An image-based model of calcium waves in differentiated neuroblastoma cells

A three-dimensional model of intercellular calcium signaling in epithelial cells

We have developed a fully three-dimensional (3D) model of calcium signaling in epithelial cells based on a set of reaction diffusion equations that are solved on a large-scale finite-element code in three dimensions. We have explicitly included the cellular compartments including the cell nucleus, cytoplasm, and gap junctions. The model allows for buffering of free Ca2+, calcium-induced calcium release, and the explicit inclusion of mobile buffers. To make quantitative comparisons to experimental results, we used fluorescence microscopy images of cells to generate an accurate mesh describing cell morphology. We found that Ca2+ wave propagation through the tissue is a function of both initial conditions used to start the wave and various geometrical parameters that affect propagation such as gap junction density and distribution, and the presence of nuclei. The exogenous dyes used in experimental imaging also affect wave propagation.

Evolving a lingua franca and associated software infrastructure for computational systems biology: the Systems Biology Markup Language (SBML) project

Biologists are increasingly recognising that computational modelling is crucial for making sense of the vast quantities of complex experimental data that are now being collected. The systems biology field needs agreed-upon information standards if models are to be shared, evaluated and developed cooperatively. Over the last four years, our team has been developing the Systems Biology Markup Language (SBML) in collaboration with an international community of modellers and software developers. SBML has become a de facto standard format for representing formal, quantitative and qualitative models at the level of biochemical reactions and regulatory networks. In this article, we summarise the current and upcoming versions of SBML and our efforts at developing software infrastructure for supporting and broadening its use. We also provide a brief overview of the many SBML-compatible software tools available today.

Compartment-specific feedback loop and regulated trafficking can result in sustained activation of Ras at the Golgi

Imaging experiments have shown that cell signaling components such as Ras can be activated by growth factors at distinct subcellular locations. Trafficking between these subcellular locations is a regulated dynamic process. The effects of trafficking and the molecular mechanisms underlying compartment-specific Ras activation were studied using numerical simulations of an ordinary differential equation-based multi-compartment model. The simulations show that interplay between two distinct mechanisms, a palmitoylation cycle that controls Ras trafficking and a phospholipase C-epsilon (PLC-epsilon) driven feedback loop, can convert a transient calcium signal into prolonged Ras activation at the Golgi. Detailed analysis of the network identified PLC-epsilon as a key determinant of "compartment switching". Modulation of PLC-epsilon activity switches the location of activated Ras between the plasma membrane and Golgi through a new mechanism termed "kinetic scaffolding". These simulations indicate that multiple biochemical mechanisms, when appropriately coupled, can give rise to an intracellular compartment-specific sustained Ras activation in response to stimulation of growth factor receptors at the plasma membrane.

An efficient stochastic diffusion algorithm for modeling second messengers in dendrites and spines

Intracellular signaling pathways, which encompass both biochemical reactions and second messenger diffusion, interact non-linearly with neuronal membrane properties in their role as essential intermediaries for synaptic plasticity and neuromodulation. Computational modeling is a productive approach for investigating these phenomena; however, most current strategies for modeling neurons exclude signaling pathways. To overcome this deficiency, a new algorithm is presented to simulate stochastic diffusion in a highly efficient manner. The gain in speed is obtained by considering collections of molecules, instead of tracking the movement of individual molecules. The probability of a molecule leaving a spatially discrete compartment is used to create a lookup table that stores the probability of k(m) molecules leaving the compartment as a function of the total number of molecules in the compartment. During the simulation, the number of molecules leaving the compartment is determined using a uniform random number as an index into the lookup table. Simulations illustrate the accuracy of this algorithm by comparing it with the theoretical solution for deterministic diffusion. Additional simulations show how spines on a dendritic branch compartmentalize diffusible molecules. The efficiency of the algorithm is sufficient to allow simulation of second messenger pathways in a multitude of spines on an entire neuron.

Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations

Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.

Endogenous inhibitors of InsP3-induced Ca2+ release in neuroblastoma cells

Cerebellar Purkinje neurons and neuroblastoma N1E-115 cells require 10-50 times more InsP3 to induce Ca2+ release than do a variety of non-neuronal cells (including astrocytes, hepatocytes, endothelial cells, or smooth muscle cells). Given the importance of InsP3-induced Ca2+ release for the development of synaptic plasticity in Purkinje neurons, a low InsP3 sensitivity may facilitate the integration of numerous synaptic inputs before initiating a change in synaptic strength. In the present study, attention is directed at the mechanism underlying this low InsP3 sensitivity of Ca2+ release. We show that permeabilization of neuroblastoma cells with saponin increased InsP3 sensitivity of Ca2+ release, indicating the presence of a diffusible, cytosolic inhibitor(s) of Ca2+ release. Consistent with this hypothesis, gel filtration of the neuroblastoma cytosol yielded three peaks that inhibited InsP3-induced Ca2+ release from permeabilized cells. The prominent inhibitory peak decreased the InsP3 sensitivity of Ca2+ release from permeabilized cells, did not bind 3H-InsP3, and was present in sufficient levels to account for the low InsP3 sensitivity of Ca2+ release in intact neuroblastoma cells. Purification of this prominent inhibitory fraction yielded a protein band that was identified by mass spectrometry as stress-induced phosphoprotein 1 (mSTI1). Furthermore, immunoprecipitation of mSTI1 decreased the inhibitory activity of N1E-115 cytosol, indicating that mSTI1 contributes to the inhibition of InsP3-induced Ca2+ release. Thus, the low InsP3 sensitivity of Ca2+ release in neuroblastoma cells can be explained by the presence of cytosolic inhibitors of Ca2+ release and include stress-induced phosphoprotein 1.

Pluronic F-127 affects the regulation of cytoplasmic Ca2+ in neuronal cells

Fura-2 is one of the most widely used cytoplasmic Ca2+ ([Ca2+]cyt) sensors. In studies using isolated dorsal root ganglion (DRG) neurons, the loading of Fura-2 AM is often facilitated by the use of pluronic F-127. In preliminary studies, we detected that the use of pluronic F-127 appeared to be affecting the depolarization-evoked [Ca2+]cyt transient in DRG neurons. To determine whether this was the case, we conducted a systematic study. Adult rat DRG neurons were cultured, and their response to 50 mM KCl was measured in sister cultured cells (isolated on the same day) that were loaded with 5 microM Fura-2AM in the absence or in the presence of 0.02% pluronic F-127. In the absence of pluronic F-127, the KCl-evoked [Ca2+]cyt transient changed with time, being wider on day 1 than on day 2 after plating. On day 2, the KCl-evoked [Ca2+]cyt transient was wider in neurons Fura-2 loaded in the presence of pluronic F-127. These results indicate that pluronic F-127 significantly alters depolarization-evoked [Ca2+]cyt transients, which may reflect alteration in regulation of [Ca2+]cyt in neuronal cells.

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

Modeling and simulation of the calcium signaling events that precede long-term depression of synaptic activity in cerebellar Purkinje cells are performed using the Virtual Cell biological modeling framework. It is found that the unusually high density and low sensitivity of inositol-1,4,5-trisphosphate receptors (IP3R) are critical to the ability of the cell to generate and localize a calcium spike in a single dendritic spine. The results also demonstrate the model's capability to simulate the supralinear calcium spike observed experimentally during coincident activation of the parallel and climbing fibers. The sensitivity of the calcium spikes to certain biological and geometrical effects is investigated as well as the mechanisms that underlie the cell's ability to generate the supralinear spike. The sensitivity of calcium release rates from the IP3R to calcium concentrations, as well as IP3 concentrations, allows the calcium spike to form. The diffusion barrier caused by the small radius of the spine neck is shown to be important, as a threshold radius is observed above which a spike cannot be formed. Additionally, the calcium buffer capacity and diffusion rates from the spine are found to be important parameters in shaping the calcium spike.

Calcium gradients and exocytosis in bovine adrenal chromaffin cells

The relationship between the localized Ca(2+) concentration and depolarization-induced exocytosis was studied in patch-clamped adrenal chromaffin cells using pulsed-laser Ca(2+) imaging and membrane capacitance measurements. Short depolarizing voltage steps induced Ca(2+) gradients and small "synchronous" increases in capacitance during the pulses. Longer pulses increased the capacitance changes, which saturated at 16 fF, suggesting the presence of a small immediately releasable pool of fusion-ready vesicles. A Hill plot of the capacitance changes versus the estimated Ca(2+) concentration in a thin (100 nm) shell beneath the membrane gave n = 2.3 and K(d) = 1.4 microM. Repetitive stimulation elicited a more complex pattern of exocytosis: early pulses induced synchronous capacitance increases, but after five or more pulses there was facilitation of the synchronous responses and gradual increases in capacitance continued between pulses (asynchronous exocytosis) as the steep submembrane Ca(2+) gradients collapsed. Raising the pipette Ca(2+) concentration led to early facilitation of the synchronous response and early appearance of asynchronous exocytosis. We used this data to develop a kinetic model of depolarization-induced exocytosis, where Ca(2+)-dependent fusion of vesicles occurs from a small immediately releasable pool with an affinity of 1-2 microM and vesicles are mobilized to this pool in a Ca(2+)-dependent manner.

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.

Computational approaches for modeling regulatory cellular networks

Cellular components interact with each other to form networks that process information and evoke biological responses. A deep understanding of the behavior of these networks requires the development and analysis of mathematical models. In this article, different types of mathematical representations for modeling signaling networks are described, and the advantages and disadvantages of each type are discussed. Two experimentally well-studied signaling networks are then used as examples to illustrate the insight that could be gained through modeling. Finally, the modeling approach is expanded to describe how signaling networks might regulate cellular machines and evoke phenotypic behaviors.

Neuronal differentiation of P19 embryonal carcinoma cells modulates kinin B2 receptor gene expression and function

Kinins are vasoactive oligopeptides generated upon proteolytic cleavage of low and high molecular weight kininogens by kallikreins. These peptides have a well established signaling role in inflammation and homeostasis. Nevertheless, emerging evidence suggests that bradykinin and other kinins are stored in the central nervous system and may act as neuromediators in the control of nociceptive response. Here we show that the kinin-B2 receptor (B2BKR) is differentially expressed during in vitro neuronal differentiation of P19 cells. Following induction by retinoic acid, cells form embryonic bodies and then undergo neuronal differentiation, which is complete after 8 and 9 days. Immunochemical staining revealed that B2BKR protein expression was below detection limits in nondifferentiated P19 cells but increased during the course of neuronal differentiation and peaked on days 8 and 9. Measurement of [Ca(2+)](i) in the absence and presence of bradykinin showed that most undifferentiated cells are unresponsive to bradykinin application, but following differentiation, P19 cells express high molecular weight neurofilaments, secrete bradykinin into the culture medium, and respond to bradykinin application with a transient increase in [Ca(2+)](i). However, inhibition of B2BKR activity with HOE-140 during early differentiation led to a decrease in the size of embryonic bodies formed. Pretreatment of differentiating P19 cells with HOE-140 on day 5 resulted in a reduction of the calcium response induced by the cholinergic agonist carbamoylcholine and decreased expression levels of M1-M3 muscarinic acetylcholine receptors, indicating crucial functions of the B2BKR during neuronal differentiation.

A signal transduction pathway model prototype II: Application to Ca2+-calmodulin signaling and myosin light chain phosphorylation

An agonist-initiated Ca(2+) signaling model for calmodulin (CaM) coupled to the phosphorylation of myosin light chains was created using a computer-assisted simulation environment. Calmodulin buffering was introduced as a module for directing sequestered CaM to myosin light chain kinase (MLCK) through Ca(2+)-dependent release from a buffering protein. Using differing simulation conditions, it was discovered that CaM buffering allowed transient production of more Ca(2+)-CaM-MLCK complex, resulting in elevated myosin light chain phosphorylation compared to nonbuffered control. Second messenger signaling also impacts myosin light chain phosphorylation through the regulation of myosin light chain phosphatase (MLCP). A model for MLCP regulation via its regulatory MYPT1 subunit and interaction of the CPI-17 inhibitor protein was assembled that incorporated several protein kinase subsystems including Rho-kinase, protein kinase C (PKC), and constitutive MYPT1 phosphorylation activities. The effects of the different routes of MLCP regulation depend upon the relative concentrations of MLCP compared to CPI-17, and the specific activities of protein kinases such as Rho and PKC. Phosphorylated CPI-17 (CPI-17P) was found to dynamically control activity during agonist stimulation, with the assumption that inhibition by CPI-17P (resulting from PKC activation) is faster than agonist-induced phosphorylation of MYPT1. Simulation results are in accord with literature measurements of MLCP and CPI-17 phosphorylation states during agonist stimulation, validating the predictive capabilities of the system.

A signal transduction pathway model prototype I: From agonist to cellular endpoint

The postgenomic era is providing a wealth of information about the genes involved in many cellular processes. However, the ability to apply this information to understanding cellular signal transduction is limited by the lack of tools that quantitatively describe cellular signaling processes. The objective of the current studies is to provide a framework for modeling cellular signaling processes beginning at a plasma membrane receptor and ending with a measurable endpoint in the signaling process. Agonist-induced Ca(2+) mobilization coupled to down stream phosphorylation events was modeled using knowledge of in vitro and in vivo process parameters. The simulation process includes several modules that describe cellular processes involving receptor activation phosphoinositide metabolism, Ca(2+)-release, and activation of a calmodulin-dependent protein kinase. A Virtual Cell-based simulation was formulated using available literature data and compared to new and existing experimental results. The model provides a new approach to facilitate hypothesis-driven investigation and experimental design based upon simulation results. These investigations may be directed at the timing of multiple phosphorylation/dephosphorylation events affecting key enzymatic activities in the signaling pathway.

Rearrangement of the endoplasmic reticulum and calcium transient formation: The computational approach

Experiments affecting calcium signaling often lead to changes in the calcium transient height. The present work is designed to approach this effect theoretically. Use of computational model let us to follow results of precisely designed changes in the endoplasmic reticulum distribution as a possible cause of cytoplasmic free calcium ion level. Obtained results suggest that indeed, rearrangement of the endoplasmic reticulum elements may be responsible for modulation of calcium signal's strength. We have also noticed that even if the endoplasmic reticulum concentration levels are local, the resulting changes in free calcium concentration are global and evenly distributed throughout the cell. The used mathematical method proved to be a powerful tool which made us understand the chemical dynamics of nonequilibrium processes of calcium transient formation. Presented data show how Ca2+ signal resulting from IP3 provoked release of calcium from the endoplasmic reticulum may depend on the cytoskeleton structure.

Signaling in small subcellular volumes. I. Stochastic and diffusion effects on individual pathways

Many cellular signaling events occur in small subcellular volumes and involve low-abundance molecular species. This context introduces two major differences from mass-action analyses of nondiffusive signaling. First, reactions involving small numbers of molecules occur in a probabilistic manner which introduces scatter in chemical activities. Second, the timescale of diffusion of molecules between subcellular compartments and the rest of the cell is comparable to the timescale of many chemical reactions, altering the dynamics and outcomes of signaling reactions. This study examines both these effects on information flow through four protein kinase regulatory pathways. The analysis uses Monte Carlo simulations in a subcellular volume diffusively coupled to a bulk cellular volume. Diffusion constants and the volume of the subcellular compartment are systematically varied to account for a range of cellular conditions. Each pathway is characterized in terms of the probabilistic scatter in active kinase levels as a measure of "noise" on the pathway output. Under the conditions reported here, most signaling outcomes in a volume below one femtoliter are severely degraded. Diffusion and subcellular compartmentalization influence the signaling chemistry to give a diversity of signaling outcomes. These outcomes may include washout of the signal, reinforcement of signals, and conversion of steady responses to transients.

Modeling cell signaling networks

Cell signaling pathways interact with one another to form networks in mammalian systems. Such networks are complex in their organization and exhibit emergent properties such as bistability and ultrasensitivity. Analysis of signaling networks requires a combination of experimental and theoretical approaches including the development and analysis of models. This review focuses on theoretical approaches to understanding cell signaling networks. Using heterotrimeric G protein pathways an example, we demonstrate how interactions between two pathways can result in a network that contains a positive feedback loop and function as a switch. Different mathematical approaches that are currently used to model signaling networks are described, and future challenges including the need for databases as well as enhanced computing environments are discussed.

Connectivity, clusters, and transport: use of percolation concepts and atomistic simulation to track intracellular ion migration

The cytoskeleton is an intracellular highway system, teaming with signalling ions that zip from site to site along filaments. These tiny particles alternately embrace and slip free of protein receptors with wide-ranging affinities, as they propagate in a blur of motion along cytoskeletal corridors at transport rates far exceeding ordinary diffusive motion. Recent experimental breakthroughs have enabled optical tracking of these single ion-binding events in the physiological and diseased states. However, traditional continuum modelling methods have proven ineffective for modelling migration of biometals such as copper and zinc, whose cytosolic concentrations are putatively vanishingly small, or very tightly controlled. Rather, the key modelling problem that must be solved for biometals is determination of the optimal placement of biosensors that bind and detect the metal ions within the heterogeneous environment of the cell. We discuss herein how percolation concepts, in combination with atomistic simulation and sensor delivery models, have been used to gain insights on this problem, and a roadmap for future breakthroughs.

Simulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor

Fertilization triggers repetitive waves of cytosolic Ca2+ in the egg of many species. The mechanism involved in the generation of Ca2+ waves has been studied in much detail in mature ascidian eggs, by raising artificially the level of inositol 1,4,5-trisphosphate [Ins(1,4,5)P3] or of its poorly metabolizable analogue, glycero-myo-phosphatidylinositol 4,5-bisphosphate [gPtdIns(4,5)P2]. Here, we use this strategy and the experimental results it provides to develop a realistic theoretical model for repetitive Ca2+ wave generation and propagation in mature eggs. The model takes into account the heterogeneous spatial distribution of the endoplasmic reticulum. Our results corroborate the hypothesis that Ca2+ wave pacemakers are associated with cortical accumulations of endoplasmic reticulum. The model is first tested and validated by the adequate match between its theoretical predictions and the observed effects of localized injections of massive amounts of Ins(1,4,5)P3 analogues. In a second step, we use the model to make some propositions about the possible characteristics of the sperm factor. We find that to account for the spatial characteristics of the first series of Ca2+ waves seen at fertilization in ascidian eggs, it has to be assumed that, if the sperm factor is a phospholipase C, it is Ca2+-sensitive and highly diffusible. Although the actual state of knowledge does not allow us to explain the observed relocalization of the Ca2+ wave pacemaker site, the model corroborates the assumption that PtdIns(4,5)P2, the substrate for phospholipase C is distributed over the entire egg. We also predict that the dose of sperm factor injected into the egg should modulate the temporal characteristics of the first, long-lasting fertilization wave.

Spatial distribution of Ca(2+) signals during repetitive depolarizing stimuli in adrenal chromaffin cells

Exocytosis in adrenal chromaffin cells is strongly influenced by the pattern of stimulation. To understand the dynamic and spatial properties of the underlying Ca(2+) signal, we used pulsed laser Ca(2+) imaging to capture Ca(2+) gradients during stimulation by single and repetitive depolarizing stimuli. Short single pulses (10-100 ms) lead to the development of submembrane Ca(2+) gradients, as previously described (F. D. Marengo and J. R. Monck, 2000, Biophysical Journal, 79:1800-1820). Repetitive stimulation with trains of multiple pulses (50 ms each, 2Hz) produce a pattern of intracellular Ca(2+) increase that progressively changes from the typical Ca(2+) gradient seen after a single pulse to a Ca(2+) increase throughout the cell that peaks at values 3-4 times higher than the maximum values obtained at the end of single pulses. After seven or more pulses, the fluorescence increase was typically larger in the interior of the cell than in the submembrane region. The pattern of Ca(2+) gradient was not modified by inhibitors of Ca(2+)-induced Ca(2+) release (ryanodine), inhibitors of IP(3)-induced Ca(2+) release (xestospongin), or treatments designed to deplete intracellular Ca(2+) stores (thapsigargin). However, we found that the large fluorescence increase in the cell interior spatially colocalized with the nucleus. These results can be simulated using mathematical models of Ca(2+) redistribution in which the nucleus takes up Ca(2+) by active or passive transport mechanisms. These results show that chromaffin cells can respond to depolarizing stimuli with different dynamic Ca(2+) signals in the submembrane space, the cytosol, and the nucleus.

Localized chemical release from an artificial synapse chip

A device that releases chemical compounds in small volumes and at multiple, well defined locations would be a powerful tool for clinical therapeutics and biological research. Many biomedical devices such as neurotransmitter-based prostheses or drug delivery devices require precise release of chemical compounds. Additionally, the ability to control chemical gradients will have applications in basic research such as studies of cell microenvironments, stem cell niches, metaplasia, or chemotaxis. We present such a device with repeatable delivery of chemical compounds at multiple locations on a chip surface. Using electroosmosis to drive flow through microfluidic channels, we pulse minute quantities of a bradykinin solution through four 5-microm apertures onto PC12 cells and show stimulation of individual cells using a Ca(2+)-sensitive fluorescent dye. We also present basic computational results with experimental verification of both fluid ejection and fluid withdrawal by imaging pH changes by using a fluorescent dye. This "artificial synapse chip" is a prototype neural interface that introduces a new paradigm for neural stimulation, with eventual application in treating macular degeneration and other neurological disorders.

Vanilloid receptor 1 regulates multiple calcium compartments and contributes to Ca2+-induced Ca2+ release in sensory neurons

Vanilloid receptor 1 belongs to the transient receptor potential ion channel family and transduces sensations of noxious heat and inflammatory hyperalgesia in nociceptive neurons. These neurons contain two vanilloid receptor pools, one in the plasma membrane and the other in the endoplasmic reticulum. The present experiments characterize these two pools and their functional significance using calcium imaging and 45Ca uptake in stably transfected cells or dorsal root ganglion neurons. The plasma membrane localized receptor is directly activated by vanilloids. The endoplasmic reticulum pool was demonstrated to be independently activated with 20 microm capsaicin or 1.6 microm resiniferatoxin using a bathing solution containing 10 microm Ruthenium Red (to selectively block plasma membrane-localized receptors) and 100 microm EGTA. We also demonstrate an overlap between the endoplasmic reticulum-localized vanilloid receptor regulated stores and thapsigargin-sensitive stores. Direct depletion of calcium via activation of endoplasmic reticulum-localized vanilloid receptor 1 triggered store operated calcium entry. Furthermore, we found that, in the presence of low extracellular calcium (10(-5) m), either 2 microm capsaicin or 0.1 nm-1.6 microm resiniferatoxin caused a pronounced calcium-induced calcium release in either vanilloid receptor-expressing neurons or heterologous expression systems. This phenomenon may allow new insight into how nociceptive neuron function in response to a variety of nociceptive stimuli both acutely and during prolonged nociceptive signaling.

Toward Automated Cell Model Development through Information Theory†

The objective of this paper is to present a methodology for developing and calibrating models of complex reaction/transport systems. In particular, the complex network of biochemical reaction/transport processes and their spatial organization make the development of a predictive model of a living cell a grand challenge for the 21st century. However, advances in reaction/transport modeling and the exponentially growing databases of genomic, proteomic, metabolic, and bioelectric data make cell modeling feasible, if these two elements can be automatically integrated in an unbiased fashion. In this paper, we present a procedure to integrate data with a new cell model, Karyote, that accounts for many of the physical processes needed to attain the goal of predictive modeling. Our integration methodology is based on the use of information theory. The model is integrated with a variety of types and qualities of experimental data using an objective error assessment approach. Data that can be used in this approach include NMR, spectroscopy, microscopy, and electric potentiometry. The approach is demonstrated on the well-studied Trypanosoma brucei system. A major obstacle for the development of a predictive cell model is that the complexity of these systems makes it unlikely that any model presently available will soon be complete in terms of the set of processes accounted for. Thus, one is faced with the challenge of calibrating and running an incomplete model. We present a probability functional method that allows the integration of experimental data and soft information such as choice of error measure, a priori information, and physically motivated regularization to address the incompleteness challenge.

Modeling the dependence of the period of intracellular Ca2+ waves on SERCA expression

Contrary to intuitive expectations, overexpression of sarco-endoplasmic reticulum (ER) Ca(2+) ATPases (SERCAs) in Xenopus oocytes leads to a decrease in the period and an increase in the amplitude of intracellular Ca(2+) waves. Here we examine these experimental findings by modeling Ca(2+) release using a modified Othmer-Tang-model. An increase in the period and a reduction in the amplitude of Ca(2+) wave activity are obtained when increases in SERCA density are simulated while keeping all other parameters of the model constant. However, Ca(2+) wave period can be reduced and the wave amplitude and velocity can be significantly increased when an increase in the luminal ER Ca(2+) concentration due to SERCA overexpression is incorporated into the model. Increased luminal Ca(2+) occurs because increased SERCA activity lowers cytosolic Ca(2+), which is partially replenished by Ca(2+) influx across the plasma membrane. These simulations are supported by experimental data demonstrating higher luminal Ca(2+) levels, decreased periods, increased amplitude, and increased velocity of Ca(2+) waves in response to increased SERCA density.

Activation of phospholipase C increases intramembrane electric fields in N1E-115 neuroblastoma cells

We imaged the intramembrane potential (a combination of transmembrane, surface, and dipole potential) on N1E-115 neuroblastoma cells with a voltage-sensitive dye. After activation of the B(2) bradykinin receptor, the electric field sensed by the dye increased by an amount equivalent to a depolarization of 83 mV. The increase in intramembrane potential was blocked by the phospholipase C (PLC) inhibitors U-73122 and neomycin, and was invariably accompanied by a transient rise of [Ca(2+)](i). A depolarized inner surface potential, as the membrane loses negative charges via phosphatidylinositol 4,5-bisphosphate (PIP(2)) hydrolysis, and an increase in the dipole potential, as PIP(2) is hydrolyzed to 1,2-diacylglycerol (DAG), can each account for a small portion of the change in intramembrane potential. The primary contribution to the measured change in intramembrane potential may arise from an increased dipole potential, as DAG molecules are generated from hydrolysis of other phospholipids. We found bradykinin produced an inhibition of a M-type voltage-dependent K(+) current (I(K(M))). This inhibition was also blocked by the PLC inhibitors and had similar kinetics as the bradykinin-induced modulation of intramembrane potential. Our results suggest that the change in the local intramembrane potential induced by bradykinin may play a role in mediating the I(K(M)) inhibition.

Kinetic analysis of receptor-activated phosphoinositide turnover

We studied the bradykinin-induced changes in phosphoinositide composition of N1E-115 neuroblastoma cells using a combination of biochemistry, microscope imaging, and mathematical modeling. Phosphatidylinositol-4,5-bisphosphate (PIP2) decreased over the first 30 s, and then recovered over the following 2-3 min. However, the rate and amount of inositol-1,4,5-trisphosphate (InsP3) production were much greater than the rate or amount of PIP2 decline. A mathematical model of phosphoinositide turnover based on this data predicted that PIP2 synthesis is also stimulated by bradykinin, causing an early transient increase in its concentration. This was subsequently confirmed experimentally. Then, we used single-cell microscopy to further examine phosphoinositide turnover by following the translocation of the pleckstrin homology domain of PLCdelta1 fused to green fluorescent protein (PH-GFP). The observed time course could be simulated by incorporating binding of PIP2 and InsP3 to PH-GFP into the model that had been used to analyze the biochemistry. Furthermore, this analysis could help to resolve a controversy over whether the translocation of PH-GFP from membrane to cytosol is due to a decrease in PIP2 on the membrane or an increase in InsP3 in cytosol; by computationally clamping the concentrations of each of these compounds, the model shows how both contribute to the dynamics of probe translocation.

Responses of Ca2+-binding proteins to localized, transient changes in intracellular [Ca2+]

In smooth muscle cells, various transient, localized [Ca(2+)] changes have been observed that are thought to regulate cell function without necessarily inducing contraction. Although a great deal of effort has been put into detecting these transients and elucidating the mechanisms involved in their generation, the extent to which these transient Ca(2+) signals interact with intracellular Ca(2+)-binding molecules remains relatively unknown. To understand how the spatial and temporal characteristics of an intracellular Ca(2+) signal influence its interaction with Ca(2+)-binding proteins, mathematical models of Ca(2+) diffusion and regulation in smooth muscle cells were used to study Ca(2+) binding to prototypical proteins with one or two Ca(2+)-binding sites. Simulations with the models: (1) demonstrate the extent to which the rate constants for Ca(2+)-binding to proteins and the spatial and temporal characteristics of different Ca(2+) transients influence the magnitude and time course of the responses of these proteins to the transients; (2) predict significant differences in the responses of proteins with one or two Ca(2+)-binding sites to individual Ca(2+) transients and to trains of transients; (3) demonstrate how the kinetic characteristics determine the fidelity with which the responses of Ca(2+)-sensitive molecules reflect the magnitude and time course of transient Ca(2+) signals. Overall, this work demonstrates the clear need for complete information about the kinetics of Ca(2+) binding for determining how well Ca(2+)-binding molecules respond to different types of Ca(2+) signals. These results have important implications when considering the possible modulation of Ca(2+)- and Ca(2+)/calmodulin-dependent proteins by localized intracellular Ca(2+) transients in smooth muscle cells and, more generally, in other cell types.

The community of the self

Good health, which reflects the harmonious integration of molecules, cells, tissues and organs, is dynamically stable: when displaced by disease, compensation and correction are common, even without medical care. Physiology and computational biology now suggest that healthy dynamic stability arises through the combination of specific feedback mechanisms and spontaneous properties of interconnected networks. Today's physicians are already testing to 'see if the network is right'; tomorrow's physicians may well use therapies to 'make the network right'.

On the conservation of fast calcium wave speeds

Calcium waves were first seen about 25 years ago as the giant, 10 micro m/s wave or tsunami which crosses the cytoplasm of an activating medaka fish egg [J Cell Biol 76 (1978) 448]. By 1991, reports of such waves with approximately 10 micro m/s velocities through diverse, activating eggs and with approximately 30 micro m/s velocities through diverse, fully active systems had been compiled to form a class of what are now called fast calcium waves [Proc Natl Acad Sci USA 88 (1991) 9883; Bioessays 21 (1999) 657]. This compilation is now updated to include organisms from algae and sponges up to blowflies, squid and men and organizational levels from mammalian brains and hearts as well as chick embryos down to muscle, nerve, epithelial, blood and cancer cells and even cell-free extracts. Plots of these data confirm the narrow, 2-3-fold ranges of fast wave speeds through activating eggs and 3-4-fold ones through fully active systems at a given temperature. This also indicate Q(10)'s of 2.7-fold per 10 degrees C for both activating eggs and for fully activated cells.Speeds through some ultraflat preparations which are a few-fold above the conserved range are attributed to stretch propagated calcium entry (SPCE) rather than calcium-induced calcium release (CICR).

IP(3)-mediated Ca(2+) signals in human neuroblastoma SH-SY5Y cells with exogenous overexpression of type 3 IP(3) receptor

Human neuroblastoma SH-SY5Y cells, predominantly expressing type 1 inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R), were stably transfected with IP(3)R type 3 (IP(3)R3) cDNA. Immunocytochemistry experiments showed a homogeneous cytoplasmic distribution of type 3 IP(3)Rs in transfected and selected high expression cloned cells. Using confocal Ca(2+) imaging, carbachol (CCh)-induced Ca(2+) release signals were studied. Low CCh concentrations (< or = 750 nM) evoked baseline Ca(2+) oscillations. Transfected cells displayed a higher CCh responsiveness than control or cloned cells. Ca(2+) responses varied between fast, large Ca(2+) spikes and slow, small Ca(2+) humps, while in the clone only Ca(2+) humps were observed. Ca(2+) humps in the transfected cells were associated with a high expression level of IP(3)R3. At high CCh concentrations (10 microM) Ca(2+) transients in transfected and cloned cells were similar to those in control cells. In the clone exogenous IP(3)R3 lacked the C-terminal channel domain but IP(3)-binding capacity was preserved. Transfected cells mainly expressed intact type 3 IP(3)Rs but some protein degradation was also observed. We conclude that in transfected cells expression of functional type 3 IP(3)Rs causes an apparent higher affinity for IP(3). In the clone, the presence of degraded receptors leads to an efficient cellular IP(3) buffer and attenuated IP(3)-evoked Ca(2+) release.

Computational cell biology: spatiotemporal simulation of cellular events

The field of computational cell biology has emerged within the past 5 years because of the need to apply disciplined computational approaches to build and test complex hypotheses on the interacting structural, physical, and chemical features that underlie intracellular processes. To meet this need, newly developed software tools allow cell biologists and biophysicists to build models and generate simulations from them. The construction of general-purpose computational approaches is especially challenging if the spatial complexity of cellular systems is to be explicitly treated. This review surveys some of the existing efforts in this field with special emphasis on a system being developed in the authors' laboratory, Virtual Cell. The theories behind both stochastic and deterministic simulations are discussed. Examples of respective applications to cell biological problems in RNA trafficking and neuronal calcium dynamics are provided to illustrate these ideas.

Distinct intracellular calcium transients in neurites and somata integrate neuronal signals

Intracellular calcium signals have distinct temporal and spatial patterns in neurons in which signal initiation and repetitive spiking occurs predominantly in the neurite. We investigated the functional implications of the coexpression of different isoforms of ryanodine receptors (RyR) and inositol 1,4,5-trisphosphate receptors (InsP3Rs) using immunocytochemistry, Western blotting, and calcium imaging in neuronally differentiated PC12 cells. InsP3R type III, an isoform that has been shown to be upregulated in neuronal apoptosis, is exclusively expressed in the soma, serving as a gatekeeper for high-magnitude calcium surges. InsP3R type I is expressed throughout the cell and can be related to signal initiation and repetitive spiking in the neurite. RyR types 2 and 3 are distributed throughout the cell. In the soma, they serve as amplifying molecular switches, facilitating recruitment of the InsP3R type III-dependent pool. In the neurite, they decrease the probability of repetitive spiking. Use of a cell-permeant analog of InsP3 suggested that regional specificity in InsP3 production and surface-to-volume effects play minor roles in determining temporal and spatial calcium signaling patterns in neurons. Our findings suggest that additional modulatory processes acting on the intracellular channels are necessary to generate spatially specific calcium signaling.

Exploring the formation of Alzheimer's disease senile plaques in silico

An experimental simulation environment suitable for exploring the neuroinflammatory hypothesis of Alzheimer's disease (AD) has been developed. Using scientific literature, we have calculated parameters and rates and constructed an interactive model system. The simulation can be manipulated to explore competing hypotheses about AD pathology, i.e. can be used as an experimental "in silico" system. In this paper, we outline the assumptions and aspects of the model, and illustrate qualitative and quantitative findings. The interactions of amyloid beta deposits, glial cell dynamics, inflammation and secreted cytokines, and the stress, recovery, and death of neuronal tissue are investigated. The model leads to qualitative insights about relative roles of the cells and chemicals in the disease pathology.

Regulation of intracellular calcium in N1E-115 neuroblastoma cells: the role of Na(+)/Ca(2+) exchange

In fura 2-loaded N1E-115 cells, regulation of intracellular Ca(2+) concentration ([Ca(2+)](i)) following a Ca(2+) load induced by 1 microM thapsigargin and 10 microM carbonylcyanide p-trifluoromethyoxyphenylhydrazone (FCCP) was Na(+) dependent and inhibited by 5 mM Ni(2+). In cells with normal intracellular Na(+) concentration ([Na(+)](i)), removal of bath Na(+), which should result in reversal of Na(+)/Ca(2+) exchange, did not increase [Ca(2+)](i) unless cell Ca(2+) buffer capacity was reduced. When N1E-115 cells were Na(+) loaded using 100 microM veratridine and 4 microg/ml scorpion venom, the rate of the reverse mode of the Na(+)/Ca(2+) exchanger was apparently enhanced, since an approximately 4- to 6-fold increase in [Ca(2+)](i) occurred despite normal cell Ca(2+) buffering. In SBFI-loaded cells, we were able to demonstrate forward operation of the Na(+)/Ca(2+) exchanger (net efflux of Ca(2+)) by observing increases (approximately 6 mM) in [Na(+)](i). These Ni(2+) (5 mM)-inhibited increases in [Na(+)](i) could only be observed when a continuous ionomycin-induced influx of Ca(2+) occurred. The voltage-sensitive dye bis-(1,3-diethylthiobarbituric acid) trimethine oxonol was used to measure changes in membrane potential. Ionomycin (1 microM) depolarized N1E-115 cells (approximately 25 mV). This depolarization was Na(+) dependent and blocked by 5 mM Ni(2+) and 250-500 microM benzamil. These data provide evidence for the presence of an electrogenic Na(+)/Ca(2+) exchanger that is capable of regulating [Ca(2+)](i) after release of Ca(2+) from cell stores.

Signaling microdomains define the specificity of receptor-mediated InsP(3) pathways in neurons

M(1) muscarinic (M(1)AChRs) and B(2) bradykinin (B(2)Rs) receptors are two PLCbeta-coupled receptors that mobilize Ca(2+) in nonexcitable cells. In many neurons, however, B(2)Rs but not M(1)AChRs mobilize intracellular Ca(2+). We have studied the membrane organization and dynamics underlying this coupling specificity by using Trp channels as biosensors for real-time detection of PLCbeta products. We found that, in sympathetic neurons, although both receptors rapidly produced DAG and InsP(3) as messengers, only InsP(3) formed by B(2)Rs has the ability to activate IP(3)Rs. This exclusive coupling results from spatially restricted complexes linking B(2)Rs to IP(3)Rs, a missing partnership for M(1)AChRs. These complexes allow fast and localized rises of InsP(3), necessary to activate the low-affinity neuronal IP(3)R. Thus, these signaling microdomains are of critical importance for the induction of selective responses, discriminating proinflammatory information associated with B(2)Rs from cholinergic neurotransmission.

The Virtual Cell: a software environment for computational cell biology

The newly emerging field of computational cell biology requires software tools that address the needs of a broad community of scientists. Cell biological processes are controlled by an interacting set of biochemical and electrophysiological events that are distributed within complex cellular structures. Computational modeling is familiar to researchers in fields such as molecular structure, neurobiology and metabolic pathway engineering, and is rapidly emerging in the area of gene expression. Although some of these established modeling approaches can be adapted to address problems of interest to cell biologists, relatively few software development efforts have been directed at the field as a whole. The Virtual Cell is a computational environment designed for cell biologists as well as for mathematical biologists and bioengineers. It serves to aid the construction of cell biological models and the generation of simulations from them. The system enables the formulation of both compartmental and spatial models, the latter with either idealized or experimentally derived geometries of one, two or three dimensions.

Calcium waves in agarose gel with cell organelles: implications of the velocity curvature relationship

Calcium oscillations and waves have been observed not only in several types of living cells but also in less complex systems of isolated cell organelles. Here we report the determination of apparent Ca2+ diffusion coefficients in a novel excitable medium of agarose gel with homogeneously distributed vesicles of skeletal sarcoplasmic reticulum. Spatiotemporal calcium patterns were visualized by confocal laser scanning fluorescence microscopy. To obtain characteristic parameters of the velocity curvature relationship, namely, apparent diffusion coefficient, velocity of plane calcium waves, and critical radius, positively and negatively curved wave fronts were analyzed. It is demonstrated that gel-immobilized cell organelles reveal features of an excitable medium. Apparent Ca2+ diffusion coefficients of the in vitro system, both in the absence or in the presence of mitochondria, were found to be higher than in cardiac myocytes and lower than in unbuffered agarose gel. Plane calcium waves propagated markedly slower in the in vitro system than in rat cardiac myocytes. Whereas mitochondria significantly reduced the apparent Ca2+ diffusion coefficient of the in vitro system, propagation velocity and critical size of calcium waves were found to be nearly unchanged. These results suggest that calcium wave propagation depends on the kinetics of calcium release rather than on diffusion.

Analysis of nonlinear dynamics on arbitrary geometries with the Virtual Cell

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