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arXiv2018

MCell-R: A particle-resolution network-free spatial modeling framework

Spatial heterogeneity can have dramatic effects on the biochemical networks that drive cell regulation and decision-making. For this reason, a number of methods have been developed to model spatial heterogeneity and incorporated into widely used modeling platforms. Unfortunately, the standard approaches for specifying and simulating chemical reaction networks become untenable when dealing with multi-state, multi-component systems that are characterized by combinatorial complexity. To address this issue, we developed MCell-R, a framework that extends the particle-based spatial Monte Carlo simulator, MCell, with the rule-based model specification and simulation capabilities provided by BioNetGen and NFsim. The BioNetGen syntax enables the specification of biomolecules as structured objects whose components can have different internal states that represent such features as covalent modification and conformation and which can bind components of other molecules to form molecular complexes. The network-free simulation algorithm used by NFsim enables efficient simulation of rule-based models even when the size of the network implied by the biochemical rules is too large to enumerate explicitly, which frequently occurs in detailed models of biochemical signaling. The result is a framework that can efficiently simulate systems characterized by combinatorial complexity at the level of spatially-resolved individual molecules over biologically relevant time and length scales.

q-bio.SC↗

arXiv2018

The Range of Cooperativity Modulates Actin Binding Protein Cluster Size, Density and Dynamics

The actin cytoskeleton is composed of multiple networks which are specialized for several processes such as cell motility or cell division. Each of these networks are composed of organized actin microfilaments which are decorated with specific sets of actin binding proteins (ABPs). The molecular mechanisms guiding ABPs to specific actin networks are still poorly understood, but cooperativity, the mechanism by which the binding of an ABP is positively influenced by proximal bound ABPs, plays a crucial role in generating locally dense stretches of ABPs. Cooperative binding is characterized by its amplitude, but also by the range at which its effects are propagated along an actin filament through long-range allosteric interactions. The range of these allosteric effects is still debated, but is likely to be significant at the lengthscale of actin filaments in cells. Here, we investigated how cooperativity influences the clustering of ABPs, using a stochastic computational model of binding of ABPs to actin filaments. The model reproduces the formation of ABP clusters observed experimentally at the single filament scale, and provides a theoretical estimation of the range of cooperativity for proteins such as ADF/cofilin. We found that both the amplitude and the spatial range of cooperativity dramatically impact the properties of clustering. However, the parameters of cooperativity modulate differently the rate of assembly, size and dynamics of the ABP clusters, suggesting that cooperativity is an efficient mechanism to regulate precisely the recruitment of ABPs in cells. This work provides a more general framework for future understanding of how actin networks acquire distinct and specific protein compositions from a common cytoplasm.

physics.bio-ph↗

arXiv2018

Numerical parameter space compression and its application to microtubule dynamic instability

Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously identifying this subset of "stiff" parameters has been made possible by the development of parameter space compression (PSC). However, PSC has only been applied to analytically-solvable physical models. We have generalized this powerful method by developing a numerical approach to PSC that can be applied to any computational model. We validated our method against analytically-solvable models of random walk with drift and protein production and degradation. We then applied our method to an active area of biophysics research, namely to a simple computational model of microtubule dynamic instability. Such models have become increasingly complex, perhaps unnecessarily. By adding two new parameters that account for prominent structural features of microtubules, we identify one that can be "compressed away" (the "seam" in the microtubule) and another that is essential to model performance (the "tapering" of microtubule ends). Furthermore, we show that the microtubule model has an underlying, low-dimensional structure that explains the vast majority of our experimental data. We argue that numerical PSC can identify the low-dimensional structure of any computational model in biophysics. The low-dimensional structure of a model is easier to interpret and identifies the mechanisms and experiments that best characterize the system.

physics.bio-ph↗

arXiv2018

Speed-detachment tradeoff and its effect on track bound transport of single motor protein

The transportation of the cargoes in biological cells is primarily driven by the motor proteins on filamentous protein tracks. The stochastic nature of the motion of motor protein often leads to its spontaneous detachment from the track. Using the available experimental data, we demonstrate a tradeoff between the speed of the motor and its rate of spontaneous detachment from the track. Further, it is also shown that this speed-detachment relation follows a power law where its exponent dictates the nature of the motor protein processivity. We utilize this information to study the motion of motor protein on track using a random-walk model. We obtain the average distance travelled in fixed duration and average time required for covering a given distance by the motor protein. These analyses reveal non-monotonic dependence of the motor protein speed on its transport and, therefore, optimal motor speeds can be identified for the time and distance controlled conditions.

q-bio.SC↗

arXiv2018

The effect of the filament-obstacle interaction on the force-velocity relation of a growing biopolymer

We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential. Both the on- and off-rates depend not only on the average force on the obstacle, but also on the shape of the potential on the nanometer length scale. Basing obstacle-induced reduction of the on-rate entirely on the force overestimates the stall force when there are fluctuations in the force exerted on a filament tip. We then perform simulations and analytic calculations using the thermodynamic relationship. We find, consistent with expectations from general thermodynamic relations, that the "Brownian-Ratchet" model is an upper bound to the growth velocity and that for purely repulsive potentials the growth velocity is essentially that predicted by the Brownian-Ratchet model. For shallow potential wells of depth ~ 5k_BT, which might correspond to transient filament-membrane attachments, the zero-force velocity is a substantial fraction of the free-filament velocity. In this case, the growth velocity can depend strongly on the obstacle diffusion coefficient even when the dimensionless diffusion coefficient is large. The velocity also drops more rapidly than predicted by the Brownian-ratchet model, in some cases by as much as a factor of 50 at an opposing force of 1 pN. For deep potential wells, as might result from strong filament-membrane links, both the on- and off-rates are reduced significantly, slowing polymerization. Such potentials can sustain pulling forces while polymerizing, but only if the attractive well has a "shelf" comparable to or greater than the monomer size.

physics.bio-ph↗

arXiv2018

Murburn scheme for thermogenesis mediated by uncoupling protein

Thermogenesis by uncoupling protein (UCP) has traditionally been explained as the dissipation of proton gradient across the inner mitochondrial membrane into heat. Herein, we propose that UCPs, aided by the large pore and positively charged amino acids of suspended loops, enable protonation and transport of DROS. Thus, UCP facilitates DROS-reactions amongst themselves, forming water and liberating heat around the inner mitochondrial membrane. Thereby, the simple murburn scheme for biothermogenesis integrates structural information of UCP with its attributed physiological function.

q-bio.SC↗

arXiv2018

Theoretical Insights into Mechanisms of Stochastic Gating in Channel-Facilitated Molecular Transport

Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically fluctuate between several conformations during the translocation. Although this phenomenon has been intensively investigated, many properties of translocation in dynamically changing environment remain not well understood microscopically. We developed a discrete-state stochastic framework to analyze the molecular mechanisms of transport processes with stochastic gating by explicitly calculating molecular fluxes through the pores. Two scenarios are specifically investigated: 1) symmetry preserving stochastic gating with free-energy changes, and 2) stochastic gating with symmetry changes but without modifications in the overall particle-pore interactions. It is found that stochastic gating can both accelerate or slow down the molecular translocation depending on the specific parameters of the system. We argue that biological systems might optimize their performance by utilizing conformational fluctuations of channels. Our theoretical analysis clarifies physical-chemical aspects of the molecular mechanisms of transport with stochastic gating.

physics.chem-ph↗

arXiv2019

Further Thoughts on Abnormal Chromatin Configuration and Oncogenesis

More than 30 years ago, we published a paper entitled as abnormal chromatin configuration and oncogenesis, which proposed the first hypothesis that links oncogenesis to abnormal three-dimensional (3D) genome structure. Recently, many studies have demonstrated that the 3D genome structure plays a major role in oncogenesis, which strongly supports our hypothesis. In this paper, further thoughts about our hypothesis is presented.

q-bio.SC↗

arXiv2019

Centre-finding in E. coli and the role of mathematical modelling: past, present and future

We review the key role played by mathematical modelling in elucidating two centre-finding patterning systems in E. coli: midcell division positioning by the MinCDE system and DNA partitioning by the ParABS system. We focus particularly on how, despite much experimental effort, these systems were simply too complex to unravel by experiments alone, and instead required key injections of quantitative, mathematical thinking. We conclude the review by analysing the frequency of modelling approaches in microbiology over time. We find that while such methods are increasing in popularity, they are still probably heavily under-utilised for optimal progress on complex biological questions.

q-bio.SC↗

arXiv2019

Generalized Rayleigh-Plesset Theory for Cell Size Maintenance in Viruses and Bacteria

The envelopes covering bacterial cytoplasm possess remarkable elastic properties. They are rigid enough to resist large pressures while being flexible enough to adapt to growth under environmental constraints. Similarly, the virus shells play an important role in their functions. However, the effects of mechanical properties of the outer shell in controlling and maintaining the sizes of bacteria or viruses are unknown. Here, we present a hydrodynamic "bubbles with shell" model, motivated by the study of bubble stability in fluids, to demonstrate that shell rigidity and turgor pressure control the sizes of bacteria and viruses. A dimensionless compliance parameter, expressed in terms of the elastic modulus of the shell, its thickness and the turgor pressure, determines membrane response to deformation and the size of the organisms. By analyzing experiment data, we show that bacterial and viral sizes correlate with shell elasticity, which plays a critical role in regulating size.

physics.bio-ph↗

arXiv2019

ABM of osteoblast's mechanotransduction pathway: time patterns of critical events

Background: Mechanotransduction in bone cells plays a pivotal role in osteoblast differentiation and bone remodelling. Mechanotransduction provides the link between modulation of the extracellular matrix and intracellular actions. By controlling the balance between the intracellular and extracellular domains, the mechanotransduction process determines optimal functionality of the skeletal dynamics, and it is one of the possible causes of osteophatological diseases. Results: Mechanotransduction in a single osteoblast under external mechanical perturbations has been modelled in the agent based framework to reproduce the dynamics of the stochastic reaction diffusion process among molecules in the cytoplasm, nuclear and extracellular domains. The amount of molecules and fluctuations of each molecular class has been analysed in terms of recurrences of critical events. A numerical approach has been developed to invert subordination processes and to extract the directing processes from the molecular signals in order to derive the distribution of recurrence of events. Conclusions: We observed large fluctuations enclose information hidden in the noise which is beyond the dynamic variations of molecular baselines. Studying the system under different parametric conditions and stimuli, the results have shown that the waiting time distributions of each molecule are a signature of the system's dynamics. The behaviours of the molecular waiting times change with the changing of parameters presenting the same variation of patterns for similar interacting molecules and identifying specific alterations for key molecules in the mechanotransduction pathway.

q-bio.SC↗

arXiv2019

Ribosome flow model with different site sizes

We introduce and analyze two general dynamical models for unidirectional movement of particles along a circular chain and an open chain of sites. The models include a soft version of the simple exclusion principle, that is, as the density in a site increases the effective entry rate into this site decreases. This allows to model and study the evolution of "traffic jams" of particles along the chain. A unique feature of these two new models is that each site along the chain can have a different size. Although the models are nonlinear, they are amenable to rigorous asymptotic analysis. In particular, we show that the dynamics always converges to a steady-state, and that the steady-state densities along the chain and the steady-state output flow rate from the chain can be derived from the spectral properties of a suitable matrix, thus eliminating the need to numerically simulate the dynamics until convergence. This spectral representation also allows for powerful sensitivity analysis, i.e. understanding how a change in one of the parameters in the models affects the steady-state. We show that the site sizes and the transition rates from site to site play different roles in the dynamics, and that for the purpose of maximizing the steady-state output (or production) rate the site sizes are more important than the transition rates. We also show that the problem of finding parameter values that maximize the production rate is tractable. We believe that the models introduced here can be applied to study various natural and artificial processes including ribosome flow during mRNA translation, the movement of molecular motors along filaments of the cytoskeleton, pedestrian and vehicular traffic, evacuation dynamics, and more.

q-bio.QM↗

arXiv2019

Physical parameters describing neuronal cargo transport by kinesin UNC-104

In this review, we focus on the kinesin-3 family molecular motor protein UNC-104 and its regulatory protein ARL-8. UNC-104, originally identified in Caenorhabditis elegans (C. elegans), has a primary role transporting synaptic vesicle precursors (SVPs). Although in vitro single-molecule experiments have been performed to primarily investigate the kinesin motor domain, these have not addressed the in vivo reality of the existence of regulatory proteins, such as ARL-8, that control kinesin attachment to/detachment from cargo vesicles, which is essential to the overall transport efficiency of cargo vesicles. To quantitatively understand the role of the regulatory protein, we review the in vivo physical parameters of UNC-104-mediated SVP transport, including force, velocity, run length and run time, derived from wild-type and arl-8-deletion mutant C. elegans. Our future aim is to facilitate the construction of a consensus physical model to connect SVP transport with pathologies related to deficient synapse construction caused by the deficient UNC-104 regulation. We hope that the physical parameters of SVP transport summarized in this review become a useful guide for the development of such model.

physics.bio-ph↗

arXiv2019

Solvated Membrane Nanodiscoids: A Probe For The Effects Of Gaussian Curvature

Several methods now exist to solvate lipid bilayer discoids at the scale of tens of nanometres. Due to their size, such nanodiscoids have a comparatively large boundary-to-area ratio, making them unusually well-suited to probing the effects of Gaussian curvature. Arguing that fluctuations in discoid size and shape are quenched on formation, we quantify the stability, in terms of size and shape, of near-solvation discoid-like flaps that are subject to thermal fluctuations. Using cryo-Electron Microscopy images of Styrene Maleic Acid stabilised discoids, we deduce that stable, saddle-like discoids (with high Gaussian curvature) can likely be solvated from bulk lamellar ($L_α$) phase at moderate-to-high surface tensions ($>10^{-4}$ N/m). We then describe how such tension-controlled solvation can be used for both measuring, and fractionating membrane components according-to, the modulus of Gaussian rigidity $\barκ$. Opportunities for investigating the effects of Gaussian curvature on membrane-embedded proteins, which can be co-solvated during the formation process, are also discussed.

cond-mat.soft↗

arXiv2020

Molecular Self-Organization of Three-Component Lipid Membranes

By constructing a Landau-like energy functional, we investigate the molecular organization of a three-component mixture in cell membranes. In the strongly interacting limit, we model the interaction between molecules using pseudospin variables and convert them into non-interacting variables using a mean-field theory. Next, we construct the two-order parameter Landau-type energy functional through the Helmholtz free energy. By analyzing the Landau free energy, we map out the phase diagram focusing on homogeneous and various phase separated states on the cell membrane.

physics.bio-ph↗

arXiv2019

A buckling instability and its influence on microtubule orientation in plant cells

In growing plant cells, parallel ordering of microtubules (MTs) along the inner surface of the cell membrane influences the direction of cell expansion and thereby plant morphology. For correct expansion of organs that primarily grow by elongating, such as roots and stems, MTs must bend in the high-curvature direction along the cylindrically shaped cell membrane in order to form the required circumferential arrays. Computational studies, which have recapitulated the self-organization of these arrays, ignored MT mechanics and assumed MTs follow geodesics of the cell surface. Here, we show, through analysis of a derived Euler-Lagrange equation, that an elastic MT constrained to a cylindrical surface will deflect away from geodesics and toward low curvature directions to minimize bending energy. This occurs when the curvature of the cell surface is relatively high for a given anchor density. In the limit of infinite anchor density, MTs always follow geodesics. We compare our analytical predictions to measured curvatures and anchor densities and find that the regime in which cells are forming these cortical arrays straddles the region of parameter space in which arrays must form under the antagonistic influence of this mechanically induced deflection. Although this introduces a potential obstacle to forming circumferentially orientated arrays that needs to be accounted for in the models, it also raises the question of whether plants use this mechanical phenomenon to regulate array orientation. The model also constitutes an elegant generalization of the classical Euler-bucking instability along with an intrinsic unfolding of the associated pitchfork bifurcation.

physics.bio-ph↗

arXiv2019

Collective dynamics of microtubule-based 3D active fluids from single microtubules

Self-organization of kinesin-driven, microtubule-based 3D active fluids relies on the collective dynamics of single microtubules. However, the connection between macroscopic fluid flows and microscopic motion of microtubules remains unclear. In this work, the motion of single microtubules was characterized by means of 2D gliding assays and compared with the flows of 3D active fluids. While the scales of the two systems differ by 1,000x, both were driven by processive, non-processive or an equal mixture of both molecular motor proteins. To search for the dynamic correlation between both systems, the motor activities were tuned by varying temperature and ATP concentration, and the changes in both systems were compared. Motor processivity played an important role in active fluid flows but only when the fluids were nearly motionless; otherwise, flows were dominated by hydrodynamic resistance controlled by sample size. Furthermore, while the motors' thermal reaction led active fluids to flow faster with increasing temperature, such temperature dependence could be reversed by introducing temperature-varying depletants, emphasizing the potential role of the depletant in designing an active fluid's temperature response. The temperature response of active fluids was nearly immediate (<10 sec). Such a characteristic enables active fluids to be controlled with a temperature switch. Overall, this work not only clarifies the role of temperature in active fluid activity, but also sheds light on the underlying principles of the relationship between the collective dynamics of active fluids and the dynamics of their constituent single microtubules.

cond-mat.soft↗

arXiv2021

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time-varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including crossbridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation but remains significant at all conditions. Akin to "breathing," advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.

q-bio.SC↗