Modeling sRNA-regulated Plasmid Maintenance

We study a theoretical model for the toxin-antitoxin (hok/sok) mechanism for plasmid maintenance in bacteria. Toxin-antitoxin systems enforce the maintenance of a plasmid through post-segregational killing of cells that have lost the plasmid. Key to their function is the tight regulation of expression of a protein toxin by an sRNA antitoxin. Here, we focus on the nonlinear nature of the regulatory circuit dynamics of the toxin-antitoxin mechanism. The mechanism relies on a transient increase in protein concentration rather than on the steady state of the genetic circuit. Through a systematic analysis of the parameter dependence of this transient increase, we confirm some known design features of this system and identify new ones: for an efficient toxin-antitoxin mechanism, the synthesis rate of the toxin's mRNA template should be lower that of the sRNA antitoxin, the mRNA template should be more stable than the sRNA antitoxin, and the mRNA-sRNA complex should be more stable than the sRNA antitoxin. Moreover, a short half-life of the protein toxin is also beneficial to the function of the toxin-antitoxin system. In addition, we study a therapeutic scenario in which a competitor mRNA is introduced to sequester the sRNA antitoxin, causing the toxic protein to be expressed.Comment: 25 pages, 8 figure

Buckling of elastic filaments by discrete magnetic moments

We study the buckling of an idealized, semiflexible filament along whose contour magnetic moments are placed. {We give analytic expressions for the critical stiffness of the filament below which it buckles due to the magnetic compression. For this, we consider various scenarios of the attachment of the magnetic particles to the filament. One possible application for this model are the magnetosome chains of magnetotactic bacteria. An estimate of the critical bending stiffness indicates that buckling may occur within the range of biologically relevant parameters and suggests a role for the bending stiffness of the filament to stabilize the filament against buckling, which would compromise the functional relevance of the bending stiffness of the used filament.Comment: accepted for publication in EPJ

Force-dependent unbinding rate of molecular motors from stationary optical trap data

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show that this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1

Movements of molecular motors: Ratchets, random walks and traffic phenomena

Processive molecular motors which drive the traffic of organelles in cells move in a directed way along cytoskeletal filaments. On large time scales, they perform motor walks, i.e., peculiar random walks which arise from the repeated unbinding from and rebinding to filaments. Unbound motors perform Brownian motion in the surrounding fluid. In addition, the traffic of molecular motors exhibits many cooperative phenomena. In particular, it faces similar problems as the traffic on streets such as the occurrence of traffic jams and the coordination of (two-way) traffic. These issues are studied here theoretically using lattice models.Comment: latex, uses elsart.cls and phyeauth.cls (included), 10 pages, 6 figures, to appear in the proceedings of FQMT'04, Pragu

Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size $\ell \leq \ell_\text{max}$. With various choices of the interaction range, $\ell_\text{max}$, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.Comment: 13 pages, 8 figure

Cooperative transport by small teams of molecular motors

Molecular motors power directed transport of cargoes within cells. Even if a single motor is sufficient to transport a cargo, motors often cooperate in small teams. We discuss the cooperative cargo transport by several motors theoretically and explore some of its properties. In particular we emphasize how motor teams can drag cargoes through a viscous environment.Comment: 9 pages, 1 figure, uses ws-brl.cls, presented at Bio-Systems conference, Berlin, June 200

Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors

Intracellular transport is based on molecular motors that pull cargos along cytoskeletal filaments. One motor species always moves in one direction, e.g. conventional kinesin moves to the microtubule plus end, while cytoplasmic dynein moves to the microtubule minus end. However, many cellular cargos are observed to move bidirectionally, involving both plus-end and minus-end directed motors. The presumably simplest mechanism for such bidirectional transport is provided by a tug-of-war between the two motor species. This mechanism is studied theoretically using the load-dependent transport properties of individual motors as measured in single-molecule experiments. In contrast to previous expectations, such a tug-of-war is found to be highly cooperative and to exhibit seven different motility regimes depending on the precise values of the single motor parameters. The sensitivity of the transport process to small parameter changes can be used by the cell to regulate its cargo traffic.Comment: 17 pages, latex, 11 figures, 4 tables, includes Supporting Informatio

Is F-1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip

We present a chemomechanical network model of the rotary molecular motor F1-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F1-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40–80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque

Transcriptional Proofreading in Dense RNA Polymerase Traffic

The correction of errors during transcription involves the diffusive backward translocation (backtracking) of RNA polymerases (RNAPs) on the DNA. A trailing RNAP on the same template can interfere with backtracking as it progressively restricts the space that is available for backward translocation and thereby ratchets the backtracked RNAP forward. We analyze the resulting negative impact on proofreading theoretically using a driven lattice gas model of transcription under conditions of dense RNAP traffic. The fraction of errors that are corrected is calculated exactly for the case of a single RNAP; for multi-RNAP transcription, we use simulations and an analytical approximation and find a decrease with increasing traffic density. Moreover, we ask how the parameters of the system have to be set to keep down the impact of the interference of a trailing RNAP. Our analysis uncovers a surprisingly simple picture of the design of the error correction system: its efficiency is essentially determined by the rate for the initial backtracking step, while the value of the cleavage rate ensures that the correction mechanism remains efficient at high transcription rates. Finally, we argue that our analysis can also be applied to cases with transcription-translation coupling where the leading ribosome on the transcript assumes the role of the trailing RNAP