Microscopic origins of anisotropic active stress in motor-driven nematic liquid crystals.

The cytoskeleton, despite comprising relatively few building blocks, drives an impressive variety of cellular phenomena ranging from cell division to motility. These building blocks include filaments, motor proteins, and static crosslinkers. Outside of cells, these same components can form novel materials exhibiting active flows and nonequilibrium contraction or extension. While dipolar extensile or contractile active stresses are common in nematic motor-filament systems, their microscopic origin remains unclear. Here we study a minimal physical model of filaments, crosslinking motors, and static crosslinkers to dissect the microscopic mechanisms of stress generation in a two-dimensional system of orientationally aligned rods. We demonstrate the essential role of filament steric interactions which have not previously been considered to significantly contribute to active stresses. With this insight, we are able to tune contractile or extensile behavior through the control of motor-driven filament sliding and crosslinking. This work provides a roadmap for engineering stresses in active liquid crystals. The mechanisms we study may help explain why flowing nematic motor-filament mixtures are extensile while gelled systems are contractile.

Multiscale polar theory of microtubule and motor-protein assemblies.

Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new "bioactive" liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.

Biophysics of filament length regulation by molecular motors.

Regulating physical size is an essential problem that biological organisms must solve from the subcellular to the organismal scales, but it is not well understood what physical principles and mechanisms organisms use to sense and regulate their size. Any biophysical size-regulation scheme operates in a noisy environment and must be robust to other cellular dynamics and fluctuations. This work develops theory of filament length regulation inspired by recent experiments on kinesin-8 motor proteins, which move with directional bias on microtubule filaments and alter microtubule dynamics. Purified kinesin-8 motors can depolymerize chemically-stabilized microtubules. In the length-dependent depolymerization model, the rate of depolymerization tends to increase with filament length, because long filaments accumulate more motors at their tips and therefore shorten more quickly. When balanced with a constant filament growth rate, this mechanism can lead to a fixed polymer length. However, the mechanism by which kinesin-8 motors affect the length of dynamic microtubules in cells is less clear. We study the more biologically realistic problem of microtubule dynamic instability modulated by a motor-dependent increase in the filament catastrophe frequency. This leads to a significant decrease in the mean filament length and a narrowing of the filament length distribution. The results improve our understanding of the biophysics of length regulation in cells.

Microtubule depolymerization by the Kinesin-8 motor Kip3p: a mathematical model.

Proteins from the kinesin-8 family promote microtubule (MT) depolymerization, a process thought to be important for the control of microtubule length in living cells. In addition to this MT shortening activity, kinesin 8s are motors that show plus-end directed motility on MTs. Here we describe a simple model that incorporates directional motion and destabilization of the MT plus-end by kinesin 8. Our model quantitatively reproduces the key features of length-versus-time traces for stabilized MTs in the presence of purified kinesin 8, including length-dependent depolymerization. Comparison of model predictions with experiments suggests that kinesin 8 depolymerizes processively, i.e., one motor can remove multiple tubulin dimers from a stabilized MT. Fluctuations in MT length as a function of time are related to depolymerization processivity. We have also determined the parameter regime in which the rate of MT depolymerization is length dependent: length-dependent depolymerization occurs only when MTs are sufficiently short; this crossover is sensitive to the bulk motor concentration.

Two-state model for helicase translocation and unwinding of nucleic acids.

Helicases are molecular motors that unwind double-stranded nucleic acids (dsNA), such as DNA and RNA. Typically a helicase translocates along one of the NA single strands while unwinding and uses adenosine triphosphate (ATP) hydrolysis as an energy source. Here we model a helicase motor that can switch between two states, which could represent two different points in the ATP hydrolysis cycle. Our model is an extension of the earlier Betterton-Jülicher model of helicases to incorporate switching between two states. The main predictions of the model are the speed of unwinding of the dsNA and fluctuations around the average unwinding velocity. Motivated by a recent claim that the NS3 helicase of Hepatitis C virus follows a flashing-ratchet mechanism, we have compared the experimental results for the NS3 helicase with a special limit of our model which corresponds to the flashing-ratchet scenario. Our model accounts for one key feature of the experimental data on NS3 helicase. However, contradictory observations in experiments carried out under different conditions limit the ability to compare the model to experiments.

Collective clog control: Optimizing traffic flow in confined biological and robophysical excavation.

Groups of interacting active particles, insects, or humans can form clusters that hinder the goals of the collective; therefore, development of robust strategies for control of such clogs is essential, particularly in confined environments. Our biological and robophysical excavation experiments, supported by computational and theoretical models, reveal that digging performance can be robustly optimized within the constraints of narrow tunnels by individual idleness and retreating. Tools from the study of dense particulate ensembles elucidate how idleness reduces the frequency of flow-stopping clogs and how selective retreating reduces cluster dissolution time for the rare clusters that still occur. Our results point to strategies by which dense active matter and swarms can become task capable without sophisticated sensing, planning, and global control of the collective.

Elasticity of short DNA molecules: theory and experiment for contour lengths of 0.6-7 microm.

The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters-the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm-7.03 microm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length p(wlc) depended on L; even for moderately long DNA molecules (L = 1300 nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the "finite wormlike chain (FWLC)," to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of p(wlc) on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of p(fwlc) on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.

Using the nucleotide substitution rate matrix to detect horizontal gene transfer.

BACKGROUND: Horizontal gene transfer (HGT) has allowed bacteria to evolve many new capabilities. Because transferred genes perform many medically important functions, such as conferring antibiotic resistance, improved detection of horizontally transferred genes from sequence data would be an important advance. Existing sequence-based methods for detecting HGT focus on changes in nucleotide composition or on differences between gene and genome phylogenies; these methods have high error rates. RESULTS: First, we introduce a new class of methods for detecting HGT based on the changes in nucleotide substitution rates that occur when a gene is transferred to a new organism. Our new methods discriminate simulated HGT events with an error rate up to 10 times lower than does GC content. Use of models that are not time-reversible is crucial for detecting HGT. Second, we show that using combinations of multiple predictors of HGT offers substantial improvements over using any single predictor, yielding as much as a factor of 18 improvement in performance (a maximum reduction in error rate from 38% to about 3%). Multiple predictors were combined by using the random forests machine learning algorithm to identify optimal classifiers that separate HGT from non-HGT trees. CONCLUSION: The new class of HGT-detection methods introduced here combines advantages of phylogenetic and compositional HGT-detection techniques. These new techniques offer order-of-magnitude improvements over compositional methods because they are better able to discriminate HGT from non-HGT trees under a wide range of simulated conditions. We also found that combining multiple measures of HGT is essential for detecting a wide range of HGT events. These novel indicators of horizontal transfer will be widely useful in detecting HGT events linked to the evolution of important bacterial traits, such as antibiotic resistance and pathogenicity.

Opening of nucleic-acid double strands by helicases: active versus passive opening.

Helicase proteins move along double-stranded nucleic-acid molecules and unwind the double helix. This paper presents a theoretical study of the coupling between helicase translocation and duplex unwinding. Two different cases-active and passive opening-are usually distinguished. In active opening, the helicase directly destabilizes the double-stranded nucleic acid (dsNA) to promote opening. Passive opening implies that the helicase binds ssNA available when a thermal fluctuation partially opens the dsNA. We formulate a discrete model for helicase motion. An interaction potential describes how the helicase affects duplex unwinding when near a junction between single-stranded and double-stranded NA. Different choices of the potential correspond to the cases of active and passive opening. An optimal choice of interaction potential leads to a helicase which can unwind NA as rapidly as it translocates on single strands.

Velocity and processivity of helicase unwinding of double-stranded nucleic acids.

Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded (ss) nucleic acids, and couple their directional translocation to strand separation. A model of the coupling between translocation and unwinding uses an interaction potential to represent passive and active helicase mechanisms. A passive helicase must wait for thermal fluctuations to open dsNA base pairs before it can advance and inhibit NA closing. An active helicase directly destabilizes dsNA base pairs, accelerating the opening rate. Here we extend this model to include helicase unbinding from the nucleic-acid strand. The helicase processivity depends on the form of the interaction potential. A passive helicase has a mean attachment time which does not change between ss translocation and ds unwinding, while an active helicase in general shows a decrease in attachment time during unwinding relative to ss translocation. In addition, we describe how helicase unwinding velocity and processivity vary if the base-pair binding free energy is changed.

Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods.

Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.

Multiscale modeling and simulation of microtubule-motor-protein assemblies.

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.

Theory of structure formation in snowfields motivated by penitentes, suncups, and dirt cones.

Penitentes and suncups are structures formed as snow melts, typically high in the mountains. When the snow is dirty, dirt cones and other structures can form instead. Building on previous field observations and experiments, this paper presents a theory of ablation morphologies, and the role of surface dirt in determining the structures formed. The glaciological literature indicates that sunlight, heating from air, and dirt all play a role in the formation of structure on an ablating snow surface. The present paper formulates a minimal model for the formation of ablation morphologies as a function of measurable parameters and considers the linear stability of this model. The dependence of ablation morphologies on weather conditions and initial dirt thickness is studied, focusing on the initial growth of perturbations away from a flat surface. We derive a single-parameter expression for the melting rate as a function of dirt thickness, which agrees well with a set of measurements by Driedger. An interesting result is the prediction of a dirt-induced traveling instability for a range of parameters.

Collapsing bacterial cylinders.

Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process, from the structure of the collapsing cylinder to the spacing of the final aggregates. We show that cylindrical collapse involves a delicate balance in which bacterial attraction and diffusion nearly cancel, leading to corrections to the collapse laws expected from dimensional analysis. The instability of a collapsing cylinder is composed of two distinct stages: Initially, slow modulations to the cylinder develop, which correspond to a variation of the collapse time along the cylinder axis. Ultimately, one point on the cylinder pinches off. At this final stage of the instability, a front propagates from the pinch into the remainder of the cylinder. The spacing of the resulting spherical aggregates is determined by the front propagation.

Regulation of chromosome speeds in mitosis.

When chromosome are being separated in preparation for cell division, their motions are slow (~16 nm/s) relative to the speed at which many motor enzymes can move their cellular cargoes (160-1000 nm/s and sometimes even faster) and at which microtubules (MTs) depolymerize (~200 nm/s). Indeed, anaphase chromosome speeds are so slow that viscous drag puts little load on the mechanisms that generate the relevant forces [35]. Available evidence suggests that chromosome speed is due to some form of regulation. For example, big and little chromosomes move at about the same speed, chromosomes that have farther to go move faster than others, and chromosome speed is affected by both temperature and an experimentally applied load. In this essay we review data on these phenomena and present our ideas about likely properties of the mechanisms that regulate chromosome speed.

Multiple pattern matching: a Markov chain approach.

RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text.

Activating and inhibiting connections in biological network dynamics.

BACKGROUND: Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos. RESULTS: Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate. CONCLUSION: The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks. REVIEWERS: Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

Controlled irradiative formation of penitentes.

Spike-shaped structures are produced by light-driven ablation in very different contexts. Penitentes 1-4 m high are common on Andean glaciers, where their formation changes glacier dynamics and hydrology. Laser ablation can produce cones 10-100 microm high with a variety of proposed applications in materials science. We report the first laboratory generation of centimeter-scale snow and ice penitentes. Systematically varying conditions allows identification of the parameters controlling the formation of ablation structures. We demonstrate that penitente initiation and coarsening require cold temperatures, so that ablation leads to sublimation. Once penitentes have formed, further growth of height can occur by melting. The penitentes initially appear as small structures (3 mm high) and grow by coarsening to 1-5 cm high. Our results are an important step towards understanding ablation morphologies.

Systems theory of Smad signalling.

Transforming growth factor-beta (TGFbeta) signalling is an important regulator of cellular growth and differentiation. The principal intracellular mediators of TGFbeta signalling are the Smad proteins, which upon TGFbeta stimulation accumulate in the nucleus and regulate the transcription of target genes. To investigate the mechanisms of Smad nuclear accumulation, we developed a simple mathematical model of canonical Smad signalling. The model was built using both published data and our experimentally determined cellular Smad concentrations (isoforms 2, 3 and 4). We found in mink lung epithelial cells that Smad2 (8.5-12 x 10(4) molecules cell(-1)) was present in similar amounts to Smad4 (9.3-12 x 10(4) molecules cell(-1)), whereas both were in excess of Smad3 (1.1-2.0 x 10(4) molecules cell(-1)). Variation of the model parameters and statistical analysis showed that Smad nuclear accumulation is most sensitive to parameters affecting the rates of R-Smad phosphorylation and dephosphorylation and Smad complex formation/ dissociation in the nucleus. Deleting Smad4 from the model revealed that rate-limiting phospho-R-Smad dephosphorylation could be an important mechanism for Smad nuclear accumulation. Furthermore, we observed that binding factors constitutively localised to the nucleus do not efficiently mediate Smad nuclear accumulation, if dephosphorylation is rapid. We therefore conclude that an imbalance in the rates of R-Smad phosphorylation and dephosphorylation is likely an important mechanism of Smad nuclear accumulation during TGFbeta signalling.

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 catalyse 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.