A framework for whole-cell mathematical modeling

The default framework for modeling biochemical processes is that of a constant-volume reactor operating under steady-state conditions. This is satisfactory for many applications, but not for modeling growth and division of cells. In this study, a whole-cell modeling framework is developed that assumes expanding volumes and a cell-division cycle. A spherical newborn cell is designed to grow in volume during the growth phase of the cycle. After 80% of the cycle period, the cell begins to divide by constricting about its equator, ultimately affording two spherical cells with total volume equal to twice that of the original. The cell is partitioned into two regions or volumes, namely the cytoplasm (Vcyt) and membrane (Vmem), with molecular components present in each. Both volumes change during the cell cycle; Vcyt changes in response to osmotic pressure changes as nutrients enter the cell from the environment, while Vmem changes in response to this osmotic pressure effect such that membrane thickness remains invariant. The two volumes change at different rates; in most cases, this imposes periodic or oscillatory behavior on all components within the cell. Since the framework itself rather than a particular set of reactions and components is responsible for this behavior, it should be possible to model various biochemical processes within it, affording stable periodic solutions without requiring that the biochemical process itself generates oscillations as an inherent feature. Given that these processes naturally occur in growing and dividing cells, it is reasonable to conclude that the dynamics of component concentrations will be more realistic than when modeled within constant-volume and/or steady-state frameworks. This approach is illustrated using a symbolic whole cell model.     

Mathematical modeling of a minimal protocell with coordinated growth and division

Self-replication is an essential attribute of life but the molecular-level mechanisms involved are not well understood. Cellular self-replication requires not only duplicating all cellular components and doubling volume and membrane area, but also replicating cellular geometry. A whole-cell modeling framework is presented in which an assumed reaction network determines both concentration changes of cellular components and cell geometry. Cell shape is calculated by minimizing membrane-bending energy. Using this framework, simultaneous doubling of volume, surface area, and all components was found to be insufficient to provide mid-cell “pinching” of the parental cell to form two daughter cells. This prompted the design of a minimal protocell that includes a growing shell, a cell-cycle engine, and a contractile ring to enforce cytokinesis. Kinetic parameters were found such that the system exhibited periodic behavior with fundamental aspects of self-replication. This involved simultaneous doubling of all cellular components during a cell cycle, doubling cell volume and membrane area, achieving periodic changes in surface/volume ratio, and forming daughter cells that were geometrically equivalent to each other and to the “newborn” parental cell. The results presented here impact the design of laboratory protocells and the development of a modular strategy for constructing a comprehensive in silico whole-cell model.     

Astrocyte swelling leads to membrane unfolding, not membrane insertion

The mechanisms mediating the release of chemical transmitters from astrocytes are the subject of intense research. Recent experiments have shown that hypotonic conditions stimulate the release of glutamate and ATP from astrocytes, but a mechanistic understanding of this process is not available. To determine whether hypotonicity activates the process of regulated exocytosis, we monitored membrane capacitance by the whole-cell patch-clamp technique whilst a hypotonic medium was applied to cultured astrocytes. If exocytosis is triggered under hypotonic conditions, as it is following increases in cytosolic calcium, a net increase in membrane surface area, monitored by measuring the whole-cell membrane capacitance, is expected. Simultaneous measurements of cell size and whole-cell membrane conductance and surface area demonstrated that hypotonic medium (210 mOsm for 200 s) resulted in an increase in membrane conductance and in the swelling of cultured astrocytes by an average of 40%, as monitored by cell cross-sectional area, but without any corresponding change in membrane surface area. As we have demonstrated that capacitance measurements have the sensitivity to detect increases in cell surface area as small as 0.5%, we conclude that cell swelling occurs via an exocytosis-independent mechanism, probably involving the unfolding of the plasma membrane.     

Changes in surface area of intact guard cells are correlated with membrane internalization

Guard cells must maintain the integrity of the plasma membrane as they undergo large, rapid changes in volume. It has been assumed that changes in volume are accompanied by changes in surface area, but mechanisms for regulating plasma membrane surface area have not been identified in intact guard cells, and the extent to which surface area of the guard cells changes with volume has never been determined. The alternative hypothesis-that surface area remains approximately constant because of changes in shape-has not been investigated. To address these questions, we determined surface area for intact guard cells of Vicia faba as they underwent changes in volume in response to changes in the external osmotic potential. We also estimated membrane internalization for these cells. Epidermal peels were subjected to external solutions of varying osmotic potential to shrink and swell the guard cells. A membrane-specific fluorescent dye was used to identify the plasma membrane, and confocal microscopy was used to acquire a series of optical paradermal sections of the guard cell pair at each osmotic potential. Solid digital objects representing the guard cells were created from the membrane outlines identified in these paradermal sections, and surface area, volume, and various linear dimensions were determined for these solid objects. Surface area decreased by as much as 40% when external osmotic potential was increased from 0 to 1.5 MPa, and surface area varied linearly with volume. Membrane internalization was approximated by determining the amount of the fluorescence in the cell's interior. This value was shown to increase approximately linearly with decreases in the cell's surface area. The changes in surface area, volume, and membrane internalization were reversible when the guard cells were returned to a buffer solution with an osmotic potential of approximately zero. The data show that intact guard cells undergo changes in surface area that are too large to be accommodated by plasma membrane stretching and shrinkage and suggest that membrane is reversibly internalized to maintain cell integrity.     

Macromolecular crowding and volume perception in dog red cells

To differentiate whether the primary volume signal in dog red cells arises from a change in cell configuration or the concentration and dilution of cell contents, we prepared resealed ghosts that had the same surface area and hemoglobin concentration as intact cells but less than 1/3 their volume. Shrinkage of both intact cells and resealed ghosts triggered Na/H exchange. Activation of this transporter in the two preparations correlated closely with cytosolic protein concentration but not at all with volume. The Na/H exchanger was more sensitive to shrinkage in albumin-loaded resealed ghosts than in intact cells or ghosts containing only hemoglobin. Similar results were obtained for the swelling-induced [K-Cl] cotransporter. We believe perception of cell volume originates with changes in cytoplasmic protein concentration. We think the kinases and phosphatases that control the activation of membrane transporters in response to cell swelling or shrinkage are regulated by the mechanism of macromolecular crowding.     

Deformation-induced lipid trafficking in alveolar epithelial cells

Mechanical ventilation with a high tidal volume results in lung injury that is characterized by blebbing and breaks both between and through alveolar epithelial cells. We developed an in vitro model to simulate ventilator-induced deformation of the alveolar basement membrane and to investigate, in a direct manner, epithelial cell responses to deforming forces. Taking advantage of the novel fluorescent properties of BODIPY lipids and the fluorescent dye FM1-43, we have shown that mechanical deformation of alveolar epithelial cells results in lipid transport to the plasma membrane. Deformation-induced lipid trafficking (DILT) was a vesicular process, rapid in onset, and was associated with a large increase in cell surface area. DILT could be demonstrated in all cells; however, only a small percentage of cells developed plasma membrane breaks that were reversible and nonlethal. Therefore, DILT was not only involved in site-directed wound repair but might also have served as a cytoprotective mechanism against plasma membrane stress failure. This study suggests that DILT is a regulatory mechanism for membrane trafficking in alveolar epithelia and provides a novel biological framework within which to consider alveolar deformation injury and repair.     

Calcium dependence of bleb formation and cell death in hepatocytes

Calcium dependence of bleb formation and cell death was evaluated in rat hepatocytes following ATP depletion by metabolic inhibition with KCN and iodoacetate ('chemical hypoxia'). Cytosolic free Ca2+ was measured in single cells by ratio imaging of Fura-2 fluorescence using multiparameter digitized video microscopy. Cells formed surface blebs within 10 to 20 minutes after chemical hypoxia and most cells lost viability within an hour. An increase of cytosolic free Ca2+ was not required for bleb formation to occur. One to a few minutes prior to the onset of cell death, free Ca2+ increased rapidly in high Ca2+ buffer (1.2 mM) but not in low Ca2+ buffer (less than 1 microM). In either buffer, the rate of cell killing was the same. As the onset of cell death was approached in both high and low Ca2+ buffers, Fura-2 began to leak from the cells at an accelerating rate indicating rapidly increasing plasma membrane permeability. In high Ca2+ buffer, cytosolic free Ca2+ increased in parallel with dye leakage. No regional changes in cytosolic free Ca2+ were observed during this metastable period of increased membrane permeability. In many experiments, actual rupture of cell surface blebs could be observed which led to micron-size discontinuities of the cell surface and cell death. We conclude that a metastable period characterized by increasing plasma membrane permeability marked the onset of cell death in cultured hepatocytes which culminated in rupture of a cell surface bleb. An increase of cytosolic free Ca2+ was not required for the metastable state to develop or cell death to occur.     

MOM22 is a receptor for mitochondrial targeting sequences and cooperates with MOM19.

Recognition of targeting signals is a crucial step in protein sorting within the cell. So far, only a few components capable of deciphering targeting signals have been identified, and insights into the chemical nature of the interaction between the signals and their receptors are scarce. Using highly purified mitochondrial outer membrane vesicles, we demonstrate that MOM22 and MOM19, components of the protein import complex of the outer membrane, bind preproteins at the mitochondrial surface in a reversible fashion. Interaction specifically and directly occurs with the N-terminal presequence and is abolished after inactivation of either MOM22 or MOM19. Binding is salt sensitive, suggesting that recognition involves electrostatic forces between the positive charges of the presequence and the acidic cytosolic domain of MOM22. MOM19 and MOM22 can be cross-linked with high efficiency. We propose that the two proteins form a complex which functions as the presequence receptor at the mitochondrial surface and facilitates the movement of preproteins into the translocation pore.     

Sequential-replenishment mechanism of exocytosis in pancreatic acini

Here we report exocytosis of zymogen granules, as examined by multiphoton excitation imaging in intact pancreatic acini. Cholecystokinin induces Ca 2+ oscillations that trigger exocytosis when the cytosolic Ca 2+ concentration exceeds 1 microM. Zymogen granules fused with the plasma membrane maintain their Omega-shaped profile for an average of 220 s and serve as targets for sequential fusion of granules that are located within deeper layers of the cell. This secondary exocytosis occurs as rapidly as the primary exocytosis and accounts for most exocytotic events. Granule-granule fusion does not seem to precede primary exocytosis, indicating that secondary fusion events may require a plasma-membrane factor. This sequential-replenishment mechanism of exocytosis allows the cell to take advantage of a large supply of fusion-ready granules without needing to transport them to the plasma membrane.     

Active remodeling of cortical actin regulates spatiotemporal organization of cell surface molecules

Many lipid-tethered proteins and glycolipids exist as monomers and nanoclusters on the surface of living cells. The spatial distribution and dynamics of formation and breakup of nanoclusters does not reflect thermal and chemical equilibrium and is controlled by active remodeling of the underlying cortical actin. We propose a model for nanoclustering based on active hydrodynamics, wherein cell surface molecules bound to dynamic actin are actively driven to form transient clusters. This consistently explains all of our experimental observations. Using FCS and TIRF microscopy, we provide evidence for the existence of short, dynamic, polymerizing actin filaments at the cortex, a key assumption of the theoretical framework. Our theory predicts that lipid-anchored proteins that interact with dynamic actin must exhibit anomalous concentration fluctuations, and a cell membrane protein capable of binding directly to actin can form nanoclusters. These we confirm experimentally, providing an active mechanism for molecular organization and its spatiotemporal regulation on the plasma membrane.     

Parallel microchannel-based measurements of individual erythrocyte areas and volumes

We describe a microchannel device which utilizes a novel approach to obtain area and volume measurements on many individual red blood cells. Red cells are aspirated into the microchannels much as a single red blood cell is aspirated into a micropipette. Inasmuch as there are thousands of identical microchannels with defined geometry, data for many individual red cells can be rapidly acquired, and the fundamental heterogeneity of cell membrane biophysics can be analyzed. Fluorescent labels can be used to quantify red cell surface and cytosolic features of interest simultaneously with the measurement of area and volume for a given cell. Experiments that demonstrate and evaluate the microchannel measuring capabilities are presented and potential improvements and extensions are discussed.     

Studies onSargassum

Summary Cytological comparisons of homologous tissues in blades and stipes by stereological analysis have shown differences exist between blade and stipe organs inSargassum. Based on measurements of total thylakoid and cristae membrane surface areas in these organs blades were found to contain 61% more thylakoid membrane surface and 65% more cristae membrane than stipes on a per unit volume basis. Assuming photosynthesis and respiration are directly related to the surface area of the internal membranes in the respective organelles it is possible to predict that blades will have a 61% greater photosynthetic and a 65% greater respiratory potential. Photosynthetic and respiratory rates for blades and stipes were determined manometrically and show a 62% greater photosynthetic and 59% greater respiratory rates for the blade tissues agreeing very well with predicted values.Present evidence indicates that photosynthetic and respiratory rate differences observed in the blades and stipes inSargassum are the result of increased membrane surface areas in the larger cells of the tissues which make up the blade. The basic cell structure,i.e., the percent volume of cell cytoplasm occupied by each organelle, is similar in homologous tissues of both organs regardless of cell size. Therefore physiological differences between the two organs are primarily due to changes in cell size and not in basic cell construction. This provides an interesting mechanism for producing physiological differences without changing basic cell structure in the organs of this plant.     

Chemical Memory Reactions Induced Bursting Dynamics in Gene Expression

Memory is a ubiquitous phenomenon in biological systems in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. Specifically, many memorial phenomena are characterized by chemical memory reactions that may fire under particular system conditions. These conditional chemical reactions contradict to the extant stochastic approaches for modeling chemical kinetics and have increasingly posed significant challenges to mathematical modeling and computer simulation. To tackle the challenge, I proposed a novel theory consisting of the memory chemical master equations and memory stochastic simulation algorithm. A stochastic model for single-gene expression was proposed to illustrate the key function of memory reactions in inducing bursting dynamics of gene expression that has been observed in experiments recently. The importance of memory reactions has been further validated by the stochastic model of the p53-MDM2 core module. Simulations showed that memory reactions is a major mechanism for realizing both sustained oscillations of p53 protein numbers in single cells and damped oscillations over a population of cells. These successful applications of the memory modeling framework suggested that this innovative theory is an effective and powerful tool to study memory process and conditional chemical reactions in a wide range of complex biological systems.     

Methods for determination of growth-rate-dependent changes in hybridoma volume,shape and surface structure during continuous recycle

Hybridoma volume and surface membrane structure were found to vary as a function of specific growth rate using a method of cell recycle with continuous medium perfusion to vary growth rate. Mean hybridoma volume determined at constant osmolality by both electronic particle counting and scanning electron microscopic (SEM) methods indicated that rapidly growing cells are significantly larger than very slowly growing cells. We have previously determined that during both rapid and slow growth over a range of L-glutamine provision rates (Gln PR) that specific monoclonal antibody (MoAb) secretion rate was not changed. In this study a constant MoAb secretion rate per unit of membrane area was found which may indicate that changing membrane area is not a rate-determining factor in MoAb secretion. SEM methods were of limited use for accurate determination of cell volume due to cell shrinkage and large coefficients of variations. In spite of this limitation, SEM stereology methods were useful in confirming that cells remained spherical over a wide range of specific growth rates and that hybridoma cells were not circular. Sequential SEM observations also revealed that surface membrane structure of the 9.2.27 murine hybridoma investigated was correlated with growth rate. Under conditions of very slow growth, hybridoma surface microvilli density appeared to be significantly reduced.     

Ca2+ triggers massive exocytosis in Chinese hamster ovary cells.

We have tracked the cell surface area of CHO cells by measuring the membrane capacitance, Cm. An increase in cytosolic [Ca2+], [Ca2+]i, increased the cell surface area by 20-30%. At micromolar [Ca2+]i the increase occurred in minutes, while at 20 microM or higher [Ca2+]i it occurred in seconds and was transient. GTPgammaS caused a 3% increase even at 0.1 microM [Ca2+]i. We conclude that CHO cells, previously thought capable only of constitutive exocytosis, can perform Ca2+-triggered exocytosis that is both massive and rapid. Ca2+-triggered exocytosis was also observed in 3T3 fibroblasts. Our findings add evidence to the view that Ca induces exocytosis in cells other than known secretory cells.     

Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.     

Structural and functional properties of hydration and confined water in membrane interfaces

The scope of the present review focuses on the interfacial properties of cell membranes that may establish a link between the membrane and the cytosolic components. We present evidences that the current view of the membrane as a barrier of permeability that contains an aqueous solution of macromolecules may be replaced by one in which the membrane plays a structural and functional role. Although this idea has been previously suggested, the present is the first systematic work that puts into relevance the relation water-membrane in terms of thermodynamic and structural properties of the interphases that cannot be ignored in the understanding of cell function. To pursue this aim, we introduce a new definition of interphase, in which the water is organized in different levels on the surface with different binding energies. Altogether determines the surface free energy necessary for the structural response to changes in the surrounding media. The physical chemical properties of this region are interpreted in terms of hydration water and confined water, which explain the interaction with proteins and could affect the modulation of enzyme activity. Information provided by several methodologies indicates that the organization of the hydration states is not restricted to the membrane plane albeit to a region extending into the cytoplasm, in which polar head groups play a relevant role. In addition, dynamic properties studied by cyclic voltammetry allow one to deduce the energetics of the conformational changes of the lipid head group in relation to the head-head interactions due to the presence of carbonyls and phosphates at the interphase. These groups are, apparently, surrounded by more than one layer of water molecules: a tightly bound shell, that mostly contributes to the dipole potential, and a second one that may be displaced by proteins and osmotic stress. Hydration water around carbonyl and phosphate groups may change by the presence of polyhydroxylated compounds or by changing the chemical groups esterified to the phosphates, mainly choline, ethanolamine or glycerol. Thus, surface membrane properties, such as the dipole potential and the surface pressure, are modulated by the water at the interphase region by changing the structure of the membrane components. An understanding of the properties of the structural water located at the hydration sites and the functional water confined around the polar head groups modulated by the hydrocarbon chains is helpful to interpret and analyze the consequences of water loss at the membranes of dehydrated cells. In this regard, a correlation between the effects of water activity on cell growth and the lipid composition is discussed in terms of the recovery of the cell volume and their viability. Critical analyses of the properties of water at the interface of lipid membranes merging from these results and others from the literature suggest that the interface links the membrane with the aqueous soluble proteins in a functional unit in which the cell may be considered as a complex structure stabilized by water rather than a water solution of macromolecules surrounded by a semi permeable barrier.     

How does plasma membrane surface area accommodate alterations in guard cell volume during stomatal closing?

During stomatal movement, guard cells undergo considerable and repetitive variations in cell volume and consequently surface area over a period of minutes. Due to limited stretching capability of the plasma membrane, alterations in the surface area must accommodate the volume changes through membrane turnover. Using fluorescence imaging and electrophysiology techniques, extensive studies imply that endocytosis may be a critical mechanism for the plasma membrane turnover. In contrast to the conventional studies, using transmission electronic microscope in combination with laser confocal microscope so that the membrane turnover can be detected without a resolution limitation, our works, recently published in the Journal of Experimental Botany, has provided strong evidences that excretion and folding of plasma membrane are critical for the accommodation of the cell volume alterations in intact guard cells in Vicia faba L. These results have opened a new perspective on the mechanism for the membrane turnover during stomatal movement. In this addendum, we further discuss some key issues about the mechanisms for the accommodation of the cell volume alterations during stomatal movements.Key words: stomata, guard cell, plasma membrane, surface area, endocytosis, excretion, accommodationGuard cells control stomatal movement thereby regulating gas exchange in plants. During stomatal movement, guard cells undergo considerable and repetitive variations in cell volume and consequently surface area over a period of minutes. It was proposed that the alterations of the plasma membrane surface area could be up to 40%,¹ whereas the maximum possible stretching of membranes was limited to only about 2%.² Furthermore, due to the presence of a turgor pressure, it has been commonly thought that membrane infoldings should not occur in the guard cells.³ Therefore, it is reasonable to propose that alterations in the surface area must be accomplished by addition and removal of membrane material to and from the plasma membrane.⁴ While many studies imply that endocytosis most likely functions to accommodate the alterations in guard cell volume, many crucial questions about this mechanism deserve to be argued.     

Geometry and mechanics of the morphogenesis of active membranes on the example of plant trichome cells of the genus <Emphasis Type="Italic">Draba</Emphasis> L.

The stages of the early morphogenesis of simple (unbranched) and complex (branched) unicellular trichomes are studied in two species of the genus Draba—D. sibirica (Pall.) Thell. and D. daurica DC. The geometry of morphogenesis is estimated by analyzing intraindividual variation of quantitative morphological characteristics of the developing leaf blade and peduncle trichomes. The surface of all types of trichome cells first acquires a spherical shape, followed by a U-shaped configuration with cylindrical proximal and spherical distal regions. In the development of complex trichomes, the area of the distal zone grows at a higher rate, which leads to separation of its volume into individual spherical regions, the morphogenesis of which repeats the early morphogenetic stages of the overall trichome cell, forming simple (unbranched) or complex (branched) trichome rays. As a rule, the lateral polarity of a trichome cell coincides with the proximodistal polarity of the leaf. Quantitative morphological data make it possible to infer an algorithm of the changes in shape common for all trichome cells, namely, the growth cycle comprising alternation of the phases of increase and decrease in the curvature of the outer cell surface. This surface is an active membrane expanded by the internal pressure and concurrently capable of actively increasing its area by incorporation of new structural elements. A distinctive feature of the proposed model is the geometrical inhomogeneity of the surface movement, changing the radius of curvature and creating internal (active) mechanical stresses in this membrane. A decrease in the ratio of the membrane surface area to the volume deprives the spatially homogeneous shape of its stability; correspondingly, the transition from elastic resistance to internal pressure to active resistance with the help of curvature differentiation becomes more energetically favorable. The source for growth and morphogenesis of the active membrane is alternation of the phases of local curvature leveling, which “charges” the membrane with active mechanical stresses and “discharge” of these stresses, leading to differentiation of the membrane’s local curvatures.