Boris M. Slepchenko

Topology of the Mitochondrial Inner Membrane: Dynamics and Bioenergetic Implications

Electron tomography indicates that the mitochondrial inner membrane is not normally comprised of baffle‐like folds as depicted in textbooks. In actuality, this membrane is pleomorphic, with narrow tubular regions connecting the internal compartments (cristae) to each other and to the membrane periphery. The membrane topologies observed in condensed (matrix contracted) and orthodox (matrix expanded) mitochondria cannot be interconverted by passive folding and unfolding. Instead, transitions between these morphological states likely involve membrane fusion and fission. Formation of tubular junctions in the inner membrane appears to be energetically favored, because they form spontaneously in yeast mitochondria following large‐amplitude swelling and recontraction. However, aberrant, unattached, vesicular cristae are also observed in these mitochondria, suggesting that formation of cristae junctions depends on factors (such as the distribution of key proteins and/or lipids) that are disrupted during extreme swelling. Computer modeling studies using the “Virtual Cell” program suggest that the shape of the inner membrane can influence mitochondrial function. Simulations indicate that narrow cristae junctions restrict diffusion between intracristal and external compartments, causing depletion of ADP and decreased ATP output inside the cristae.

Virtual cell modelling and simulation software environment

The Virtual Cell (VCell; http://vcell.org/) is a problem solving environment, built on a central database, for analysis, modelling and simulation of cell biological processes. VCell integrates a growing range of molecular mechanisms, including reaction kinetics, diffusion, flow, membrane transport, lateral membrane diffusion and electrophysiology, and can associate these with geometries derived from experimental microscope images. It has been developed and deployed as a web-based, distributed, client-server system, with more than a thousand world-wide users. VCell provides a separation of layers (core technologies and abstractions) representing biological models, physical mechanisms, geometry, mathematical models and numerical methods. This separation clarifies the impact of modelling decisions, assumptions and approximations. The result is a physically consistent, mathematically rigorous, spatial modelling and simulation framework. Users create biological models and VCell will automatically (i) generate the appropriate mathematical encoding for running a simulation and (ii) generate and compile the appropriate computer code. Both deterministic and stochastic algorithms are supported for describing and running non-spatial simulations; a full partial differential equation solver using the finite volume numerical algorithm is available for reaction-diffusion-advection simulations in complex cell geometries including 3D geometries derived from microscope images. Using the VCell database, models and model components can be reused and updated, as well as privately shared among collaborating groups, or published. Exchange of models with other tools is possible via import/export of SBML, CellML and MatLab formats. Furthermore, curation of models is facilitated by external database binding mechanisms for unique identification of components and by standardised annotations compliant with the MIRIAM standard. VCell is now open source, with its native model encoding language (VCML) being a public specification, which stands as the basis for a new generation of more customised, experiment-centric modelling tools using a new plug-in based platform.

Centrosome positioning in interphase cells

The position of the centrosome is actively maintained at the cell center, but the mechanisms of the centering force remain largely unknown. It is known that centrosome positioning requires a radial array of cytoplasmic microtubules (MTs) that can exert pushing or pulling forces involving MT dynamics and the activity of cortical MT motors. It has also been suggested that actomyosin can play a direct or indirect role in this process. To examine the centering mechanisms, we introduced an imbalance of forces acting on the centrosome by local application of an inhibitor of MT assembly (nocodazole), and studied the resulting centrosome displacement. Using this approach in combination with microinjection of function-blocking probes, we found that a MT-dependent dynein pulling force plays a key role in the positioning of the centrosome at the cell center, and that other forces applied to the centrosomal MTs, including actomyosin contractility, can contribute to this process.

Determination of time-dependent inositol-1,4,5-trisphosphate concentrations during calcium release in a smooth muscle cell.

The level of [InsP3]cyt required for calcium release in A7r5 cells, a smooth muscle cell line, was determined by a new set of procedures using quantitative confocal microscopy to measure release of InsP3 from cells microinjected with caged InsP3. From these experiments, the [InsP3]cyt required to evoke a half-maximal calcium response is 100 nM. Experiments with caged glycerophosphoryl-myo-inositol 4, 5-bisphosphate (GPIP2), a slowly metabolized analogue of InsP3, gave a much slower recovery and a half-maximal response of an order of magnitude greater than InsP3. Experimental data and highly constrained variables were used to construct a mathematical model of the InsP3-dependent [Ca2+]cyt changes; the resulting simulations show high fidelity to experiment. Among the elements considered in constructing this model were the mechanism of the InsP3-receptor, InsP3 degradation, calcium buffering in the cytosol, and refilling of the ER stores via sarcoplasmic endoplasmic reticulum ATPase (SERCA) pumps. The model predicts a time constant of 0.8 s for InsP3 degradation and 13 s for GPIP2. InsP3 degradation was found to be a prerequisite for [Ca2+]cyt recovery to baseline levels and is therefore critical to the pattern of the overall [Ca2+]cyt signal. Analysis of the features of this model provides insights into the individual factors controlling the amplitude and shape of the InsP3-mediated calcium signal.

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. We demonstrate that initiation of transport of membrane-bounded melanosomes (pigment granules) to the cell center involves their capture by MT plus ends, and that inhibition of MT dynamics or loss of the MT plus-end tracking protein CLIP-170 from MT tips dramatically inhibits pigment aggregation. We conclude that MT dynamics are required for the initiation of MT transport of membrane organelles in interphase cells, and that +TIPs such as CLIP-170 play an important role in this process.

Diffusion on a curved surface coupled to diffusion in the volume

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. Convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2. The method is applied to a cell-biological problem where a signaling molecule, G-protein Rac, cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior. Simulations on realistic cell geometry are performed to validate, and determine the accuracy of, a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching. The method is implemented within the Virtual Cell computational framework freely accessible at www.vcell.org.

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. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.

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. It is found that a simple two-parameter power law provides a remarkably accurate description of effective diffusion over the entire range of volume fractions and for any given composition of structures. This universality allows for fast computation of diffusion coefficients, once the obstacle shapes and volume fractions are specified. We demonstrate that the excluded volume effect alone can account for a four-to-sixfold reduction in diffusive transport in cells, relative to diffusion in vitro. The study lays the foundation for an accurate coarse-grain formulation that would account for cytoplasm heterogeneity on a micron scale and binding of tracers to intracellular structures.

Physiological modeling with virtual cell framework.

This article describes a computational framework for cell biological modeling and simulation that is based on the mapping of experimental biochemical and electrophysiological data onto experimental images. The framework is designed to enable the construction of complex general models that encompass the general class of problems coupling reaction and diffusion.

Analysis of nonlinear dynamics on arbitrary geometries with the Virtual Cell

The Virtual Cell is a modeling tool that allows biologists and theorists alike to specify and simulate cell-biophysical models on arbitrarily complex geometries. The framework combines an intuitive, front-end graphical user interface that runs in a web browser, sophisticated server-side numerical algorithms, a database for storage of models and simulation results, and flexible visualization capabilities. In this paper, we present an overview of the capabilities of the Virtual Cell, and, for the first time, the detailed mathematical formulation used as the basis for spatial computations. We also present summaries of two rather typical modeling projects, in order to illustrate the principal capabilities of the Virtual Cell. (c) 2001 American Institute of Physics.