An age-dependent feedback control model of calcium dynamics in yeast cells

The functional decline of selected proteins or organelles leads to aging at the intracellular level. Identification of these proteins or organelles is usually challenging to traditional single-factor approaches since these factors are inter-connected via feedback or feedforward controls. Establishing a feedback control model to simulate the interactions of multiple factors is an insightful approach to guide the search for proteins involved in aging. However, there are only a few mathematical models describing the age-dependent accumulation of DNA mutations, which are directly or indirectly induced by deterioration of the intracellular environment including alteration of calcium homeostasis, a contributor of aging. Thus, based on Cui and Kaandorp’s model, we develop an age-dependent mathematical model for the calcium homeostasis in budding yeast Saccharomyces cerevisiae. Our model contains cell cycle-dependent aging factors and can qualitatively reproduce calcium shocks and calcium accumulations in cells observed in experiments. Using this model, we predict calcium oscillations in wild type, pmc1Δ, and pmr1Δ cells. This prediction suggests that Pmr1p plays a major role in regulating cytosolic calcium. Combining the model with our experimental lifespan data, we predict an upper-limit of cytosolic calcium tolerance for cell survival. This prediction indicates that, for aged cells (>35 generations), no pmr1 Δ can tolerate the cytosolic calcium concentration of 0.1 μM while a very small fraction (1%) of aged wild type cells (>50 generations) can tolerate a high cytosolic calcium concentration of 0.5 μM.     

Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective.

Calcium is tightly regulated in mammals because of the critical role of calcium ion concentrations in many physiological functions. In this work, we develop a model for calcium homeostasis and identify integral feedback control as a functional module that maintains this homeostasis. We argue that maintaining calcium concentrations in a narrow range and perfect adaptation seen when the calcium homeostatic mechanism is subjected to extreme disturbances are the result of a feedback control system implementing integral control through specific interactions of the regulating hormones. Based on the constraints imposed by the suggested integral control, we arrive at a simple dynamical model for calcium homeostasis. We show that the model is biologically plausible and is consistent with known physiology. Furthermore, the utility of the integral-feedback model is revealed by examining an extreme calcium perturbation, parturient paresis in dairy cows.     

Model of Fission Yeast Cell Shape Driven by Membrane-Bound Growth Factors and the Cytoskeleton

Fission yeast serves as a model for how cellular polarization machinery consisting of signaling molecules and the actin and microtubule cytoskeleton regulates cell shape. In this work, we develop mathematical models to investigate how these cells maintain a tubular shape of approximately constant diameter. Many studies identify active Cdc42, found in a cap at the inner membrane of growing cell tips, as an important regulator of local cell wall remodeling, likely through control of exocyst tethering and the targeting of other polarity-enhancing structures. First, we show that a computational model with Cdc42-dependent local cell wall remodeling under turgor pressure predicts a relationship between spatial extent of growth signal and cell diameter that is in agreement with prior experiments. Second, we model the consequences of feedback between cell shape and distribution of Cdc42 growth signal at cell tips. We show that stability of cell diameter over successive cell divisions places restrictions on their mutual dependence. We argue that simple models where the spatial extent of the tip growth signal relies solely on geometrical alignment of confined microtubules might lead to unstable width regulation. Third, we study a computational model that combines a growth signal distributed over a characteristic length scale (as, for example, by a reaction-diffusion mechanism) with an axis-sensing microtubules system that places landmarks at positions where microtubule tips touch the cortex. A two-dimensional implementation of this model leads to stable cell diameter for a wide range of parameters. Changes to the parameters of this model reproduce straight, bent, and bulged cell shapes, and we discuss how this model is consistent with other observed cell shapes in mutants. Our work provides an initial quantitative framework for understanding the regulation of cell shape in fission yeast, and a scaffold for understanding this process on a more molecular level in the future.     

Calcium-Actin Waves and Oscillations of Cellular Membranes

We propose a mechanism for the formation of membrane oscillations and traveling waves, which arise due to the coupling between the actin cytoskeleton and the calcium flux through the membrane. In our model, the fluid cell membrane has a mobile but constant population of proteins with a convex spontaneous curvature, which act as nucleators of actin polymerization and adhesion. Such a continuum model couples the forces of cell-substrate adhesion, actin polymerization, membrane curvature, and the flux of calcium through the membrane. Linear stability analysis shows that sufficiently strong coupling among the calcium, membrane, and protein dynamics may induce robust traveling waves on the membrane. This result was checked for a reduced feedback scheme and is compared to the results without the effects of calcium, where permanent phase separation without waves or oscillations is obtained. The model results are compared to the published observations of calcium waves in cell membranes, and a number of testable predictions are proposed.     

Ion condensation and signal transduction

Many abiotic and other signals are transduced in eukaryotic cells by changes in the level of free calcium via pumps, channels and stores. We suggest here that ion condensation should also be taken into account. Calcium, like other counterions, is condensed onto linear polymers at a critical value of the charge density. Such condensation resembles a phase transition and has a topological basis in that it is promoted by linear as opposed to spherical assemblies of charges. Condensed counterions are delocalised and can diffuse in the so-called near region along the polymers. It is generally admitted that cytoskeletal filaments, proteins colocalised with these filaments, protein filaments distinct from cytoskeletal filaments, and filamentous assemblies of other macromolecules, constitute an intracellular macromolecular network. Here we draw attention to the fact that this network has physicochemical characteristics that enable counterion condensation. We then propose a model in which the feedback relationships between the condensation/decondensation of calcium and the activation of calcium-dependent kinases and phosphatases control the charge density of the filaments of the intracellular macromolecular network. We show how condensation might help mediate free levels of calcium both locally and globally. In this model, calcium condensation/decondensation on the macromolecular network creates coherent patterns of protein phosphorylation that integrate signals. This leads us to hypothesize that the process of ion condensation operates in signal transduction, that it can have an integrative role and that the macromolecular network serves as an integrative receptor.     

The B cell receptor-induced calcium flux involves a calcium mediated positive feedback loop

The B cell receptor (BCR)-elicited calcium flux results in activation of mature B cells. We have recently shown that the adaptor protein Swiprosin-1/EFhd2 (EFhd2) amplifies the BCR-induced calcium flux in B cell lines. EFhd2 is a calcium binding adaptor protein with two predicted EF-hands. Here we asked whether these domains are functional and control its function. Using a blot-overlay assay with radioactive calcium we show that both EF-hands of EFhd2 have an intrinsic capacity to bind calcium. Equilibrium centrifugation confirmed that EFhd2 binds 2 calcium ions, with an apparent Kd of 110 μM. Point mutations revealed that the conserved residues E116 and E152, which reside in the canonical calcium binding loop in EF-hands 1 and 2, are essential for calcium binding by EFhd2. These mutations as well as deletion of the EF-hands, in particular EF-hand 1, abolished the ability of EFhd2 to restore BCR-induced calcium signaling in EFhd2-deficient WEHI231 cells. N-terminal deletions, but not C-terminal deletions, acted similarly. Thus, the N-terminal part of EFhd2 as well as calcium binding to its EF-hands control the intracellular calcium concentration in response to BCR stimulation in WEHI231 cells. Hence, EFhd2 regulates the BCR-elicited calcium flux through a calcium-dependent positive feedback mechanism in WEHI231 cells.     

A Spatial Model for Integrin Clustering as a Result of Feedback between Integrin Activation and Integrin Binding

Integrins are transmembrane adhesion receptors that bind extracellular matrix (ECM) proteins and signal bidirectionally to regulate cell adhesion and migration. In many cell types, integrins cluster at cell-ECM contacts to create the foundation for adhesion complexes that transfer force between the cell and the ECM. Even though the temporal and spatial regulation of these integrin clusters is essential for cell migration, how cells regulate their formation is currently unknown. It has been shown that integrin cluster formation is independent of actin stress fiber formation, but requires active (high-affinity) integrins, phosphoinositol-4,5-bisphosphate (PIP2), talin, and immobile ECM ligand. Based on these observations, we propose a minimal model for initial formation of integrin clusters, facilitated by localized activation and binding of integrins to ECM ligands as a result of biochemical feedback between integrin binding and integrin activation. By employing a diffusion-reaction framework for modeling these reactions, we show how spatial organization of bound integrins into clusters may be achieved by a local source of active integrins, namely protein complexes formed on the cytoplasmic tails of bound integrins. Further, we show how such a mechanism can turn small local increases in the concentration of active talin or active integrin into integrin clusters via positive feedback. Our results suggest that the formation of integrin clusters by the proposed mechanism depends on the relationships between production and diffusion of integrin-activating species, and that changes to the relative rates of these processes may affect the resulting properties of integrin clusters.     

The role of calpain in the selective increased phosphorylation of the anion-transport protein in red cell of hypertensive subjects

The phosphorylation of the anion-transport protein (band 3) is selectively increased in human red cell membrane, following exposure of intact cells to ionophore and micromolar calcium. The phosphorylation is catalyzed by a membrane associated protein kinase distinct from either protein kinase C or Ca2+/calmodulin dependent protein kinase. We show that the increase in phosphorylation of band 3 is abolished if red cells had been pre-loaded with an inhibitor of calpain or with an anticalpain monoclonal antibody. Our findings suggest that calpain activity may control, both at a functional and at a structural level, the activity of this important transmembrane protein through the modulation of its susceptibility as a substrate of membrane bound protein kinase(s). Based on previous observations indicating the presence in erythrocytes from hypertensive patients of an uncontrolled intracellular calpain-mediated proteolytic system accompanied by an increased phosphorylation of band 3 protein(s), we suggest that our results may shed light on the type of molecular alteration which is associated with the hypertensive state.     

TRPM7 regulates cell adhesion by controlling the calcium-dependent protease calpain

m-Calpain is a protease implicated in the control of cell adhesion through focal adhesion disassembly. The mechanism by which the enzyme is spatially and temporally controlled is not well understood, particularly because the dependence of calpain on calcium exceeds the submicromolar concentrations normally observed in cells. Here we show that the channel kinase TRPM7 localizes to peripheral adhesion complexes with m-calpain, where it regulates cell adhesion by controlling the activity of the protease. Our research revealed that overexpression of TRPM7 in cells caused cell rounding with a concomitant loss of cell adhesion that is dependent upon the channel of the protein but not its kinase activities. Knockdown of m-calpain blocked TRPM7-induced cell rounding and cell detachment. Silencing of TRPM7 by RNA interference, however, strengthened cell adhesion and increased the number of peripheral adhesion complexes in the cells. Together, our results suggest that the ion channel TRPM7 regulates cell adhesion through m-calpain by mediating the local influx of calcium into peripheral adhesion complexes.     

Intelligent yeast strains with the ability to self-monitor the concentrations of intra- and extracellular phosphate or ammonium ion by emission of fluorescence from the cell surface

Saccharomyces cerevisiae strains that respond to environmental changes and transmit the information by emission of fluorescence from the cell surface were constructed. The technique of cell surface engineering enabled the yeast cells to display enhanced cyan blue fluorescent protein (ECFP) or enhanced yellow fluorescent protein (EYFP) on the surface under the control of promoters that sense environmental changes. Two model promoters were examined in this study. For monitoring the intra- and extracellular concentrations of phosphate ion, the PHO5 promoter was chosen to display ECFP. The MEP2 promoter was used to display EYFP to sense the concentrations of ammonium ion. Fluorescence was observed by fluorescence microscopy and immunofluorescence microscopy, and the intensity was measured by a flow cytometer. The relationship between ion concentration inside and outside the cells was evaluated by the change in the rate of fluorescence. This S. cerevisiae system enables environmental changes to be transmitted as intra- and extracellular information using a suitable promoter functioning at real time and in a non-invasive manner.     

Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells

Microbial populations show striking diversity in cell growth morphology and lifecycle; however, our understanding of how these factors influence the growth rate of cell populations remains limited. We use theory and simulations to predict the impact of asymmetric cell division, cell size regulation and single-cell stochasticity on the population growth rate. Our model predicts that coarse-grained noise in the single-cell growth rate λ decreases the population growth rate, as previously seen for symmetrically dividing cells. However, for a given noise in λ we find that dividing asymmetrically can enhance the population growth rate for cells with strong size control (between a “sizer” and an “adder”). To reconcile this finding with the abundance of symmetrically dividing organisms in nature, we propose that additional constraints on cell growth and division must be present which are not included in our model, and we explore the effects of selected extensions thereof. Further, we find that within our model, epigenetically inherited generation times may arise due to size control in asymmetrically dividing cells, providing a possible explanation for recent experimental observations in budding yeast. Taken together, our findings provide insight into the complex effects generated by non-canonical growth morphologies.     

Simultaneous transport of different localized mRNA species revealed by live-cell imaging

Intracellular mRNA localization is a common mechanism to achieve asymmetric distributions of proteins. Previous studies have revealed that in a number of cell types, different mRNA species are localized by the same transport machinery. However, it has been unclear if these individual mRNA species are specifically sorted into separate or common ribonucleoprotein (RNP) particles before or during transport. Using budding yeast as a model system, we analyzed the intracellular movement of individual pairs of localized mRNA in live cells. Yeast cells localize more than 20 different mRNAs to the bud with the help of the Myo4p/She3p/She2p protein complex. For live cell imaging, mRNA pairs were tagged with tandem repeats of either bacteriophage MS2 or lambda boxB RNA sequences and fluorescently labeled by fusion protein constructs that bind to the RNA tag sequences. Using three-dimensional, single-particle tracking with dual-color detection, we have tracked the transport of two different localized mRNA species in real time. Our observations show that different localized mRNAs are coassembled into common RNP particles and cotransported in a directional manner to the target site. Nonlocalized mRNAs or mutant mRNAs that lack functional localization signals form separate particles that are not transported to the bud. This study reveals a high degree of co-ordination of mRNA trafficking in budding yeast.     

An anion antiporter model of prestin, the outer hair cell motor protein

Cochlear amplification in mammalian hearing relies on an active mechanical feedback process generated by outer hair cells, driven by a protein, prestin (SLC26A5), in the lateral membrane. We have used kinetic models to understand the mechanism by which prestin might function. We show that the two previous hypotheses of prestin, which assume prestin cannot operate as a transporter, are insufficient to explain previously published data. We propose an alternative model of prestin as an electrogenic anion exchanger, exchanging one Cl(-) ion for one divalent or two monovalent anions. This model can reproduce the key aspects of previous experimental observations. The experimentally observed charge movements are produced by the translocation of one Cl(-) ion combined with intrinsic positively charged residues, while the transport of the counteranion is electroneutral. We tested the model with measurements of the Cl(-) dependence of charge movement, using SO(4)(2-) to replace Cl(-). The data was compatible with the predictions of the model, suggesting that prestin does indeed function as a transporter.     

Phosphorylation of SRSF1 is modulated by replicational stress

DNA ligase I-deficient 46BR.1G1 cells show a delay in the maturation of replicative intermediates resulting in the accumulation of single- and double-stranded DNA breaks. As a consequence the ataxia telangiectasia mutated protein kinase (ATM) is constitutively phosphorylated at a basal level. Here, we use 46BR.1G1 cells as a model system to study the cell response to chronic replication-dependent DNA damage. Starting from a proteomic approach, we demonstrate that the phosphorylation level of factors controlling constitutive and alternative splicing is affected by the damage elicited by DNA ligase I deficiency. In particular, we show that SRSF1 is hyperphosphorylated in 46BR.1G1 cells compared to control fibroblasts. This hyperphosphorylation can be partially prevented by inhibiting ATM activity with caffeine. Notably, hyperphosphorylation of SRSF1 affects the subnuclear distribution of the protein and the alternative splicing pattern of target genes. We also unveil a modulation of SRSF1 phosphorylation after exposure of MRC-5V1 control fibroblasts to different exogenous sources of DNA damage. Altogether, our observations indicate that a relevant aspect of the cell response to DNA damage involves the post-translational regulation of splicing factor SRSF1 which is associated with a shift in the alternative splicing program of target genes to control cell survival or cell death.