Bridging molecular to cellular scales for models of membrane receptor signaling.

Biochemical interactions at membranes are the starting points for cell signaling networks. But bimolecular reaction kinetics are difficult to experimentally measure on 2-dimensional membranes and are usually measured in volumetric assays. Membrane tethering produces confinement and steric effects that will significantly impact binding rates in ways that are not readily estimated from volumetric measurements.

Asymmetric stem cell division maintains genetic heterogeneity of tissue cells.

Within a given tissue, the stem cell niche provides the microenvironment for stem cells suitable for their self-renewal. Conceptually, the niche space constrains the size of a stem-cell pool, as the cells sharing the niche compete for its space. It has been suggested that either neutral- or non-neutral-competition of stem cells changes the clone dynamics of stem cells.

A model of actin-driven endocytosis explains differences of endocytic motility in budding and fission yeast.

A comparative study (Sun , 2019) showed that the abundance of proteins at sites of endocytosis in fission and budding yeast is more similar in the two species than previously thought, yet membrane invaginations in fission yeast elongate twofold faster and are nearly twice as long as in budding yeast. Here we use a three-dimensional model of a motile endocytic invagination (Nickaeen , 2019) to investigate factors affecting elongation of the invaginations. We found that differences in turgor pressure in the two yeast species can largely explain the paradoxical differences observed experimentally in endocytic motility.

Mad dephosphorylation at the nuclear pore is essential for asymmetric stem cell division.

Stem cells divide asymmetrically to generate a stem cell and a differentiating daughter cell. Yet, it remains poorly understood how a stem cell and a differentiating daughter cell can receive distinct levels of niche signal and thus acquire different cell fates (self-renewal versus differentiation), despite being adjacent to each other and thus seemingly exposed to similar levels of niche signaling. In the ovary, germline stem cells (GSCs) are maintained by short range bone morphogenetic protein (BMP) signaling; the BMP ligands activate a receptor that phosphorylates the downstream molecule mothers against decapentaplegic (Mad).

Actin assembly produces sufficient forces for endocytosis in yeast.

We formulated a spatially resolved model to estimate forces exerted by a polymerizing actin meshwork on an invagination of the plasma membrane during endocytosis in yeast cells. The model, which approximates the actin meshwork as a visco-active gel exerting forces on a rigid spherocylinder representing the endocytic invagination, is tightly constrained by experimental data. Simulations of the model produce forces that can overcome resistance of turgor pressure in yeast cells.

A free-boundary model of a motile cell explains turning behavior.

To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method.

A conservative algorithm for parabolic problems in domains with moving boundaries.

We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior.

Recycling of kinesin-1 motors by diffusion after transport.

Kinesin motors drive the long-distance anterograde transport of cellular components along microtubule tracks. Kinesin-dependent transport plays a critical role in neurogenesis and neuronal function due to the large distance separating the soma and nerve terminal. The fate of kinesin motors after delivery of their cargoes is unknown but has been postulated to involve degradation at the nerve terminal, recycling via retrograde motors, and/or recycling via diffusion.

Spatial modeling of cell signaling networks.

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model.

Virtual Cell: computational tools for modeling in cell biology.

The Virtual Cell (VCell) is a general computational framework for modeling physicochemical and electrophysiological processes in living cells. Developed by the National Resource for Cell Analysis and Modeling at the University of Connecticut Health Center, it provides automated tools for simulating a wide range of cellular phenomena in space and time, both deterministically and stochastically. These computational tools allow one to couple electrophysiology and reaction kinetics with transport mechanisms, such as diffusion and directed transport, and map them onto spatial domains of various shapes, including irregular three-dimensional geometries derived from experimental images.

Diffusion amid random overlapping obstacles: similarities, invariants, approximations.

Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (D(eff)) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (φ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of D(eff) (φ) for obstacles of any given shape.

Use of virtual cell in studies of cellular dynamics.

The Virtual Cell (VCell) is a unique computational environment for modeling and simulation of cell biology. It has been specifically designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists. The models created with VCell can range from the simple, to evaluate hypotheses or to interpret experimental data, to complex multilayered models used to probe the predicted behavior of spatially resolved, highly nonlinear systems.

Quantifying a pathway: kinetic analysis of actin dendritic nucleation.

Progress in uncovering the reaction networks that underlie important cell functions is laying the groundwork for quantitative identification of protein-interaction pathways. Since direct measurement of rate constants is not always feasible, the parameters are often inferred from multiple pieces of data using kinetic analyses based on appropriate mathematical models. The success of this approach relies on the sufficiency of available experimental data for a unique parameterization of the network.

CLIP-170-dependent capture of membrane organelles by microtubules initiates minus-end directed transport.

Cytoplasmic microtubules (MTs) continuously grow and shorten at free plus ends. During mitosis, this dynamic behavior allows MTs to capture chromosomes to initiate their movement to the spindle poles; however, the role of MT dynamics in capturing organelles for transport in interphase cells has not been demonstrated. Here we use Xenopus melanophores to test the hypothesis that MT dynamics significantly contribute to the efficiency of MT minus-end directed transport of membrane organelles.

Diffusion in cytoplasm: effects of excluded volume due to internal membranes and cytoskeletal structures.

The intricate geometry of cytoskeletal networks and internal membranes causes the space available for diffusion in cytoplasm to be convoluted, thereby affecting macromolecule diffusivity. We present a first systematic computational study of this effect by approximating intracellular structures as mixtures of random overlapping obstacles of various shapes. Effective diffusion coefficients are computed using a fast homogenization technique.

Actin dynamics is essential for myosin-based transport of membrane organelles.

Actin filaments that serve as "rails" for the myosin-based transport of membrane organelles [1-4] continuously turn over by concurrent growth and shortening at the opposite ends [5]. Although it is known that dynamics of actin filaments is essential for many of the actin cytoskeleton functions, the role of such dynamics in myosin-mediated organelle transport was never studied before. Here, we addressed the role of turnover of actin filaments in the myosin-based transport of membrane organelles by treating cells with the drugs that suppress actin-filament dynamics and found that such a suppression significantly inhibited organelle transport along the actin filaments without inhibiting their intracellular distribution or the activity of the myosin motors.

Actin bundling: initiation mechanisms and kinetics.

Bundling of rapidly polymerizing actin filaments underlies the dynamics of filopodial protrusions that play an important role in cell migration and cell-cell interaction. Recently, the formation of actin bundles has been reconstituted in vitro, and two scenarios of bundle initiation, involving binding of two filament tips and, alternatively, linking of the tip of one filament to the side of the other, have been discussed. A first theoretical analysis is presented indicating that the two mechanisms can be distinguished experimentally.

Diffusion on a Curved Surface Coupled to Diffusion in the Volume: Application to Cell Biology.

An algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume, a problem often arising in cell biology. It applies to pixilated surfaces obtained from experimental images and performs at low computational cost. In the method, the Laplace-Beltrami operator is approximated locally by the Laplacian on the tangential plane and then a finite volume discretization scheme based on a Voronoi decomposition is applied.

On sensitivity amplification in intracellular signaling cascades.

Sensitivity amplification has long been regarded as a virtually universal property of signal transduction cascades, yet a comprehensive parameter analysis remains a challenge even for relatively simple networks. We use a fast and accurate method to compute properties of multilevel cascades of activation-inactivation cycles and show that the monocyclic cascades amplify sensitivity only under specific conditions. In particular, it is found that efficient sensitivity amplification in a cascade, relative to the sensitivities of individual cycles, requires asymmetry in saturation of converter enzymes, with inhibitors much more saturated than activators.

A model of the kinetics of lanthanum in human bone, using data collected during the clinical development of the phosphate binder lanthanum carbonate.

Objective: Lanthanum carbonate (Fosrenol) is a non-calcium phosphate binder that controls hyperphosphataemia without increasing calcium intake above guideline targets. The biological fate and bone load of lanthanum were modelled with the aid of a four-compartment kinetic model, analogous to that of calcium.

Methods: The model used data from healthy subjects who received intravenous lanthanum chloride or oral lanthanum carbonate, and bone lanthanum concentration data collected from dialysis patients during three long-term trials (up to 5 years).

Quantitative analysis of G-actin transport in motile cells.

Cell migration is based on an actin treadmill, which in turn depends on recycling of G-actin across the cell, from the rear where F-actin disassembles, to the front, where F-actin polymerizes. To analyze the rates of the actin transport, we used the Virtual Cell software to solve the diffusion-drift-reaction equations for the G-actin concentration in a realistic three-dimensional geometry of the motile cell. Numerical solutions demonstrate that F-actin disassembly at the cell rear and assembly at the front, along with diffusion, establish a G-actin gradient that transports G-actin forward "globally" across the lamellipod.

Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubule-based transport.

Intracellular transport of membrane organelles occurs along microtubules (MTs) and actin filaments (AFs). Although transport along each type of the cytoskeletal tracks is well characterized, the switching between the two types of transport is poorly understood because it cannot be observed directly in living cells. To gain insight into the regulation of the switching of membrane organelles between the two major transport systems, we developed a novel approach that combines live cell imaging with computational modeling.

In vivo dynamics of Rac-membrane interactions.

The small GTPase Rac cycles between the membrane and the cytosol as it is activated by nucleotide exchange factors (GEFs) and inactivated by GTPase-activating proteins (GAPs). Solubility in the cytosol is conferred by binding of Rac to guanine-nucleotide dissociation inhibitors (GDIs). To analyze the in vivo dynamics of Rac, we developed a photobleaching method to measure the dissociation rate constant (k(off)) of membrane-bound GFP-Rac.

Modeling and analysis of calcium signaling events leading to long-term depression in cerebellar Purkinje cells.

Modeling and simulation of the calcium signaling events that precede long-term depression of synaptic activity in cerebellar Purkinje cells are performed using the Virtual Cell biological modeling framework. It is found that the unusually high density and low sensitivity of inositol-1,4,5-trisphosphate receptors (IP3R) are critical to the ability of the cell to generate and localize a calcium spike in a single dendritic spine. The results also demonstrate the model's capability to simulate the supralinear calcium spike observed experimentally during coincident activation of the parallel and climbing fibers.