A wave of IP3 production accompanies the fertilization Ca2+ wave in the egg of the frog, Xenopus laevis: theoretical and experimental support

Modelling spatio-temporal interactions between second messengers Ca 2 + and cAMP in a pancreatic β -cell

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca2 + ), and linkages between Ca2 + and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca2 + levels in pancreatic β -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca2 + in β -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca2 + and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the β -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca2 + and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the β -cell. The model gives the individual effect of each parameter on the regulation of Ca2 + and cAMP profiles in a β -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

Cross Talking Calcium, IP3 and Buffer Dynamics Alters ATP and NADH Level in Obese and Normal Hepatocyte Cell

The cross talk between calcium (Ca2+), IP3 and buffer dynamics regulate various mechanisms in hepatocyte cells. The study of independent systems of calcium, IP3, and buffer signaling provides limited information about cell dynamics. In the current study, coupled reaction-diffusion equations are used to design a cross-talk model for IP3, buffer, and calcium dynamics in a hepatocyte cell. The one-way feedback of calcium, buffer, and IP3 in ATP production, ATP degradation, and NADH production rate is incorporated into the model. Numerical simulation has been done using the Finite Element Method (FEM) along the spatial direction and the Crank-Nicolson (C-N) method along the temporal direction. The numerical results are analysed to determine the effects of alterations in processes of cross-talking dynamics of IP3, buffer, and calcium on ATP and NADH production and degradation rate of ATP in a hepatocyte cell under normal and obesity conditions. The comparative analysis of these findings unveils notable distinctions induced by obesity in calcium dynamics, ATP and NADH synthesis, and ATP degradation kinetics.

Regulatory disturbances in the dynamical signaling systems of C a 2 + and NO in fibroblasts cause fibrotic disorders

Studying the calcium dynamics within a fibroblast cell individually has provided only a restricted understanding of its functions. However, research efforts focusing on systems biology approaches for such investigations have been largely neglected by researchers until now. Fibroblast cells rely on signaling from calcium ( C a 2 + ) and nitric oxide (NO) to maintain their physiological functions and structural stability. Various studies have demonstrated the correlation between NO and the control of C a 2 + dynamics in cells. However, there is currently no existing model to assess the disruptions caused by various factors in regulatory dynamics, potentially resulting in diverse fibrotic disorders. A mathematical model has been developed to investigate the effects of changes in parameters such as buffer, receptor, sarcoplasmic endoplasmic reticulum C a 2 + -ATPase (SERCA) pump, and source influx on the regulation and dysregulation of spatiotemporal calcium and NO dynamics in fibroblast cells. This model is based on a system of reaction-diffusion equations, and numerical simulations are conducted using the finite element method. Disturbances in key processes related to calcium and nitric oxide, including source influx, buffer mechanism, SERCA pump, and inositol trisphosphate ( I P 3 ) receptor, may contribute to deregulation in the calcium and NO dynamics within fibroblasts. The findings also provide new insights into the extent and severity of disorders resulting from alterations in various parameters, potentially leading to deregulation and the development of fibrotic disease.

Modelling Cross Talk in the Spatiotemporal System Dynamics of Calcium, IP3 and Nitric Oxide in Neuron Cells

The bioenergetic system of calcium ([Ca2+]), inositol 1, 4, 5-trisphophate (IP3) and nitric oxide (NO) regulate the diverse mechanisms in neurons. The dysregulation in any or all of the calcium, IP3 and nitric oxide dynamics may cause neurotoxicity and cell death. Few studies are noted in the literature on the interactions of two systems like [Ca2+] with IP3 and [Ca2+] with nitric oxide in neuron cells, which gives limited insights into regulatory and dysregulatory processes in neuron cells. But, no study is available on the cross talk in dynamics of three systems [Ca2+], IP3 and NO in neurons. Thus, the cross talk in the system dynamics of [Ca2+], IP3 and NO regulation processes in neurons have been studied using mathematical model. The two-way feedback process between [Ca2+] and IP3 and two-way feedback process between [Ca2+] and NO through cyclic guanosine monophosphate (cGMP) with plasmalemmal [Ca2+]-ATPase (PMCA) have been incorporated in the proposed model. This coupling handles the indirect two-way feedback process between IP3 and nitric oxide in neuronal cells automatically. The numerical outcomes were acquired by employing the finite element method (FEM) with the Crank-Nicholson scheme (CNS). The present model incorporating the sodium-calcium exchanger (NCX) and voltage-gated calcium channel (VGCC) provides novel insights into the various regulatory and dysregulatory processes due to buffer, IP3-receptor, ryanodine receptor, cGMP kinetics through PMCA channel, etc. and their impacts on the interactive spatiotemporal system dynamics of [Ca2+], IP3 and NO in neurons. It is concluded that the behavior of different crucial mechanisms is quite different for interactions of two systems of [Ca2+] and NO and the interactions of three systems of [Ca2+], IP3 and nitric oxide in neuronal cell due to mutual regulatory adjustments. The association of several neurological disorders with the alterations in calcium, IP3 and NO has been explored in neurons.

Model of Calcium Dynamics Regulating [Formula: see text], ATP and Insulin Production in a Pancreatic [Formula: see text]-Cell

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ([Formula: see text]) and adenosine triphosphate (ATP) in various cells including pancreatic [Formula: see text]-cells. The calcium signaling mechanisms regulating [Formula: see text], ATP and insulin responsible for various functions of [Formula: see text]-cells are still not well understood. Any disturbance in these mechanisms can alter the functions of [Formula: see text]-cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for calcium dynamics and a system of first-order differential equations for [Formula: see text], ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of [Formula: see text]-production and degradation, ATP production and insulin secretion on calcium dynamics in a [Formula: see text]-cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of [Formula: see text], ATP and insulin levels in a [Formula: see text]-cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of [Formula: see text], ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in [Formula: see text], ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases.

Impact of Interdependent Ca2+ and IP3 Dynamics On ATP Regulation in A Fibroblast Model

The vital participation of Ca2+ in human organ functions such as muscular contractions, heartbeat, brain functionality, skeletal activity, etc, motivated the scientists to thoroughly research the mechanisms of calcium (Ca2+) signalling in distinct human cells. Ca2+, inositol triphosphate (IP3), and adenosine triphosphate (ATP) play important roles in cell signaling and physiological processes. ATP and its derivatives are hypothesized to be important in the pathogenic process that leads to fibrotic illnesses like fibrosis. Fluctuations in Ca2+ and IP3 in a fibroblast cell influence ATP production. To date, no evidence of coupled Ca2+ and IP3 mechanics regulating ATP generation in a fibroblast cell during fibrotic disease has been found. The current work suggests an integrated mechanism for Ca2+ and IP3 dynamics in a fibroblast cell that regulates ATP generation. Simulation has been carried out using the finite element approach. The mechanics of interdependent systems findings vary dramatically from the results of basic independent system mechanics and give fresh information about the two systems' activities. The numerical results provide new insights into the impacts of disturbances in source influx, the serca pump, and buffers on interdependent Ca2+ and IP3 dynamics and ATP synthesis in a fibroblast cell. According to the findings of this study, fibrotic disorders cannot be attributed solely to disruptions in the processes of calcium signaling mechanics but also to disruptions in IP3 regulation mechanisms affecting the regulation of calcium in the fibroblast cell and ATP release.

Study of disorders in regulatory spatiotemporal neurodynamics of calcium and nitric oxide

Experimental studies have reported the dependence of nitric oxide (NO) on the regulation of neuronal calcium ([Ca2+]) dynamics in neurons. But, there is no model available to estimate the disorders caused by various parameters in their regulatory dynamics leading to various neuronal disorders. A mathematical model to analyze the impacts due to alterations in various parameters like buffer, ryanodine receptor, serca pump, source influx, etc. leading to regulation and dysregulation of the spatiotemporal calcium and NO dynamics in neuron cells is constructed using a system of reaction-diffusion equations. The numerical simulation is performed with the finite element approach. The disturbances in the different constitutive processes of [Ca2+] and nitric oxide including source influx, buffer mechanism, ryanodine receptor, serca pump, IP3 receptor, etc. can be responsible for the dysregulation in the [Ca2+] and NO dynamics in neurons. Also, the results reveal novel information about the magnitude and intensity of disorders in response to a range of alterations in various parameters of this neuronal dynamics, which can cause dysregulation leading to neuronal diseases like Parkinson's, cerebral ischemia, trauma, etc.

TMEM16A activation for the fast block to polyspermy in the African clawed frog does not require conventional activation of egg PLCs

Fertilization of an egg by more than one sperm, a condition known as polyspermy, leads to gross chromosomal abnormalities and is embryonic lethal for most animals. Consequently, eggs have evolved multiple processes to stop supernumerary sperm from entering the nascent zygote. For external fertilizers, such as frogs and sea urchins, fertilization signals a depolarization of the egg membrane, which serves as the fast block to polyspermy. Sperm can bind to, but will not enter, depolarized eggs. In eggs from the African clawed frog, Xenopus laevis, the fast block depolarization is mediated by the Ca2+-activated Cl- channel TMEM16A. To do so, fertilization activates phospholipase C, which generates IP3 to signal a Ca2+ release from the ER. Currently, the signaling pathway by which fertilization activates PLC during the fast block remains unknown. Here, we sought to uncover this pathway by targeting the canonical activation of the PLC isoforms present in the X. laevis egg: PLCγ and PLCβ. We observed no changes to the fast block in X. laevis eggs inseminated in inhibitors of tyrosine phosphorylation, used to stop activation of PLCγ, or inhibitors of Gαq/11 pathways, used to stop activation of PLCβ. These data suggest that the PLC that signals the fast block depolarization in X. laevis is activated by a novel mechanism.

Simulation of biochemical dynamics of [Formula: see text] and [Formula: see text] in fibroblast cell

Calcium dynamics is not only responsible for maintaining the framework and functions of the cell but also plays a role in the dynamics of other biochemical systems in the cell. Phospholipase C-[Formula: see text] l ([Formula: see text]) has a crucial role in the function of fibroblast cells. Experiments have shown that [Formula: see text] and [Formula: see text] have interdependent dynamics in fibroblast cells. However, no reaction-diffusion model exists for the two-way feedback system dynamics of [Formula: see text] and [Formula: see text] in fibroblasts till date. The computational model is designed to investigate the impact of variations in several processes, such as the [Formula: see text] pump, buffer process, source inflow, etc., on the system dynamics of [Formula: see text] and [Formula: see text] in fibroblast cells. The computational findings are obtained using finite element techniques, and the consequences of dysregulation in various processes on the spatiotemporal calcium and [Formula: see text] dynamics in fibroblasts are investigated. The results lead to the conclusion that the effects of buffer, source influx, diffusion, and [Formula: see text] pump can cause fluctuations in the dynamics of [Formula: see text] and [Formula: see text] in fibroblasts. Disruptions in these constitutive processes can result in changes in the dynamics of calcium and [Formula: see text]. Thus, the current model provides new/novel information regarding the precise dysregulatory constitutive systems that regulate calcium and [Formula: see text] kinetics, such as source inflow, diffusion, [Formula: see text], and buffer, can be responsible for excessive calcium and [Formula: see text] concentrations leading to fibrotic illnesses such as cancer and fibrosis.

Spatio temporal interdependent calcium and buffer dynamics regulating DAG in a hepatocyte cell due to obesity

Calcium ions (Ca2+) serve as a crucial signaling mechanism in almost all cells. The buffers are proteins that bind free Ca2+ to reduce the cell's Ca2+ concentration. The most studies reported in the past on calcium signaling in various cells have considered the buffer concentration as constant in the cell. However, buffers also diffuse and their concentration varies dynamically in the cells. Almost no work has been reported on interdependent calcium and buffer dynamics in the cells. In the present study, a model is proposed for inter-dependent spatio-temporal dynamics of calcium and buffer by coupling reaction-diffusion equations of Ca2+ and buffer in a hepatocyte cell. Boundary and initial conditions are framed based on the physiological state of the cell. The effect of various parameters viz. inositol 1,4,5-triphosphate receptor (IP3R), diffusion coefficient, SERCA pump and ryanodine receptor (RyR) on spatio-temporal dynamics of calcium and buffer regulating diacylglycerol (DAG) in a normal and obese hepatocyte cell has been studied using finite element simulation. From the results, it is concluded that the dynamics of calcium and buffer impact each other significantly along the spatio-temporal dimensions, thereby affecting the regulation of all the processes including DAG in a hepatocyte cell. The proposed model is more realistic than the existing ones, as the interdependent system dynamics of calcium and buffer have different regulatory impacts as compared to the individual and independent dynamics of these signaling processes in a hepatocyte cell.

Disturbances in system dynamics of [Formula: see text] and [Formula: see text] perturbing insulin secretion in a pancreatic [Formula: see text]-cell due to type-2 diabetes

The individual study of [Formula: see text] and [Formula: see text] dynamics respectively in a [Formula: see text]-cell has yielded limited information about the cell functions. But the systems biology approaches for such studies have received very little attention by the research workers in the past. In the present work, a system-dynamics model for the interdependent [Formula: see text] and [Formula: see text] signaling that controls insulin secretion in a [Formula: see text]-cell has been suggested. A two-way feedback system of [Formula: see text] and [Formula: see text] has been considered and one-way feedback between [Formula: see text] and insulin has been implemented in the model. The finite element method along with the Crank-Nicolson method have been applied for simulation. Numerical results have been used to analyze the impact of perturbations in [Formula: see text] and [Formula: see text] dynamics on insulin secretion for normal and Type-2 diabetic conditions. The results reveal that Type-2 diabetes comes from abnormalities in insulin secretion caused by the perturbation in buffers and pumps (SERCA and PMCA).

Cellular nitric oxide synthesis is affected by disorders in the interdependent [Formula: see text] and [Formula: see text] dynamics during cystic fibrosis disease

Calcium ([Formula: see text]), inositol trisphosphate ([Formula: see text]), and nitric oxide (NO) signaling are essential to maintain the structural integrity and physiological activity of fibroblast cells. The accumulation of excess quantity of NO for longer periods can lead to a variety of fibrotic disorders, including heart disease, penile fibrosis in Peyronie's disease (PD), and cystic fibrosis. The dynamics of these three signaling processes and their interdependence in fibroblast cells are not clearly known to date. A systems biology model is proposed using reaction-diffusion equations for calcium, [Formula: see text], and calcium-dependent NO synthesis in fibroblast cells. The finite element method (FEM) is used to examine [Formula: see text], [Formula: see text], and NO regulation and dysregulation in cells. The results throw light on the conditions that disturb the coupled [Formula: see text] and [Formula: see text] dynamics and the influence of these factors on the levels of NO concentration in the fibroblast cell. The findings suggest that changes in source inflow, buffers, and diffusion coefficient might induce an increase or reduction in nitric oxide and [Formula: see text] synthesis, resulting in fibroblast cell diseases. Furthermore, the findings provide new information regarding the size and intensity of diseases in response to changes in several factors of their dynamics, which has been linked to the development of cystic fibrosis and cancer. This knowledge could be valuable for developing novel approaches to the diagnosis of diseases and therapies for various disorders of fibroblast cells.

Mechanistic insights of neuronal calcium and IP3 signaling system regulating ATP release during ischemia in progression of Alzheimer's disease

The mechanisms of calcium ([Ca²⁺]) signaling in various human cells have been widely analyzed by scientists due to its crucial role in human organs like the heartbeat, muscle contractions, bone activity, brain functionality, etc. No study is reported for interdependent [Ca²⁺] and IP₃ mechanics regulating the release of ATP in neuron cells during Ischemia in Alzheimer's disease advancement. In the present investigation, a finite element method (FEM) is framed to explore the interdependence of spatiotemporal [Ca²⁺] and IP₃ signaling mechanics and its role in ATP release during Ischemia as well as in the advancement of Alzheimer's disorder in neuron cells. The results provide us insights of the mutual spatiotemporal impacts of [Ca²⁺] and IP₃ mechanics as well as their contributions to ATP release during Ischemia in neuron cells. The results obtained for the mechanics of interdependent systems differ significantly from the results of simple independent system mechanics and provide new information about the processes of the two systems. From this study, it is concluded that neuronal disorders cannot only be simply attributed to the disturbance caused directly in the processes of calcium signaling mechanics, but also to the disturbances caused in IP₃ regulation mechanisms impacting the calcium regulation in the neuron cell and ATP release.

Effect of disturbances in neuronal calcium and IP3 dynamics on β-amyloid production and degradation

Overproduction and accumulation of β-amyloid and its improper clearance can cause neurotoxicity leading to Alzheimer's disease. The production and degradation of β-amyloid depend on the calcium ([Ca2+]) and IP3 dynamics in the nerve cells. Thus, there is a need to understand the impacts of disturbances in the processes of [Ca2+] and IP3 dynamics on β-amyloid production and its degradation. Here, a model is proposed to investigate the role of [Ca2+] and IP3 dynamics on β-amyloid production and degradation. The problem is formulated in terms of the initial boundary value problem involving the system of two reaction-diffusion equations respectively for [Ca2+] and IP3 in the nerve cell. The solution is obtained by employing the Finite element approach. The numerical results are used to analyze the impact of various mechanisms of calcium and IP3 dynamics on β-amyloid production and degradation in a neuron cell. The results indicate that disturbances in any of the constitutive processes of interdependent calcium and IP3 dynamics like source influx, buffering, serca pump, and IP3 dynamics, etc. can cause dynamic changes in β-amyloid production and degradation, which in turn can be the cause of neurotoxicity and neuronal disorders like Alzheimer's disease. Thus, the relationships obtained by the proposed model among various mechanisms can be useful in addressing the challenges of identifying specific constitutive processes causing neuronal disorders like Alzheimer's disease, etc., and developing the framework for their diagnosis and treatment.

Changes in Ca2+ Removal Can Mask the Effects of Geometry During IP3R Mediated Ca2+ Signals

Calcium (Ca²⁺) signals are ubiquitous. Most intracellular Ca²⁺ signals involve the release of Ca²⁺ from the endoplasmic reticulum (ER) through Inositol 1,4,5-Trisphosphate Receptors (IP₃Rs). The non-uniform spatial organization of IP₃Rs and the fact that their individual openings are coupled via cytosolic Ca²⁺ are key factors for the variety of spatio-temporal distributions of the cytosolic [Ca²⁺] and the versatility of the signals. In this paper we combine experiments performed in untreated and in progesterone-treated Xenopus laevis oocytes and mathematical models to investigate how the interplay between geometry (the IP₃R spatial distribution) and dynamics (the processes that characterize the release, transport, and removal of cytosolic Ca²⁺) affects the resulting signals. Signal propagation looks more continuous and spatially uniform in treated (mature) than in untreated (immature) oocytes. This could be due to the different underlying IP₃R spatial distribution that has been observed in both cell types. The models, however, show that the rate of cytosolic Ca²⁺ removal, which is also different in both cell types, plays a key role affecting the coupling between Ca²⁺ release sites in such a way that the effect of the underlying IP₃R spatial distribution can be modified.

Insemination or phosphatidic acid induces an outwardly spiraling disk of elevated Ca2+ to produce the Ca2+ wave during Xenopus laevis fertilization

During Xenopus fertilization, the initial intracellular calcium ((Ca²⁺)_i) release at the sperm-egg binding site (hot spot) has not been described without the use of inhibitors, nor related to underlying ER structure. Without inhibitors, we now report that sperm induce an initial hot spot after sperm addition to Xenopus eggs that was ~25 µm. This area is consistent with the size of ER patches and clusters of IP3 receptors that have enhanced activity. Furthermore, we find a new mechanism for the fertilization (Ca²⁺)_i wave; instead of outward diffusion of inositol 1,4,5-trisphosphate (IP₃), we find that the wave was generated by an outward, clockwise rotation of a ~63 µm disk of elevated (Ca²⁺)_i moving very rapidly at ~65 µm/s. We also suggest a new mechanism for the acceleration of the fertilization (Ca²⁺)_i wave as the disk accelerated and was joined by other rotating disks (some rotating counterclockwise) at a time when the speed of the (Ca²⁺)_i wave increases. To examine the role of phosphatidic acid (PA) in the release of (Ca²⁺)_i during Xenopus fertilization, we find that two inhibitors of PA production delayed the appearance of fertilization hot spots by ~9-12 min but did not reduce the size of hot spots and actually accelerated the later (Ca²⁺)_i wave. Surprisingly, global addition of PA to Xenopus eggs induced localized hot spots at a time and size that was similar to those induced after sperm addition. In contrast, sperm induce a rapid (Ca²⁺)_i wave (~4 µm/s) within ~30 s after hot spot appearance, whereas hot spots induced by PA required an ~32 min to induce a very slow (~1 µm/s) (Ca²⁺)_i wave with a lower peak of (Ca²⁺)_i. Thus, PA may not be required for the initial release of (Ca²⁺)_i at the sperm-egg binding site, but mimics sperm by inducing a similarly sized localized (Ca²⁺)_i release. As compared with sperm, PA may induce a weak, slow (Ca²⁺)_i wave by slowly increasing IP3 receptor clustering. Addition of PA to Xenopus oocytes, or Ca²⁺ ionophore to either Xenopus oocytes or eggs, did not induce hot spots but a global (Ca²⁺)_i wave that rapidly moved at ~12 µm/s.

Three dimensional coupled reaction–diffusion modeling of calcium and inositol 1,4,5-trisphosphate dynamics in cardiomyocytes

Nanoparticles have shown great promise in improving cancer treatment efficacy by changing the intracellular calcium level through activation of intracellular mechanisms. One of the mechanisms of the killing of the cancerous cell by a nanoparticle is through elevation of the intracellular calcium level. Evidence accumulated over the past decade indicates a pivotal role for the IP₃ receptor mediated Ca²⁺ release in the regulation of the cytosolic and the nuclear Ca²⁺ signals. There have been various studies done suggesting the role of IP₃ receptors (IP₃R) and IP₃ production and degradation in cardiomyocytes. In the present work, we have proposed a three-dimensional unsteady-state mathematical model to describe the mechanism of cardiomyocytes which focuses on evaluation of various parameters that affect these coupled dynamics and elevate the cytosolic calcium concentration which can be helpful to search for novel therapies to cure these malignancies by targeting the complex calcium signaling process in cardiomyocytes. Our study suggests that there are other factors involved in this signaling which can increase the calcium level, which can help in finding treatment for cancer. The cytosolic calcium level may be controlled by IP₃ signaling, leak, source influx of calcium (σ) and maximum production of IP₃ (V_P). We believe that the proposed model suggests new insight into finding treatment for cancer in cardiomyocytes through elevation of the cytosolic Ca²⁺ concentration by various parameters like leak, σ, V_P and especially by other complex cell signaling dynamics, namely IP₃ dynamics.

We propose a three-dimensional unsteady-state mathematical model to describe the mechanism of cardiomyocytes.

Extracellular Ca2+ Is Required for Fertilization in the African Clawed Frog, Xenopus laevis

Background

The necessity of extracellular Ca²⁺ for fertilization and early embryonic development in the African clawed frog, Xenopus laevis, is controversial. Ca²⁺ entry into X. laevis sperm is reportedly required for the acrosome reaction, yet fertilization and embryonic development have been documented to occur in high concentrations of the Ca²⁺ chelator BAPTA. Here we sought to resolve this controversy.

Methodology/principal finding

Using the appearance of cleavage furrows as an indicator of embryonic development, we found that X. laevis eggs inseminated in a solution lacking added divalent cations developed normally. By contrast, eggs inseminated in millimolar concentrations of BAPTA or EGTA failed to develop. Transferring embryos to varying solutions after sperm addition, we found that extracellular Ca²⁺ is specifically required for events occurring within the first 30 minutes after sperm addition, but not after. We found that the fluorescently stained sperm were not able to penetrate the envelope of eggs inseminated in high BAPTA, whereas several had penetrated the vitelline envelope of eggs inseminated without a Ca²⁺ chelator, or with BAPTA and saturating CaCl₂. Together these results indicate that fertilization does not occur in high concentrations of Ca²⁺ chelators. Finally, we found that the jelly coat includes >5 mM of readily diffusible Ca²⁺.

Conclusions/Significance

Taken together, these data are consistent with requirement of extracellular Ca²⁺ for fertilization. Based on our findings, we hypothesize that the jelly coat surrounding the egg acts as a reserve of readily available Ca²⁺ ions to foster fertilization in changing extracellular milieu.

Calcium regulation of HCN channels supports persistent activity in a multiscale model of neocortex

Neuronal persistent activity has been primarily assessed in terms of electrical mechanisms, without attention to the complex array of molecular events that also control cell excitability. We developed a multiscale neocortical model proceeding from the molecular to the network level to assess the contributions of calcium (Ca(2+)) regulation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels in providing additional and complementary support of continuing activation in the network. The network contained 776 compartmental neurons arranged in the cortical layers, connected using synapses containing AMPA/NMDA/GABAA/GABAB receptors. Metabotropic glutamate receptors (mGluR) produced inositol triphosphate (IP3) which caused the release of Ca(2+) from endoplasmic reticulum (ER) stores, with reuptake by sarco/ER Ca(2+)-ATP-ase pumps (SERCA), and influence on HCN channels. Stimulus-induced depolarization led to Ca(2+) influx via NMDA and voltage-gated Ca(2+) channels (VGCCs). After a delay, mGluR activation led to ER Ca(2+) release via IP3 receptors. These factors increased HCN channel conductance and produced firing lasting for ∼1min. The model displayed inter-scale synergies among synaptic weights, excitation/inhibition balance, firing rates, membrane depolarization, Ca(2+) levels, regulation of HCN channels, and induction of persistent activity. The interaction between inhibition and Ca(2+) at the HCN channel nexus determined a limited range of inhibition strengths for which intracellular Ca(2+) could prepare population-specific persistent activity. Interactions between metabotropic and ionotropic inputs to the neuron demonstrated how multiple pathways could contribute in a complementary manner to persistent activity. Such redundancy and complementarity via multiple pathways is a critical feature of biological systems. Mediation of activation at different time scales, and through different pathways, would be expected to protect against disruption, in this case providing stability for persistent activity.

Egg Activation at Fertilization by a Soluble Sperm Protein

The most fundamental unresolved issue of fertilization is to define how the sperm activates the egg to begin embryo development. Egg activation at fertilization in all species thus far examined is caused by some form of transient increase in the cytoplasmic free Ca2+ concentration. What has not been clear, however, is precisely how the sperm triggers the large changes in Ca2+ observed within the egg cytoplasm. Here, we review the studies indicating that the fertilizing sperm stimulates a cytosolic Ca2+ increase in the egg specifically by delivering a soluble factor that diffuses into the cytosolic space of the egg upon gamete membrane fusion. Evidence is primarily considered in species of eggs where the sperm has been shown to elicit a cytosolic Ca2+ increase by initiating Ca2+ release from intracellular Ca2+ stores. We suggest that our best understanding of these signaling events is in mammals, where the sperm triggers a prolonged series of intracellular Ca2+ oscillations. The strongest empirical studies to date suggest that mammalian sperm-triggered Ca2+ oscillations are caused by the introduction of a sperm-specific protein, called phospholipase C-zeta (PLCζ) that generates inositol trisphosphate within the egg. We will discuss the role and mechanism of action of PLCζ in detail at a molecular and cellular level. We will also consider some of the evidence that a soluble sperm protein might be involved in egg activation in nonmammalian species.

The role of IP3 receptor channel clustering in Ca2+ wave propagation during oocyte maturation

During oocyte maturation, the calcium-signaling machinery undergoes a dramatic remodeling resulting in distinctly different calcium-release patterns on all organizational scales from puffs to waves. The dynamics of the Ca(2+) release wave in mature as compared to immature oocytes are defined by a slower propagation speed and longer duration of the high Ca(2+) plateau. In this chapter, we use computational modeling to identify the changes in the signaling machinery, which contribute most significantly to the alterations observed in Ca(2+) wave propagation during Xenopus oocyte maturation. In addition to loss of store-operated calcium entry and internalization of plasma membrane pumps, we propose that spatial reorganization of the IP3 receptors in the plane of the ER membrane is a key factor for the observed signaling changes in Ca(2+) wave propagation.

Neuronal calcium wave propagation varies with changes in endoplasmic reticulum parameters: a computer model

Calcium (Ca²⁺) waves provide a complement to neuronal electrical signaling, forming a key part of a neuron's second messenger system. We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate (IP₃), diffusible Ca²⁺, IP₃ receptors (IP₃Rs), endoplasmic reticulum (ER) Ca²⁺ leak, and ER pump (SERCA) on ER. Ca²⁺ is released from ER stores via IP₃Rs upon binding of IP₃ and Ca²⁺. This results in Ca²⁺-induced-Ca²⁺-release (CICR) and increases Ca²⁺ spread. At least two modes of Ca²⁺ wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell and a pseudo-saltatory model where Ca²⁺ regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized IP₃R distribution: (1) continuous homogeneous ER, (2) hotspots with increased IP₃R density (IP₃R hotspots), and (3) areas of increased ER density (ER stacks). All three modes produced Ca²⁺ waves with velocities similar to those measured in vitro (approximately 50-90 μm /sec). Continuous ER showed high sensitivity to IP₃R density increases, with time to onset reduced and speed increased. Increases in SERCA density resulted in opposite effects. The measures were sensitive to changes in density and spacing of IP₃R hotspots and stacks. Increasing the apparent diffusion coefficient of Ca²⁺ substantially increased wave speed. An extended electrochemical model, including voltage-gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent Ca²⁺ wave amplitude and duration. Our modeling suggests that pharmacological targeting of IP₃Rs and SERCA could allow modulation of Ca²⁺ wave propagation in diseases where Ca²⁺ dysregulation has been implicated.

Phospholipase C and D regulation of Src, calcium release and membrane fusion during Xenopus laevis development

This review emphasizes how lipids regulate membrane fusion and the proteins involved in three developmental stages: oocyte maturation to the fertilizable egg, fertilization and during first cleavage. Decades of work show that phosphatidic acid (PA) releases intracellular calcium, and recent work shows that the lipid can activate Src tyrosine kinase or phospholipase C during Xenopus fertilization. Numerous reports are summarized to show three levels of increase in lipid second messengers inositol 1,4,5-trisphosphate and sn 1,2-diacylglycerol (DAG) during the three different developmental stages. In addition, possible roles for PA, ceramide, lysophosphatidylcholine, plasmalogens, phosphatidylinositol 4-phosphate, phosphatidylinositol 5-phosphate, phosphatidylinositol 4,5-bisphosphate, membrane microdomains (rafts) and phosphatidylinositol 3,4,5-trisphosphate in regulation of membrane fusion (acrosome reaction, sperm-egg fusion, cortical granule exocytosis), inositol 1,4,5-trisphosphate receptors, and calcium release are discussed. The role of six lipases involved in generating putative lipid second messengers during fertilization is also discussed: phospholipase D, autotaxin, lipin1, sphingomyelinase, phospholipase C, and phospholipase A2. More specifically, proteins involved in developmental events and their regulation through lipid binding to SH3, SH4, PH, PX, or C2 protein domains is emphasized. New models are presented for PA activation of Src (through SH3, SH4 and a unique domain), that this may be why the SH2 domain of PLCγ is not required for Xenopus fertilization, PA activation of phospholipase C, a role for PA during the calcium wave after fertilization, and that calcium/calmodulin may be responsible for the loss of Src from rafts after fertilization. Also discussed is that the large DAG increase during fertilization derives from phospholipase D production of PA and lipin dephosphorylation to DAG.

Calcium signaling and meiotic exit at fertilization in Xenopus egg

Calcium is a universal messenger that mediates egg activation at fertilization in all sexually reproducing species studied. However, signaling pathways leading to calcium generation and the mechanisms of calcium-induced exit from meiotic arrest vary substantially among species. Here, we review the pathways of calcium signaling and the mechanisms of meiotic exit at fertilization in the eggs of the established developmental model, African clawed frog, Xenopus laevis. We also discuss calcium involvement in the early fertilization-induced events in Xenopus egg, such as membrane depolarization, the increase in intracellular pH, cortical granule exocytosis, cortical contraction, contraction wave, cortical rotation, reformation of the nuclear envelope, sperm chromatin decondensation and sister chromatid segregation.

Activation of Src and release of intracellular calcium by phosphatidic acid during Xenopus laevis fertilization

We report a new step in the fertilization in Xenopus laevis which has been found to involve activation of Src tyrosine kinase to stimulate phospholipase C-γ (PLC-γ) which increases inositol 1,4,5-trisphosphate (IP3) to release intracellular calcium ([Ca](i)). Molecular species analysis and mass measurements suggested that sperm activate phospholipase D (PLD) to elevate phosphatidic acid (PA). We now report that PA mass increased 2.7 fold by 1 min after insemination and inhibition of PA production by two methods inhibited activation of Src and PLCγ, increased [Ca](i) and other fertilization events. As compared to 14 other lipids, PA specifically bound Xenopus Src but not PLCγ. Addition of synthetic PA activated egg Src (an action requiring intact lipid rafts) and PLCγ as well as doubling the amount of PLCγ in rafts. In the absence of elevated [Ca](i), PA addition elevated IP3 mass to levels equivalent to that induced by sperm (but twice that achieved by calcium ionophore). Finally, PA induced [Ca](i) release that was blocked by an IP3 receptor inhibitor. As only PLD1b message was detected, and Western blotting did not detect PLD2, we suggest that sperm activate PLD1b to elevate PA which then binds to and activates Src leading to PLCγ stimulation, IP3 elevation and [Ca](i) release. Due to these and other studies, PA may also play a role in membrane fusion events such as sperm-egg fusion, cortical granule exocytosis, the elevation of phosphatidylinositol 4,5-bisphosphate and the large, late increase in sn 1,2-diacylglycerol in fertilization.

Monitoring gene expression in a single Xenopus oocyte using multiple cytoplasmic collections and quantitative RT-PCR

Oocytes and eggs of the African clawed frog, Xenopus laevis, are commonly used in gene expression studies. However, monitoring transcript levels in the individual living oocytes remains challenging. To address this challenge, we used a technique based on multiple repeated collections of nanoliter volumes of cytoplasmic material from a single oocyte. Transcript quantification was performed by quantitative RT-PCR. The technique allowed monitoring of heterologous gene expression in a single oocyte without affecting its viability. We also used this approach to profile the expression of endogenous genes in living Xenopus oocytes. Although frog oocytes are traditionally viewed as a homogenous cell population, a significant degree of gene expression variation was observed among the individual oocytes. A lognormal distribution of transcript levels was revealed in the oocyte population. Finally, using this technique, we observed a dramatic decrease in the content of various cytoplasmic mRNAs in aging unfertilized eggs but not in oocytes, suggesting a link between mRNA degradation and egg apoptosis.

Comparative biology of sperm factors and fertilization-induced calcium signals across the animal kingdom

Fertilization causes mature oocytes or eggs to increase their concentrations of intracellular calcium ions (Ca²⁺) in all animals that have been examined, and such Ca²⁺ elevations, in turn, provide key activating signals that are required for non-parthenogenetic development. Several lines of evidence indicate that the Ca²⁺ transients produced during fertilization in mammals and other taxa are triggered by soluble factors that sperm deliver into oocytes after gamete fusion. Thus, for a broad-based analysis of Ca²⁺ dynamics during fertilization in animals, this article begins by summarizing data on soluble sperm factors in non-mammalian species, and subsequently reviews various topics related to a sperm-specific phospholipase C, called PLCζ, which is believed to be the predominant activator of mammalian oocytes. After characterizing initiation processes that involve sperm factors or alternative triggering mechanisms, the spatiotemporal patterns of Ca²⁺ signals in fertilized oocytes or eggs are compared in a taxon-by-taxon manner, and broadly classified as either a single major transient or a series of repetitive oscillations. Both solitary and oscillatory types of fertilization-induced Ca²⁺ signals are typically propagated as global waves that depend on Ca²⁺ release from the endoplasmic reticulum in response to increased concentrations of inositol 1,4,5-trisphosphate (IP₃). Thus, for taxa where relevant data are available, upstream pathways that elevate intraoocytic IP3 levels during fertilization are described, while other less-common modes of producing Ca²⁺ transients are also examined. In addition, the importance of fertilization-induced Ca²⁺ signals for activating development is underscored by noting some major downstream effects of these signals in various animals.

How to make a good egg!: The need for remodeling of oocyte Ca(2+) signaling to mediate the egg-to-embryo transition

The egg-to-embryo transition marks the initiation of multicellular organismal development and is mediated by a specialized Ca(2+) transient at fertilization. This explosive Ca(2+) signal has captured the interest and imagination of scientists for many decades, given its cataclysmic nature and necessity for the egg-to-embryo transition. Learning how the egg acquires the competency to generate this Ca(2+) transient at fertilization is essential to our understanding of the mechanisms controlling egg and the transition to embryogenesis. In this review we discuss our current knowledge of how Ca(2+) signaling pathways remodel during oocyte maturation in preparation for fertilization with a special emphasis on the frog oocyte as additional reviews in this issue will touch on this in other species.

The activity of spontaneous action potentials in developing hair cells is regulated by Ca(2+)-dependence of a transient K+ current

Spontaneous action potentials have been described in developing sensory systems. These rhythmic activities may have instructional roles for the functional development of synaptic connections. The importance of spontaneous action potentials in the developing auditory system is underpinned by the stark correlation between the time of auditory system functional maturity, and the cessation of spontaneous action potentials. A prominent K(+) current that regulates patterning of action potentials is I(A). This current undergoes marked changes in expression during chicken hair cell development. Although the properties of I(A) are not normally classified as Ca(2+)-dependent, we demonstrate that throughout the development of chicken hair cells, I(A) is greatly reduced by acute alterations of intracellular Ca(2+). As determinants of spike timing and firing frequency, intracellular Ca(2+) buffers shift the activation and inactivation properties of the current to more positive potentials. Our findings provide evidence to demonstrate that the kinetics and functional expression of I(A) are tightly regulated by intracellular Ca(2+). Such feedback mechanism between the functional expression of I(A) and intracellular Ca(2+) may shape the activity of spontaneous action potentials, thus potentially sculpting synaptic connections in an activity-dependent manner in the developing cochlea.

The low conductance mitochondrial permeability transition pore confers excitability and CICR wave propagation in a computational model

Mitochondria have long been known to sequester cytosolic Ca(2+) and even to shape intracellular patterns of endoplasmic reticulum-based Ca(2+) signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca(2+) induced Ca(2+) release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca(2+) handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus-Keizer computational model for respiration-driven Ca(2+) handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca(2+) wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca(2+) excitability seen in mitochondria.

Chemical analysis of single cells

Chemical analysis of single cells requires methods for quickly and quantitatively detecting a diverse array of analytes from extremely small volumes (femtoliters to nanoliters) with very high sensitivity and selectivity. Microelectrophoretic separations, using both traditional capillary electrophoresis and emerging microfluidic methods, are well suited for handling the unique size of single cells and limited numbers of intracellular molecules. Numerous analytes, ranging from small molecules such as amino acids and neurotransmitters to large proteins and subcellular organelles, have been quantified in single cells using microelectrophoretic separation techniques. Microseparation techniques, coupled to varying detection schemes including absorbance and fluorescence detection, electrochemical detection, and mass spectrometry, have allowed researchers to examine a number of processes inside single cells. This review also touches on a promising direction in single cell cytometry: the development of microfluidics for integrated cellular manipulation, chemical processing, and separation of cellular contents.

Modeling Ca2+ signaling differentiation during oocyte maturation

Ca2+ is a fundamental intracellular signal that mediates a variety of disparate physiological functions often in the same cell. Ca2+ signals span a wide range of spatial and temporal scales, which endow them with the specificity required to induce defined cellular functions. Furthermore, Ca2+ signaling is highly plastic as it is modulated dynamically during normal physiological development and under pathological conditions. However, the molecular mechanisms underlying Ca2+ signaling differentiation during cellular development remain poorly understood. Oocyte maturation in preparation for fertilization provides an exceptionally well-suited model to elucidate Ca2+ signaling regulation during cellular development. This is because a Ca2+ signal with specialized spatial and temporal dynamics is universally essential for egg activation at fertilization. Here we use mathematical modeling to define the critical determinants of Ca2+ signaling differentiation during oocyte maturation. We show that increasing IP3 receptor (IP3R) affinity replicates both elementary and global Ca2+ dynamics observed experimentally following oocyte maturation. Furthermore, our model reveals that because of the Ca2+ dependency of both SERCA and the IP3R, increased IP3R affinity shifts the system's equilibrium to a new steady state of high cytosolic Ca2+, which is essential for fertilization. Therefore our model provides unique insights into how relatively small alterations of the basic molecular mechanisms of Ca2+ signaling components can lead to dramatic alterations in the spatio-temporal properties of Ca2+ dynamics.

Visualization and manipulation of phosphoinositide dynamics in live cells using engineered protein domains

There is hardly a membrane-associated molecular event that is not regulated by phosphoinositides, a minor but critically important class of phospholipids of cellular membranes. The rapid formation, elimination, and conversion of these lipids in specific membrane compartments are ensured by a wealthy number of inositol lipid kinases and phosphatases with unique localization and regulatory properties. The existence of multiple inositol lipid pools have been indicated by metabolic labeling studies, but the level of functional compartmentalization revealed by the identification of numerous protein effectors acted upon by phosphoinositides could not have been foreseen. The changing perception of inositides from just serving as lipid precursors of second messengers to becoming highly dynamic local membrane-bound regulators poses new challenges concerning the detection of their rapid localized changes. Moreover, it is increasingly evident that manipulation of lipids in highly defined compartments would be a highly superior approach to soaking the cells with a particular phosphoinositide when studying the local regulation of the lipid on any effectors. In this review, we will summarize our efforts to improve our tools in studying phosphoinositide dynamics and discuss our views on the values of these methods compared to other options currently used or being explored.

Simulations of intracellular calcium release dynamics in response to a high-intensity, ultrashort electric pulse

Numerical simulations for electrically induced, intracellular calcium release from the endoplasmic reticulum are reported. A two-step model is used for self-consistency. Distributed electrical circuit representation coupled with the Smoluchowski equation yields the ER membrane nanoporation for calcium outflow based on a numerical simulation. This is combined with the continuum Li-Rinzel model and drift diffusion for calcium dynamics. Our results are shown to be in agreement with reported calcium release data. A modest increase (rough doubling) of the cellular calcium is predicted in the absence of extra-cellular calcium. In particular, the applied field of 15 kV/cm with 60 ns pulse duration makes for a strong comparison. No oscillations are predicted and the net recovery period of about 5 min are both in agreement with published experimental results. A quantitative explanation for the lack of such oscillatory behavior, based on the density dependent calcium fluxes, is also provided.

Ca2+ signaling differentiation during oocyte maturation

Oocyte maturation is an essential cellular differentiation pathway that prepares the egg for activation at fertilization leading to the initiation of embryogenesis. An integral attribute of oocyte maturation is the remodeling of Ca2+ signaling pathways endowing the egg with the capacity to produce a specialized Ca2+ transient at fertilization that is necessary and sufficient for egg activation. Consequently, mechanistic elucidation of Ca2+ signaling differentiation during oocyte maturation is fundamental to our understanding of egg activation, and offers a glimpse into Ca2+ signaling regulation during the cell cycle.

Localized sampling, electrophoresis, and biosensor analysis of Xenopus laevis cytoplasm for subcellular biochemical assays

The Xenopus oocyte is a widely used model cell for studies of signal transduction mechanisms. Advances in microanalytical methods have made it feasible to perform rapid, localized collection of cytoplasm from individual Xenopus oocytes. Analytes contained in the cytoplasmic sample are separated by electrophoresis in a capillary and simultaneously transferred to a detection region. The development of bioengineered cells as sensitive detectors of intracellular components made quantitative measurements of native signaling molecules within the electrophoresed sample possible. Local determination of the second messenger inositol 1,4,5-trisphosphate is described to illustrate the methods for the sampling, electrophoresis, detection, and quantification of signaling molecules in single oocytes.

Models of IP3 and Ca2+ oscillations: frequency encoding and identification of underlying feedbacks

Hormones that act through the calcium-releasing messenger, inositol 1,4,5-trisphosphate (IP3), cause intracellular calcium oscillations, which have been ascribed to calcium feedbacks on the IP3 receptor. Recent studies have shown that IP3 levels oscillate together with the cytoplasmic calcium concentration. To investigate the functional significance of this phenomenon, we have developed mathematical models of the interaction of both second messengers. The models account for both positive and negative feedbacks of calcium on IP3 metabolism, mediated by calcium activation of phospholipase C and IP3 3-kinase, respectively. The coupled IP3 and calcium oscillations have a greatly expanded frequency range compared to calcium fluctuations obtained with clamped IP3. Therefore the feedbacks can be physiologically important in supporting the efficient frequency encoding of hormone concentration observed in many cell types. This action of the feedbacks depends on the turnover rate of IP3. To shape the oscillations, positive feedback requires fast IP3 turnover, whereas negative feedback requires slow IP3 turnover. The ectopic expression of an IP3 binding protein has been used to decrease the rate of IP3 turnover experimentally, resulting in a dose-dependent slowing and eventual quenching of the Ca2+ oscillations. These results are consistent with a model based on positive feedback of Ca2+ on IP3 production.

Signal transduction pathways leading to Ca2+ release in a vertebrate model system: Lessons from Xenopus eggs

At fertilization, eggs unite with sperm to initiate developmental programs that give rise to development of the embryo. Defining the molecular mechanism of this fundamental process at the beginning of life has been a key question in cell and developmental biology. In this review, we examine sperm-induced signal transduction events that lead to release of intracellular Ca(2+), a pivotal trigger of developmental activation, during fertilization in Xenopus laevis. Recent data demonstrate that metabolism of inositol 1,4,5-trisphosphate (IP(3)), a second messenger for Ca(2+) release, is carefully regulated and involves phospholipase C (PLC) and the tyrosine kinase Src. Roles of other potential regulators in this pathway, such as phosphatidylinositol 3-kinase, heterotrimeric GTP-binding protein, phospholipase D (PLD) and phosphatidic acid (PA) are also discussed. Finally, we address roles of egg lipid/membrane microdomains or 'rafts' as a platform for the sperm-egg membrane interaction and subsequent signaling events of egg activation.

An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory

We have developed a firing rate network model for working memory that combines Mexican-hat-like synaptic coupling with intrinsic or cellular dynamics that are conditionally bistable. While our approach is in the spirit of Camperi and Wang (1998) we include a specific and plausible mechanism for the cellular bistability. Modulatory neurotransmitters are known to activate second messenger signaling systems, and our model includes an intracellular Ca(2+) handling subsystem whose dynamics depend upon the level of the second messenger inositol 1,4,5 trisphosphate (IP3). This Ca(2+) subsystem endows individual units with conditional intrinsic bistability for a range of IP3. The full "hybrid" network sustains IP3-dependent persistent ("bump") activity in response to a brief transient stimulus. The bump response in our hybrid model, like that of Camperi-Wang, is resistant to noise-- its position does not drift with time.

Calcium signaling differentiation during Xenopus oocyte maturation

Ca(2+) is the universal signal for egg activation at fertilization in all sexually reproducing species. The Ca(2+) signal at fertilization is necessary for egg activation and exhibits specialized spatial and temporal dynamics. Eggs acquire the ability to produce the fertilization-specific Ca(2+) signal during oocyte maturation. However, the mechanisms regulating Ca(2+) signaling differentiation during oocyte maturation remain largely unknown. At fertilization, Xenopus eggs produce a cytoplasmic Ca(2+) (Ca(2+)(cyt)) rise that lasts for several minutes, and is required for egg activation. Here, we show that during oocyte maturation Ca(2+) transport effectors are tightly modulated. The plasma membrane Ca(2+) ATPase (PMCA) is completely internalized during maturation, and is therefore unable to extrude Ca(2+) out of the cell. Furthermore, IP(3)-dependent Ca(2+) release is required for the sustained Ca(2+)(cyt) rise in eggs, showing that Ca(2+) that is pumped into the ER leaks back out through IP(3) receptors. This apparent futile cycle allows eggs to maintain elevated cytoplasmic Ca(2+) despite the limited available Ca(2+) in intracellular stores. Therefore, Ca(2+) signaling differentiates in a highly orchestrated fashion during Xenopus oocyte maturation endowing the egg with the capacity to produce a sustained Ca(2+)(cyt) transient at fertilization, which defines the egg's competence to activate and initiate embryonic development.

Direct stochastic simulation of Ca2+ motion in Xenopus eggs

The release of important intracellular ions has been widely modeled using two approaches, namely, (1) Fickian diffusion, in which sometimes tensorial diffusion coefficients are used to fit observed temporally varying concentrations of calcium, and (2) cellular automata, which produce a set of localized finite difference equations that result in complex global behavior. Here, we take a different approach, employing some assumed, a priori, distribution of ion-binding proteins in the cell, and some assumed biochemical capture and release characteristics to explain ionic motion, and ultimately, distribution. We study several scenarios for ion distribution, based on differences in binder action and distribution. The numbers and strengths of ion binders, spatial variation in inositol 1,4,5-triphosphate concentration, together with the escalating distribution of ionic diffusion speed, are found to be key factors leading to concavity in the Ca2+ wave shape. We also offer an explanation for geometrical effects on previously observed ion diffusion speeds in the cellular cortex of the Xenopus laevis egg during fertilization, based on an angle-of-view correction.

Toward predictive models of mammalian cells

Progress in experimental and theoretical biology is likely to provide us with the opportunity to assemble detailed predictive models of mammalian cells. Using a functional format to describe the organization of mammalian cells, we describe current approaches for developing qualitative and quantitative models using data from a variety of experimental sources. Recent developments and applications of graph theory to biological networks are reviewed. The use of these qualitative models to identify the topology of regulatory motifs and functional modules is discussed. Cellular homeostasis and plasticity are interpreted within the framework of balance between regulatory motifs and interactions between modules. From this analysis we identify the need for detailed quantitative models on the basis of the representation of the chemistry underlying the cellular process. The use of deterministic, stochastic, and hybrid models to represent cellular processes is reviewed, and an initial integrated approach for the development of large-scale predictive models of a mammalian cell is presented.

Intracellular Signaling: Spatial and Temporal Control

Cells integrate many inputs through complex networks of interacting signaling pathways. Systems approaches as well as computer-aided reductionist approaches attempt to “untangle the wires” and gain an intimate understanding of cells. But “understanding” any system is just the way that the human mind gains the ability to predict behavior. Computer simulations are an alternative way to achieve this goal—quite possibly the only way for complex systems. We have new tools to probe large sets of unknown interactions, and we have amassed enough detailed information to quantitatively describe many functional modules. Cell physiology has passed the threshold: the time to begin modeling is now.

Phosphoinositide metabolism at fertilization of sea urchin eggs measured with a GFP-probe

Fertilization elicits a dramatic, transient rise in Ca2+ within the egg which is an essential component of egg activation and consequent initiation of development. In the sea urchin egg, three distinct Ca2+ stores have been identified which could, either individually or in combination, initiate Ca2+ release at fertilization. Inositol 1,4,5-trisphosphate (IP3) production by phospholipase C (PLC) has been suggested as the singular signal in initiating the Ca2+ transient. Other studies indicate that Ca2+ stores gated by cyclic adenosine diphosphate ribose (cADPR) or nicotinic acid adenine dinucleotide phosphate (NAADP) are also necessary. We have examined the temporal relationship between the Ca2+ rise and IP3 production at fertilization in vivo within individual eggs using a green fluorescent protein (GFP) coupled to a pleckstrin homology (PH) domain that can detect changes in IP3. Translocation of the probe occurred after the Ca2+ rise was initiated. Earlier, and possibly smaller, IP3 changes could not be excluded due to limitations in probe sensitivity. High IP3 levels are maintained during the decline in cytoplasmic Ca2+, suggesting that later IP3 metabolism might not be related to regulation of Ca2+, but may function to modulate other PIP2 regulated events such as actin polymerization or reflect other novel phosphoinositide signaling pathways.