Theory on quench-induced pattern formation: Application to the isotropic to smectic-A phase transitions

During catastrophic processes of environmental variations of a thermodynamic system, such as rapid temperature decreasing, many novel and complex patterns often form. To understand such phenomena, a general mechanism is proposed based on the competition between heat transfer and conversion of heat to other energy forms. We apply it to the smectic-A filament growth process during quench-induced isotropic to smectic-A phase transition. Analytical forms for the buckling patterns are derived and we find good agreement with experimental observation [Phys. Rev. {\bf E55} (1997) 1655]. The present work strongly indicates that rapid cooling will lead to structural transitions in the smectic-A filament at the molecular level to optimize heat conversion. The force associated with this pattern formation process is estimated to be in the order of $10^{-1}$ piconewton.Comment: 9 pages in RevTex form, with 3 postscript figures. Accepted by PR

Energy Transduction of Isothermal Ratchets: Generic Aspects and Specific Examples Close to and Far from Equilibrium

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.Comment: 16 pages, 10 figure

The Force-Velocity Relation for Growing Biopolymers

The process of force generation by the growth of biopolymers is simulated via a Langevin-dynamics approach. The interaction forces are taken to have simple forms that favor the growth of straight fibers from solution. The force-velocity relation is obtained from the simulations for two versions of the monomer-monomer force field. It is found that the growth rate drops off more rapidly with applied force than expected from the simplest theories based on thermal motion of the obstacle. The discrepancies amount to a factor of three or more when the applied force exceeds 2.5kT/a, where a is the step size for the polymer growth. These results are explained on the basis of restricted diffusion of monomers near the fiber tip. It is also found that the mobility of the obstacle has little effect on the growth rate, over a broad range.Comment: Latex source, 9 postscript figures, uses psfig.st

Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

Comparison of the force exerted by hippocampal and DRG growth cones

Mechanical properties such as force generation are fundamental for neuronal motility, development and regeneration. We used optical tweezers to compare the force exerted by growth cones (GCs) of neurons from the Peripheral Nervous System (PNS), such as Dorsal Root Ganglia (DRG) neurons, and from the Central Nervous System (CNS) such as hippocampal neurons. Developing GCs from dissociated DRG and hippocampal neurons were obtained from P1-P2 and P10-P12 rats. Comparing their morphology, we observed that the area of GCs of hippocampal neurons was 8-10 \ub5m(2) and did not vary between P1-P2 and P10-P12 rats, but GCs of DRG neurons were larger and their area increased from P1-P2 to P10-P12 by 2-4 times. The force exerted by DRG filopodia was in the order of 1-2 pN and never exceeded 5 pN, while hippocampal filopodia exerted a larger force, often in the order of 5 pN. Hippocampal and DRG lamellipodia exerted lateral forces up to 20 pN, but lamellipodia of DRG neurons could exert a vertical force larger than that of hippocampal neurons. Force-velocity relationships (Fv) in both types of neurons had the same qualitative behaviour, consistent with a common autocatalytic model of force generation. These results indicate that molecular mechanisms of force generation of GC from CNS and PNS neurons are similar but the amplitude of generated force is influenced by their cytoskeletal properties

Stress Generation and Filament Turnover during Actin Ring Constriction

We present a physical analysis of the dynamics and mechanics of contractile actin rings. In particular, we analyze the dynamics of ring contraction during cytokinesis in the Caenorhabditis elegans embryo. We present a general analysis of force balances and material exchange and estimate the relevant parameter values. We show that on a microscopic level contractile stresses can result from both the action of motor proteins, which cross-link filaments, and from the polymerization and depolymerization of filaments in the presence of end-tracking cross-linkers

Structure–property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body

Push-me-pull-you: how microtubules organize the cell interior

Dynamic organization of the cell interior, which is crucial for cell function, largely depends on the microtubule cytoskeleton. Microtubules move and position organelles by pushing, pulling, or sliding. Pushing forces can be generated by microtubule polymerization, whereas pulling typically involves microtubule depolymerization or molecular motors, or both. Sliding between a microtubule and another microtubule, an organelle, or the cell cortex is also powered by molecular motors. Although numerous examples of microtubule-based pushing and pulling in living cells have been observed, it is not clear why different cell types and processes employ different mechanisms. This review introduces a classification of microtubule-based positioning strategies and discusses the efficacy of pushing and pulling. The positioning mechanisms based on microtubule pushing are efficient for movements over small distances, and for centering of organelles in symmetric geometries. Mechanisms based on pulling, on the other hand, are typically more elaborate, but are necessary when the distances to be covered by the organelles are large, and when the geometry is asymmetric and complex. Thus, taking into account cell geometry and the length scale of the movements helps to identify general principles of the intracellular layout based on microtubule forces