Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by $10^3$--$10^6$ compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.Comment: 54 pages, 7 figures, 1 tabl

Opening of DNA double strands by helicases. Active versus passive opening

Helicase opening of double-stranded nucleic acids may be "active" (the helicase directly destabilizes the dsNA to promote opening) or "passive" (the helicase binds ssNA available due to a thermal fluctuation which opens part of the dsNA). We describe helicase opening of dsNA, based on helicases which bind single NA strands and move towards the double-stranded region, using a discrete ``hopping'' model. The interaction between the helicase and the junction where the double strand opens is characterized by an interaction potential. The form of the potential determines whether the opening is active or passive. We calculate the rate of passive opening for the helicase PcrA, and show that the rate increases when the opening is active. Finally, we examine how to choose the interaction potential to optimize the rate of strand separation. One important result is our finding that active opening can increase the unwinding rate by 7 fold compared to passive opening.Comment: 13 pages, 3 figure

Incorporating expression data in metabolic modeling: a case study of lactate dehydrogenase

Integrating biological information from different sources to understand cellular processes is an important problem in systems biology. We use data from mRNA expression arrays and chemical kinetics to formulate a metabolic model relevant to K562 erythroleukemia cells. MAP kinase pathway activation alters the expression of metabolic enzymes in K562 cells. Our array data show changes in expression of lactate dehydrogenase (LDH) isoforms after treatment with phorbol 12-myristate 13-acetate (PMA), which activates MAP kinase signaling. We model the change in lactate production which occurs when the MAP kinase pathway is activated, using a non-equilibrium, chemical-kinetic model of homolactic fermentation. In particular, we examine the role of LDH isoforms, which catalyze the conversion of pyruvate to lactate. Changes in the isoform ratio are not the primary determinant of the production of lactate. Rather, the total concentration of LDH controls the lactate concentration.Comment: In press, Journal of Theoretical Biology. 27 pages, 9 figure

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.</p

Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.Comment: 72 pages, 18 figures, Accepted to: Reports on Progress in Physic

Formation of metre-scale bladed roughness on Europa's surface by ablation of ice

On Earth, the sublimation of massive ice deposits at equatorial latitudes under cold and dry conditions in the absence of any liquid melt leads to the formation of spiked and bladed textures eroded into the surface of the ice. These sublimation-sculpted blades are known as penitentes. For this process to take place on another planet, the ice must be sufficiently volatile to sublimate under surface conditions and diffusive processes that act to smooth the topography must operate more slowly. Here we calculate sublimation rates of water ice across the surface of Jupiter’s moon Europa. We find that surface sublimation rates exceed those of erosion by space weathering processes in Europa’s equatorial belt (latitudes below 23°), and that conditions would favour penitente growth. We estimate that penitentes on Europa could reach 15 m in depth with a spacing of 7.5 m near the equator, on average, if they were to have developed across the interval permitted by Europa’s mean surface age. Although available images of Europa have insufficient resolution to detect surface roughness at the multi-metre scale, radar and thermal data are consistent with our interpretation. We suggest that penitentes could pose a hazard to a future lander on Europa