Theoretical analysis of cargo transport by catch bonded motors in optical trapping assays.

Dynein motors exhibit catch bonding, where the unbinding rate of the motors from microtubule filaments decreases with increasing opposing load. The implications of this catch bond on the transport properties of dynein-driven cargo are yet to be fully understood. In this context, optical trapping assays constitute an important means of accurately measuring the forces generated by molecular motor proteins. We investigate, using theory and stochastic simulations, the transport properties of cargo transported by catch bonded dynein molecular motors - both singly and in teams - in a harmonic potential, which mimics the variable force experienced by cargo in an optical trap. We estimate the biologically relevant measures of first passage time - the time during which the cargo remains bound to the microtubule and detachment force - the force at which the cargo unbinds from the microtubule, using both two-dimensional and one-dimensional force balance frameworks. Our results suggest that even for cargo transported by a single motor, catch bonding may play a role depending on the force scale which marks the onset of the catch bond. By comparing with experimental measurements on single dynein-driven transport, we estimate realistic bounds of this catch bond force scale. Generically, catch bonding results in increased persistent motion, and can also generate non-monotonic behaviour of first passage times. For cargo transported by multiple motors, emergent collective effects due to catch bonding can result in non-trivial re-entrant phenomena wherein average first passage times and detachment forces exhibit non-monotonic behaviour as a function of the stall force and the motor velocity.

Anomalous diffusion of E. coli under microfluidic confinement and chemical gradient.

We report a two-layer microfluidic device to study the combined effect of confinement and chemical gradient on the motility of wild-type E. coli. We track individual E. coli in 50 µm and 10 µm wide microchannels, with a channel height of 2 µm, to generate quasi-2D conditions. We find that contrary to expectations, bacterial trajectories are superdiffusive even in the absence of a chemical (glucose) gradient. The superdiffusive behaviour becomes more pronounced upon introducing a chemical gradient or strengthening the lateral confinement. Run length distributions for weak lateral confinement in the absence of chemical gradients follow an exponential distribution. Both confinement and chemoattraction induce deviations from this behaviour, with the run length distributions approaching a power-law form under these conditions. Both confinement and chemoattraction suppress large-angle tumbles as well. Our results suggest that wild-type E. coli modulates both its runs and tumbles in a similar manner under physical confinement and chemical gradient. Our findings have implications for understanding how bacteria modulate their motility behaviour in natural habitats.

Predicting scale-dependent chromatin polymer properties from systematic coarse-graining.

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations.

Dynamic modelling predicts lactate and IL-1ß as interventional targets in metabolic-inflammation-clock regulatory loop in glioma.

In an attempt to understand the role of dysregulated circadian rhythm in glioma, our recent findings highlighted the existence of a feed-forward loop between tumour metabolite lactate, pro-inflammatory cytokine IL-1ß and circadian CLOCK. To further elucidate the implication of this complex interplay, we developed a mathematical model that quantitatively describes this lactate dehydrogenase A (LDHA)-IL-1ß-CLOCK/BMAL1 circuit and predicts potential therapeutic targets. The model was calibrated on quantitative western blotting data in two glioma cell lines in response to either lactate inhibition or IL-1ß stimulation. The calibrated model described the experimental data well and most of the parameters were identifiable, thus the model was predictive. Sensitivity analysis identified IL-1ß and LDHA as potential intervention points. Mathematical models described here can be useful to understand the complex interrelationship between metabolism, inflammation and circadian rhythm, and in designing effective therapeutic strategies. Our findings underscore the importance of including the circadian clock when developing pharmacological approaches that target aberrant tumour metabolism and inflammation. Insight box  The complex interplay of metabolism-inflammation-circadian rhythm in tumours is not well understood. Our recent findings provided evidence of a feed-forward loop between tumour metabolite lactate, pro-inflammatory cytokine IL-1ß and circadian CLOCK/BMAL1 in glioma. To elucidate the implication of this complex interplay, we developed a mathematical model that quantitatively describes this LDHA-IL-1ß-CLOCK/BMAL1 circuit and integrates experimental data to predict potential therapeutic targets. The study employed a multi-start optimization strategy and profile likelihood estimations for parameter estimation and assessing identifiability. The simulations are in reasonable agreement with the experimental data. Sensitivity analysis found LDHA and IL-1ß as potential therapeutic points. Mathematical models described here can provide insights to understand the complex interrelationship between metabolism, inflammation and circadian rhythm, and in identifying effective therapeutic targets.

Multivalent binding proteins can drive collapse and reswelling of chromatin in confinement.

Collapsed conformations of chromatin have been long suspected of being mediated by interactions with multivalent binding proteins, which can bring together distant sections of the chromatin fiber. In this study, we use Langevin dynamics simulation of a coarse grained chromatin polymer to show that the role of binding proteins can be more nuanced than previously suspected. In particular, for chromatin polymer in confinement, entropic forces can drive reswelling of collapsed chromatin with increasing binder concentrations, and this reswelling transition happens at physiologically relevant binder concentrations. Both the extent of collapse, and also of reswelling depends on the strength of confinement. We also study the kinetics of collapse and reswelling and show that both processes occur in similar timescales. We characterise this reswelling of chromatin in biologically relevant regimes and discuss the non-trivial role of multivalent binding proteins in mediating the spatial organisation of the genome.

Pseudocleavage furrows restrict plasma membrane-associated PH domain in syncytial Drosophila embryos.

Syncytial cells contain multiple nuclei and have local distribution and function of cellular components despite being synthesized in a common cytoplasm. The syncytial Drosophila blastoderm embryo shows reduced spread of organelle and plasma membrane-associated proteins between adjacent nucleo-cytoplasmic domains. Anchoring to the cytoarchitecture within a nucleo-cytoplasmic domain is likely to decrease the spread of molecules; however, its role in restricting this spread has not been assessed. In order to analyze the cellular mechanisms that regulate the rate of spread of plasma membrane-associated molecules in the syncytial Drosophila embryos, we express a pleckstrin homology (PH) domain in a localized manner at the anterior of the embryo by tagging it with the bicoid mRNA localization signal. Anteriorly expressed PH domain forms an exponential gradient in the anteroposterior axis with a longer length scale compared with Bicoid. Using a combination of experiments and theoretical modeling, we find that the characteristic distribution and length scale emerge due to plasma membrane sequestration and restriction within an energid. Loss of plasma membrane remodeling to form pseudocleavage furrows shows an enhanced spread of PH domain but not Bicoid. Modeling analysis suggests that the enhanced spread of the PH domain occurs due to the increased spread of the cytoplasmic population of the PH domain in pseudocleavage furrow mutants. Our analysis of cytoarchitecture interaction in regulating plasma membrane protein distribution and constraining its spread has implications on the mechanisms of spread of various molecules, such as morphogens in syncytial cells.

Novel mechanism for oscillations in catchbonded motor-filament complexes.

Generation of mechanical oscillations is ubiquitous to a wide variety of intracellular processes, ranging from activity of muscle fibers to oscillations of the mitotic spindle. The activity of motors plays a vital role in maintaining the integrity of the mitotic spindle structure and generating spontaneous oscillations. Although the structural features and properties of the individual motors are well characterized, their implications on the functional behavior of motor-filament complexes are more involved. We show that force-induced allosteric deformations in dynein, which result in catchbonding behavior, provide a generic mechanism to generate spontaneous oscillations in motor-cytoskeletal filament complexes. The resultant phase diagram of such motor-filament systems-characterized by force-induced allosteric deformations-exhibits bistability and sustained limit-cycle oscillations in biologically relevant regimes, such as for catchbonded dynein. The results reported here elucidate the central role of this mechanism in fashioning a distinctive stability behavior and oscillations in motor-filament complexes such as mitotic spindles.

The Accidental Ally: Nucleosome Barriers Can Accelerate Cohesin-Mediated Loop Formation in Chromatin.

An important question in the context of the three-dimensional organization of chromosomes is the mechanism of formation of large loops between distant basepairs. Recent experiments suggest that the formation of loops might be mediated by loop extrusion factor proteins such as cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low-effective-diffusion constants leads to times that are unphysically large. The puzzle then is the following: how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle and show that although at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration they can reduce loop formation times because of a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes.

Cyto-architecture constrains the spread of photoactivated tubulin in the syncytial Drosophila embryo.

Drosophila embryogenesis begins with nuclear division in a common cytoplasm forming a syncytial cell. Morphogen gradient molecules spread across nucleo-cytoplasmic domains to pattern the body axis of the syncytial embryo. The diffusion of molecules across the syncytial nucleo-cytoplasmic domains is potentially constrained by association with the components of cellular architecture. However, the extent of restriction has not been examined. Here we use photoactivation (PA) to generate a source of cytoplasmic or cytoskeletal molecules in order to monitor the kinetics of their spread in the syncytial Drosophila embryo. Photoactivated PA-GFP and PA-GFP-Tubulin generated within a fixed anterior area diffused along the antero-posterior axis. These molecules were enriched in the cortical cytoplasm above the yolk-filled center, suggesting that the cortical cytoplasm is phase separated from the yolk-filled center. The length scales of diffusion were extracted using exponential fits under steady state assumptions. PA-GFP spread a greater distance as compared to PA-GFP-Tubulin. Both molecules were more restricted when generated in the center of the embryo. The length scale of spread for PA-GFP-Tubulin increased in mutant embryos containing short plasma membrane furrows and a disrupted tubulin cytoskeleton. PA-GFP spread was unaffected by cyto-architecture perturbation. Taken together, these data show that PA-GFP-Tubulin spread is restricted by its incorporation in the microtubule network and intact plasma membrane furrows. This photoactivation based analysis of protein spread allows for interpretation of the dependence of gradient formation on syncytial cyto-architecture.

A Lamin-Associated Chromatin Model for Chromosome Organization.

We propose a simple model for chromatin organization based on the interaction of the chromatin fibers with lamin proteins along the nuclear membrane. Lamin proteins are known to be a major factor that influences chromatin organization and hence gene expression in the cells. We provide a quantitative understanding of lamin-associated chromatin organization in a crowded macromolecular environment by systematically varying the heteropolymer segment distribution and the strength of the lamin-chromatin attractive interaction. Our minimal polymer model reproduces the formation of lamin-associated-domains and provides an in silico tool for quantifying domain length distributions for different distributions of heteropolymer segments. We show that a Gaussian distribution of heteropolymer segments, coupled with strong lamin-chromatin interactions, can qualitatively reproduce observed length distributions of lamin-associated-domains. Further, lamin-mediated interaction can enhance the formation of chromosome territories as well as the organization of chromatin into tightly packed heterochromatin and the loosely packed gene-rich euchromatin regions.

Reprogramming, oscillations and transdifferentiation in epigenetic landscapes.

Waddington's epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multi-step chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of self-promoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.

Diffusion dynamics and steady states of systems of hard rods on a square lattice.

It is known from grand canonical simulations of a system of hard rods on two-dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase-segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)2470-004510.1103/PhysRevE.95.052130], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drive the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.

Effect of catch bonding on transport of cellular cargo by dynein motors.

Recent experiments have demonstrated that dynein motors exhibit catch bonding behavior, in which the unbinding rate of a single dynein decreases with increasing force, for a certain range of force. Motivated by these experiments, we study the effect of catch bonding on unidirectional transport properties of cellular cargo carried by multiple dynein motors. We introduce a threshold force bond deformation (TFBD) model, consistent with the experiments, wherein catch bonding sets in beyond a critical applied load force. We find catch bonding can result in dramatic changes in the transport properties, which are in sharp contrast to kinesin-driven unidirectional transport, where catch bonding is absent. We predict that under certain conditions, the average velocity of the cellular cargo can actually increase as applied load is increased. We characterize the transport properties in terms of a velocity profile plot in the parameter space of the catch bond strength and the stall force of the motor. This plot yields predictions that may be experimentally accessed by suitable modifications of motor transport and binding properties.

Delayed self-regulation and time-dependent chemical drive leads to novel states in epigenetic landscapes.

The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington's landscape, consisting of hills and valleys. The smooth top and valley-strewn bottom of the hill represent their undifferentiated and differentiated states, respectively. Although mathematical ideas rooted in nonlinear dynamics and bifurcation theory have been used to quantify this picture, the importance of time delays arising from multistep chemical reactions or cellular shape transformations have been ignored so far. We argue that this feature is crucial in understanding cell differentiation and explore the role of time delay in a model of a single-gene regulatory circuit. We show that the interplay of time-dependent drive and delay introduces a new regime where the system shows sustained oscillations between the two admissible steady states. We interpret these results in the light of recent perplexing experiments on inducing the pluripotent state in mouse somatic cells. We also comment on how such an oscillatory state can provide a framework for understanding more general feedback circuits in cell development.

Theory of volume transition in polyelectrolyte gels with charge regularization.

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

Thermodynamic behaviour of two-dimensional vesicles revisited.

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher (Phys. Rev. Lett. 59, 1989 (1987)). We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure [Formula: see text] , where [Formula: see text] = Np/4[Formula: see text] , with the number of monomers N [Formula: see text] ∞ and the pressure p [Formula: see text] 0 , keeping [Formula: see text] constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N -gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. Away from these limits, we argue that the transition is replaced by a sharp crossover. The area, however, scales with N(2) for all positive p in all such models, consistent with earlier scaling theories.

Monte Carlo study of the molecular mechanisms of surface-layer protein self-assembly.

The molecular mechanisms guiding the self-assembly of proteins into functional or pathogenic large-scale structures can be only understood by studying the correlation between the structural details of the monomer and the eventual mesoscopic morphologies. Among the myriad structural details of protein monomers and their manifestations in the self-assembled morphologies, we seek to identify the most crucial set of structural features necessary for the spontaneous selection of desired morphologies. Using a combination of the structural information and a Monte Carlo method with a coarse-grained model, we have studied the functional protein self-assembly into S(surface)-layers, which constitute the crystallized outer most cell envelope of a great variety of bacterial cells. We discover that only few and mainly hydrophobic amino acids, located on the surface of the monomer, are responsible for the formation of a highly ordered anisotropic protein lattice. The coarse-grained model presented here reproduces accurately many experimentally observed features including the pore formation, chemical description of the pore structure, location of specific amino acid residues at the protein-protein interfaces, and surface accessibility of specific amino acid residues. In addition to elucidating the molecular mechanisms and explaining experimental findings in the S-layer assembly, the present work offers a tool, which is chemical enough to capture details of primary sequences and coarse-grained enough to explore morphological structures with thousands of protein monomers, to promulgate design rules for spontaneous formation of specific protein assemblies.

Long-time growth kinetics of first order phase transitions in the presence of a boundary layer.

The late stage growth mechanism for a first order phase transition, either through nucleation growth or spinodal decomposition, is well understood to be an Ostwald ripening or coarsening process, in which larger domains grow at the expense of smaller ones. The growth kinetics in this regime was shown by Lifshitz and Slyozov to follow at(1/3) law. However, the kinetics is altered if there exists a barrier ahead of the growth front, irrespective of the physical origin of the boundary layer. We present an analytic calculation for the growth kinetics in the presence of a boundary layer, showing that in the limit of barrier-dominated growth, the domains grow with at(1/2) law. This result holds true in the dilute regime independent of whether the growing nuclei are spherical or cylindrical.

Phase transitions in pressurized semiflexible polymer rings.

We propose and study a model for the equilibrium statistical mechanics of a pressurized semiflexible polymer ring in two dimensions. The Hamiltonian has a term which couples to the algebraic or signed area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations, and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behavior of the area is calculated for both continuum and lattice versions of the model. For small pressures, the area is obtained through a known mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results.