Cas9 explores a long stretch of DNA containing randomly placed targets. We solve this problem by mapping it into the theory of Anderson localization in condensed matter physics. Our theoretical approach rationalizes experimental evidences on the distribution of Cas9 molecules along the DNA.Comment: 8 pages, 10 figures. Combined Main Text + SI. Accepted for publication in Physical Review Letter

Transformation of Indian Libraries: Review Based on Selected Library Websites

Abstract Indian libraries have witnessed a transformation during the past two decades. Th