Irreversible and reversible modes of operation of deterministic ratchets

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time-protocols of the outer force exist under which the operation is reversible and the ideal value of efficiency is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures

Effective rate equations for the over-damped motion in fluctuating potentials

We discuss physical and mathematical aspects of the over-damped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.Comment: 18 pages, 2 figures, standard LaTeX2

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.Comment: LaTeX v2.09, 14 pages with 4 PNG figure

The Glial Regenerative Response to Central Nervous System Injury Is Enabled by Pros-Notch and Pros-NFκB Feedback

Organisms are structurally robust, as cells accommodate changes preserving structural integrity and function. The molecular mechanisms underlying structural robustness and plasticity are poorly understood, but can be investigated by probing how cells respond to injury. Injury to the CNS induces proliferation of enwrapping glia, leading to axonal re-enwrapment and partial functional recovery. This glial regenerative response is found across species, and may reflect a common underlying genetic mechanism. Here, we show that injury to the Drosophila larval CNS induces glial proliferation, and we uncover a gene network controlling this response. It consists of the mutual maintenance between the cell cycle inhibitor Prospero (Pros) and the cell cycle activators Notch and NFκB. Together they maintain glia in the brink of dividing, they enable glial proliferation following injury, and subsequently they exert negative feedback on cell division restoring cell cycle arrest. Pros also promotes glial differentiation, resolving vacuolization, enabling debris clearance and axonal enwrapment. Disruption of this gene network prevents repair and induces tumourigenesis. Using wound area measurements across genotypes and time-lapse recordings we show that when glial proliferation and glial differentiation are abolished, both the size of the glial wound and neuropile vacuolization increase. When glial proliferation and differentiation are enabled, glial wound size decreases and injury-induced apoptosis and vacuolization are prevented. The uncovered gene network promotes regeneration of the glial lesion and neuropile repair. In the unharmed animal, it is most likely a homeostatic mechanism for structural robustness. This gene network may be of relevance to mammalian glia to promote repair upon CNS injury or disease

Lateral Gene Expression in Drosophila Early Embryos Is Supported by Grainyhead-Mediated Activation and Tiers of Dorsally-Localized Repression

The general consensus in the field is that limiting amounts of the transcription factor Dorsal establish dorsal boundaries of genes expressed along the dorsal-ventral (DV) axis of early Drosophila embryos, while repressors establish ventral boundaries. Yet recent studies have provided evidence that repressors act to specify the dorsal boundary of intermediate neuroblasts defective (ind), a gene expressed in a stripe along the DV axis in lateral regions of the embryo. Here we show that a short 12 base pair sequence (“the A-box”) present twice within the ind CRM is both necessary and sufficient to support transcriptional repression in dorsal regions of embryos. To identify binding factors, we conducted affinity chromatography using the A-box element and found a number of DNA-binding proteins and chromatin-associated factors using mass spectroscopy. Only Grainyhead (Grh), a CP2 transcription factor with a unique DNA-binding domain, was found to bind the A-box sequence. Our results suggest that Grh acts as an activator to support expression of ind, which was surprising as we identified this factor using an element that mediates dorsally-localized repression. Grh and Dorsal both contribute to ind transcriptional activation. However, another recent study found that the repressor Capicua (Cic) also binds to the A-box sequence. While Cic was not identified through our A-box affinity chromatography, utilization of the same site, the A-box, by both factors Grh (activator) and Cic (repressor) may also support a “switch-like” response that helps to sharpen the ind dorsal boundary. Furthermore, our results also demonstrate that TGF-β signaling acts to refine ind CRM expression in an A-box independent manner in dorsal-most regions, suggesting that tiers of repression act in dorsal regions of the embryo

From the cell membrane to the nucleus: unearthing transport mechanisms for Dynein

Mutations in the motor protein cytoplasmic dynein have been found to cause Charcot-Marie-Tooth disease, spinal muscular atrophy, and severe intellectual disabilities in humans. In mouse models, neurodegeneration is observed. We sought to develop a novel model which could incorporate the effects of mutations on distance travelled and velocity. A mechanical model for the dynein mediated transport of endosomes is derived from first principles and solved numerically. The effects of variations in model parameter values are analysed to find those that have a significant impact on velocity and distance travelled. The model successfully describes the processivity of dynein and matches qualitatively the velocity profiles observed in experiments

Efficient Dynamic Importance Sampling of Rare Events in One Dimension

Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of ``Dynamic Importance Sampling'' (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a $5 k_B T$ barrier height and 300 for $9 k_B T$, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instanton-like crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the ``Jacobian'' term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.Comment: version to be published in Phys. Rev.