Models of spatially restricted biochemical reaction systems

High Turnover and Rescue Effect of XRCC1 in Response to Heavy Charged Particle Radiation

The DNA damage response (DDR) is a highly orchestrated process. The involvement of the DDR factors in DNA damage response depends on their biochemical reactions with each other and with the chromatin. Using the online live-cell imaging combined with heavy ion microbeam irradiation, we studied the response of the scaffold protein X-ray repair cross complementary protein 1 (XRCC1) at the localized DNA damage in charged particle irradiated HT1080 cells expressing XRCC1 tagged RFP. The results showed that XRCC1 was recruited to the DNA damage with ultrafast kinetics in a poly ADP-ribose polymerase (PARP) dependent manner. The consecutive reaction model well explained the response of XRCC1 at ion hits, and we found that the XRCC1 recruitment was faster and dissociation was slower in the G2 phase than those in the G1 phase. The fractionated irradiation of the same cells resulted in accelerated dissociation at the previous damage sites, while the dissociated XRCC1 immediately recycled with a higher recruitment efficiency. Our data revealed XRCC1's new rescue mechanism and its high turnover in DNA damage response, which benefits our understanding of the biochemical mechanism in DNA damage response.

Stable continual learning through structured multiscale plasticity manifolds

Biological plasticity is ubiquitous. How does the brain navigate this complex plasticity space, where any component can seemingly change, in adapting to an ever-changing environment? We build a systematic case that stable continuous learning is achieved by structured rules that enforce multiple, but not all, components to change together in specific directions. This rule-based low-dimensional plasticity manifold of permitted plasticity combinations emerges from cell type-specific molecular signaling and triggers cascading impacts that span multiple scales. These multiscale plasticity manifolds form the basis for behavioral learning and are dynamic entities that are altered by neuromodulation, metaplasticity, and pathology. We explore the strong links between heterogeneities, degeneracy, and plasticity manifolds and emphasize the need to incorporate plasticity manifolds into learning-theoretical frameworks and experimental designs.

Robust emergence of sharply tuned place-cell responses in hippocampal neurons with structural and biophysical heterogeneities

Hippocampal pyramidal neurons sustain propagation of fast electrical signals and are electrotonically non-compact structures exhibiting cell-to-cell variability in their complex dendritic arborization. In this study, we demonstrate that sharp place-field tuning and several somatodendritic functional maps concomitantly emerge despite the presence of geometrical heterogeneities in these neurons. We establish this employing an unbiased stochastic search strategy involving thousands of models that spanned several morphologies and distinct profiles of dispersed synaptic localization and channel expression. Mechanistically, employing virtual knockout models (VKMs), we explored the impact of bidirectional modulation in dendritic spike prevalence on place-field tuning sharpness. Consistent with the prior literature, we found that across all morphologies, virtual knockout of either dendritic fast sodium channels or N-methyl-D-aspartate receptors led to a reduction in dendritic spike prevalence, whereas A-type potassium channel knockouts resulted in a non-specific increase in dendritic spike prevalence. However, place-field tuning sharpness was critically impaired in all three sets of VKMs, demonstrating that sharpness in feature tuning is maintained by an intricate balance between mechanisms that promote and those that prevent dendritic spike initiation. From the functional standpoint of the emergence of sharp feature tuning and intrinsic functional maps, within this framework, geometric variability was compensated by a combination of synaptic democracy, the ability of randomly dispersed synapses to yield sharp tuning through dendritic spike initiation, and ion-channel degeneracy. Our results suggest electrotonically non-compact neurons to be endowed with several degrees of freedom, encompassing channel expression, synaptic localization and morphological microstructure, in achieving sharp feature encoding and excitability homeostasis.

Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Stores, Channels, Glue, and Trees: Active Glial and Active Dendritic Physiology

Glial cells and neuronal dendrites were historically assumed to be passive structures that play only supportive physiological roles, with no active contribution to information processing in the central nervous system. Research spanning the past few decades has clearly established this assumption to be far from physiological realities. Whereas the discovery of active channel conductances and their localized plasticity was the turning point for dendritic structures, the demonstration that glial cells release transmitter molecules and communicate across the neuroglia syncytium through calcium wave propagation constituted path-breaking discoveries for glial cell physiology. An additional commonality between these two structures is the ability of calcium stores within their endoplasmic reticulum (ER) to support active propagation of calcium waves, which play crucial roles in the spatiotemporal integration of information within and across cells. Although there have been several demonstrations of regulatory roles of glial cells and dendritic structures in achieving common physiological goals such as information propagation and adaptability through plasticity, studies assessing physiological interactions between these two active structures have been few and far. This lacuna is especially striking given the strong connectivity that is known to exist between these two structures through several complex and tightly intercoupled mechanisms that also recruit their respective ER structures. In this review, we present brief overviews of the parallel literatures on active dendrites and active glial physiology and make a strong case for future studies to directly assess the strong interactions between these two structures in regulating physiology and pathophysiology of the brain.

Luminescence-activated nucleotide cyclase regulates spatial and temporal cAMP synthesis

cAMP is a ubiquitous second messenger that regulates cellular proliferation, differentiation, attachment, migration, and several other processes. It has become increasingly evident that tight regulation of cAMP accumulation and localization confers divergent yet specific signaling to downstream pathways. Currently, few tools are available that have sufficient spatial and temporal resolution to study location-biased cAMP signaling. Here, we introduce a new fusion protein consisting of a light-activated adenylyl cyclase (bPAC) and luciferase (nLuc). This construct allows dual activation of cAMP production through temporally precise photostimulation or chronic chemical stimulation that can be fine-tuned to mimic physiological levels and duration of cAMP synthesis to trigger downstream events. By targeting this construct to different compartments, we show that cAMP produced in the cytosol and nucleus stimulates proliferation in thyroid cells. The bPAC-nLuc fusion construct adds a new reagent to the available toolkit to study cAMP-regulated processes in living cells.

Active dendrites regulate the spatiotemporal spread of signaling microdomains

Microdomains that emerge from spatially constricted spread of biochemical signaling components play a central role in several neuronal computations. Although dendrites, endowed with several voltage-gated ion channels, form a prominent structural substrate for microdomain physiology, it is not known if these channels regulate the spatiotemporal spread of signaling microdomains. Here, we employed a multiscale, morphologically realistic, conductance-based model of the hippocampal pyramidal neuron that accounted for experimental details of electrical and calcium-dependent biochemical signaling. We activated synaptic N-Methyl-d-Aspartate receptors through theta-burst stimulation (TBS) or pairing (TBP) and assessed microdomain propagation along a signaling pathway that included calmodulin, calcium/calmodulin-dependent protein kinase II (CaMKII) and protein phosphatase 1. We found that the spatiotemporal spread of the TBS-evoked microdomain in phosphorylated CaMKII (pCaMKII) was amplified in comparison to that of the corresponding calcium microdomain. Next, we assessed the role of two dendritically expressed inactivating channels, one restorative (A-type potassium) and another regenerative (T-type calcium), by systematically varying their conductances. Whereas A-type potassium channels suppressed the spread of pCaMKII microdomains by altering the voltage response to TBS, T-type calcium channels enhanced this spread by modulating TBS-induced calcium influx without changing the voltage. Finally, we explored cross-dependencies of these channels with other model components, and demonstrated the heavy mutual interdependence of several biophysical and biochemical properties in regulating microdomains and their spread. Our conclusions unveil a pivotal role for dendritic voltage-gated ion channels in actively amplifying or suppressing biochemical signals and their spatiotemporal spread, with critical implications for clustered synaptic plasticity, robust information transfer and efficient neural coding.

The spatiotemporal spread of biochemical signals in neurons and other cells regulate signaling specificity, tuning of signal propagation, along with specificity and clustering of adaptive plasticity. Theoretical and experimental studies have demonstrated a critical role for cellular morphology and the topology of signaling networks in regulating this spread. In this study, we add a significantly complex dimension to this narrative by demonstrating that voltage-gated ion channels on the plasma membrane could actively amplify or suppress the strength and spread of downstream signaling components. Given the expression of different ion channels with wide-ranging heterogeneity in gating kinetics, localization and density, our results point to an increase in complexity of and degeneracy in signaling spread, and unveil a powerful mechanism for regulating biochemical-signaling pathways across different cell types.

Systems biology primer: the basic methods and approaches

Systems biology is an integrative discipline connecting the molecular components within a single biological scale and also among different scales (e.g. cells, tissues and organ systems) to physiological functions and organismal phenotypes through quantitative reasoning, computational models and high-throughput experimental technologies. Systems biology uses a wide range of quantitative experimental and computational methodologies to decode information flow from genes, proteins and other subcellular components of signaling, regulatory and functional pathways to control cell, tissue, organ and organismal level functions. The computational methods used in systems biology provide systems-level insights to understand interactions and dynamics at various scales, within cells, tissues, organs and organisms. In recent years, the systems biology framework has enabled research in quantitative and systems pharmacology and precision medicine for complex diseases. Here, we present a brief overview of current experimental and computational methods used in systems biology.

Mathematical modeling of gonadotropin-releasing hormone signaling

Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control reproduction. These are G_q-coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field.

On the importance of modelling the internal spatial dynamics of biological cells

Spatial effects such as cell shape have very often been considered negligible in models of cellular pathways, and many existing simulation infrastructures do not take such effects into consideration. Recent experimental results are reversing this judgement by showing that very small spatial variations can make a big difference in the fate of a cell. This is particularly the case when considering eukaryotic cells, which have a complex physical structure and many subtle control mechanisms, but bacteria are also interesting for the huge variation in shape both between species and in different phases of their lifecycle. In this work we perform simulations that measure the effect of three common bacterial shapes on the behaviour of model cellular pathways. To perform these experiments we develop ReDi-Cell, a highly scalable GPGPU cell simulation infrastructure for the modelling of cellular pathways in spatially detailed environments. ReDi-Cell is validated against known-good simulations, prior to its use in new work. We then use ReDi-Cell to conduct novel experiments that demonstrate the effect that three common bacterial shapes (Cocci, Bacilli and Spirilli) have on the behaviour of model cellular pathways. Pathway wavefront shape, pathway concentration gradients, and chemical species distribution are measured in the three different shapes. We also quantify the impact of internal cellular clutter on the same pathways. Through this work we show that variations in the shape or configuration of these common cell shapes alter model cell behaviour.

Membrane potential and Ca2+ concentration dependence on pressure and vasoactive agents in arterial smooth muscle: A model

A mathematical model incorporating junctional and stretch-activated microdomains and 37 protein components describes the myogenic response in arterial smooth muscle cells.

Arterial smooth muscle (SM) cells respond autonomously to changes in intravascular pressure, adjusting tension to maintain vessel diameter. The values of membrane potential (V_m) and sarcoplasmic Ca²⁺ concentration (Ca_in) within minutes of a change in pressure are the results of two opposing pathways, both of which use Ca²⁺ as a signal. This works because the two Ca²⁺-signaling pathways are confined to distinct microdomains in which the Ca²⁺ concentrations needed to activate key channels are transiently higher than Ca_in. A mathematical model of an isolated arterial SM cell is presented that incorporates the two types of microdomains. The first type consists of junctions between cisternae of the peripheral sarcoplasmic reticulum (SR), containing ryanodine receptors (RyRs), and the sarcolemma, containing voltage- and Ca²⁺-activated K⁺ (BK) channels. These junctional microdomains promote hyperpolarization, reduced Ca_in, and relaxation. The second type is postulated to form around stretch-activated nonspecific cation channels and neighboring Ca²⁺-activated Cl⁻ channels, and promotes the opposite (depolarization, increased Ca_in, and contraction). The model includes three additional compartments: the sarcoplasm, the central SR lumen, and the peripheral SR lumen. It incorporates 37 protein components. In addition to pressure, the model accommodates inputs of α- and β-adrenergic agonists, ATP, 11,12-epoxyeicosatrienoic acid, and nitric oxide (NO). The parameters of the equations were adjusted to obtain a close fit to reported V_m and Ca_in as functions of pressure, which have been determined in cerebral arteries. The simulations were insensitive to ±10% changes in most of the parameters. The model also simulated the effects of inhibiting RyR, BK, or voltage-activated Ca²⁺ channels on V_m and Ca_in. Deletion of BK β1 subunits is known to increase arterial–SM tension. In the model, deletion of β1 raised Ca_in at all pressures, and these increases were reversed by NO.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

Dendritic atrophy constricts functional maps in resonance and impedance properties of hippocampal model neurons

A gradient in the density of hyperpolarization-activated cyclic-nucleotide gated (HCN) channels is necessary for the emergence of several functional maps within hippocampal pyramidal neurons. Here, we systematically analyzed the impact of dendritic atrophy on nine such functional maps, related to input resistance and local/transfer impedance properties, using conductance-based models of hippocampal pyramidal neurons. We introduced progressive dendritic atrophy in a CA1 pyramidal neuron reconstruction through a pruning algorithm, measured all functional maps in each pruned reconstruction, and arrived at functional forms for the dependence of underlying measurements on dendritic length. We found that, across frequencies, atrophied neurons responded with higher efficiency to incoming inputs, and the transfer of signals across the dendritic tree was more effective in an atrophied reconstruction. Importantly, despite the presence of identical HCN-channel density gradients, spatial gradients in input resistance, local/transfer resonance frequencies and impedance profiles were significantly constricted in reconstructions with dendritic atrophy, where these physiological measurements across dendritic locations converged to similar values. These results revealed that, in atrophied dendritic structures, the presence of an ion channel density gradient alone was insufficient to sustain homologous functional maps along the same neuronal topograph. We assessed the biophysical basis for these conclusions and found that this atrophy-induced constriction of functional maps was mediated by an enhanced spatial spread of the influence of an HCN-channel cluster in atrophied trees. These results demonstrated that the influence fields of ion channel conductances need to be localized for channel gradients to express themselves as homologous functional maps, suggesting that ion channel gradients are necessary but not sufficient for the emergence of functional maps within single neurons.

Cross talk between CD3 and CD28 is spatially modulated by protein lateral mobility

Functional convergence of CD28 costimulation and TCR signaling is critical to T-cell activation and adaptive immunity. These receptors form complex microscale patterns within the immune synapse, although the impact of this spatial organization on cell signaling remains unclear. We investigate this cross talk using micropatterned surfaces that present ligands to these membrane proteins in order to control the organization of signaling molecules within the cell-substrate interface. While primary human CD4(+) T cells were activated by features containing ligands to both CD3 and CD28, this functional convergence was curtailed on surfaces in which engagement of these two systems was separated by micrometer-scale distances. Moreover, phosphorylated Lck was concentrated to regions of CD3 engagement and exhibited a low diffusion rate, suggesting that costimulation is controlled by a balance between the transport of active Lck to CD28 and its deactivation. In support of this model, disruption of the actin cytoskeleton increased Lck mobility and allowed functional T-cell costimulation by spatially separated CD3 and CD28. In primary mouse CD4(+) T cells, a complementary system, reducing the membrane mobility increased the sensitivity to CD3-CD28 separation. These results demonstrate a subcellular reaction-diffusion system that allows cells to sense the microscale organization of the extracellular environment.

T lymphocytes sense antigens within seconds and make a decision within one minute

Adaptive immune responses are triggered by the rapid and sensitive detection of MHC-bound peptides by TCRs. The kinetics of early TCR/APC contacts are incompletely known. In this study, we used total internal reflection fluorescence microscopy to image human T cell membranes near model surfaces: contact was mediated by mobile protrusions of <0.4 μm diameter. The mean lifetime of contacts with a neutral surface was 8.6 s. Adhesive interactions increased mean contact time to 27.6 s. Additional presence of TCR ligands dramatically decreased contact to 13.7 s, thus evidencing TCR-mediated triggering of a pulling motion within seconds after ligand encounter. After an interaction typically involving 30-40 contacts formed during a 1-min observation period, TCR stimulation triggered a rapid and active cell spreading. Pulling events and cell spreading were mimicked by pharmacological phospholipase Cγ1 activation, and they were prevented by phospholipase Cγ1 inhibition. These results provide a quantitative basis for elucidating the earliest cell response to the detection of foreign Ags.

Modeling spatiotemporal dynamics of bacterial populations

Quantitative modeling of spatiotemporal dynamics of cells facilitates understanding and engineering of biological systems. Using a synthetic bacterial ecosystem as a workbench, we present the approach to mathematically simulate the spatiotemporal population dynamics of the ecosystem. A description of ecosystem's genetic construction and model development is firstly given. Parameter estimation and computational approach for the derived partial differential equations (PDEs) are then given. Spatiotemporal pattern formation is computed by numerically solving the PDE model. Biodiversity of the ecosystem and its impacts by cellular seeding distance and motility are computed according to the cell distribution patterns.

Quantitative interactions between the A-type K+ current and inositol trisphosphate receptors regulate intraneuronal Ca2+ waves and synaptic plasticity

The A-type potassium current has been implicated in the regulation of several physiological processes. Here, we explore a role for the A-type potassium current in regulating the release of calcium through inositol trisphosphate receptors (InsP3R) that reside on the endoplasmic reticulum (ER) of hippocampal pyramidal neurons. To do this, we constructed morphologically realistic, conductance-based models equipped with kinetic schemes that govern several calcium signalling modules and pathways, and constrained the distributions and properties of constitutive components by experimental measurements from these neurons. Employing these models, we establish a bell-shaped dependence of calcium release through InsP3Rs on the density of A-type potassium channels, during the propagation of an intraneuronal calcium wave initiated through established protocols. Exploring the sensitivities of calcium wave initiation and propagation to several underlying parameters, we found that ER calcium release critically depends on dendritic diameter and that wave initiation occurred at branch points as a consequence of a high surface area to volume ratio of oblique dendrites. Furthermore, analogous to the role of A-type potassium channels in regulating spike latency, we found that an increase in the density of A-type potassium channels led to increases in the latency and the temporal spread of a propagating calcium wave. Next, we incorporated kinetic models for the metabotropic glutamate receptor (mGluR) signalling components and a calcium-controlled plasticity rule into our model and demonstrate that the presence of mGluRs induced a leftward shift in a Bienenstock-Cooper-Munro-like synaptic plasticity profile. Finally, we show that the A-type potassium current could regulate the relative contribution of ER calcium to synaptic plasticity induced either through 900 pulses of various stimulus frequencies or through theta burst stimulation. Our results establish a novel form of interaction between active dendrites and the ER membrane, uncovering a powerful mechanism that could regulate biophysical/biochemical signal integration and steer the spatiotemporal spread of signalling microdomains through changes in dendritic excitability.

Signaling network prediction by the Ontology Fingerprint enhanced Bayesian network

BACKGROUND

Despite large amounts of available genomic and proteomic data, predicting the structure and response of signaling networks is still a significant challenge. While statistical method such as Bayesian network has been explored to meet this challenge, employing existing biological knowledge for network prediction is difficult. The objective of this study is to develop a novel approach that integrates prior biological knowledge in the form of the Ontology Fingerprint to infer cell-type-specific signaling networks via data-driven Bayesian network learning; and to further use the trained model to predict cellular responses.

RESULTS

We applied our novel approach to address the Predictive Signaling Network Modeling challenge of the fourth (2009) Dialog for Reverse Engineering Assessment's and Methods (DREAM4) competition. The challenge results showed that our method accurately captured signal transduction of a network of protein kinases and phosphoproteins in that the predicted protein phosphorylation levels under all experimental conditions were highly correlated (R2 = 0.93) with the observed results. Based on the evaluation of the DREAM4 organizer, our team was ranked as one of the top five best performers in predicting network structure and protein phosphorylation activity under test conditions.

CONCLUSIONS

Bayesian network can be used to simulate the propagation of signals in cellular systems. Incorporating the Ontology Fingerprint as prior biological knowledge allows us to efficiently infer concise signaling network structure and to accurately predict cellular responses.

Exploiting mathematical models to illuminate electrophysiological variability between individuals

Across individuals within a population, several levels of variability are observed, from the differential expression of ion channels at the molecular level, to the various action potential morphologies observed at the cellular level, to divergent responses to drugs at the organismal level. However, the limited ability of experiments to probe complex interactions between components has hitherto hindered our understanding of the factors that cause a range of behaviours within a population. Variability is a challenging issue that is encountered in all physiological disciplines, but recent work suggests that novel methods for analysing mathematical models can assist in illuminating its causes. In this review, we discuss mathematical modelling studies in cardiac electrophysiology and neuroscience that have enhanced our understanding of variability in a number of key areas. Specifically, we discuss parameter sensitivity analysis techniques that may be applied to generate quantitative predictions based on considering behaviours within a population of models, thereby providing novel insight into variability. Our discussion focuses on four issues that have benefited from the utilization of these methods: (1) the comparison of different electrophysiological models of cardiac myocytes, (2) the determination of the individual contributions of different molecular changes in complex disease phenotypes, (3) the identification of the factors responsible for the variable response to drugs, and (4) the constraining of free parameters in electrophysiological models of heart cells. Together, the studies that we discuss suggest that rigorous analyses of mathematical models can generate quantitative predictions regarding how molecular-level variations contribute to functional differences between experimental samples. These strategies may be applicable not just in cardiac electrophysiology, but in a wide range of disciplines.

Modeling of spatial intracellular signaling events in neurons

A neuron is able to seamlessly respond to a number of signals, in a timely and specific manner. This process, of integrating multiple inputs, relays on the orchestration of intracellular events by signaling networks. The inherent complexity of signaling networks has made computational modeling a useful approach to understand their underlying regulatory principles. Recent advances in imaging techniques have highlighted the nonhomogeneous nature of intracellular signaling and its significant contribution to the maintenance of signal specificity. Computational modeling can provide mechanistic insight into the origins of these inhomogeneous distributions of signaling components and their role in the integrative capabilities of the neuron.

Role of computational methods in pharmaceutical sciences

Over the past two decades computational methods have eased up the financial and experimental burden of early drug discovery process. The in silico methods have provided support in terms of databases, data mining of large genomes, network analysis, systems biology on the bioinformatics front and structure-activity relationship, similarity analysis, docking, and pharmacophore methods for lead design and optimization. This review highlights some of the applications of bioinformatics and chemoinformatics methods that have enriched the field of drug discovery. In addition, the review also provided insights into the use of free energy perturbation methods for efficiently computing binding energy. These in silico methods are complementary and can be easily integrated into the traditional in vitro and in vivo methods to test pharmacological hypothesis.

Developing models in virtual cell

This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture on mathematical modeling using the Virtual Cell environment. The lectures discuss the steps involved in developing and running simulations using Virtual Cell, with particular focus on spatial partial differential equation models. We discuss how to construct both ordinary differential equation models, in which the cytoplasm is considered a well-mixed cellular compartment, and partial differential equation models, which calculate how chemical species change as a function of both time and location. The Virtual Cell environment is especially well suited for models that explore spatial specificity of cellular reactions. Partial differential equation models in Virtual Cell can give rise to simulations using predefined cellular geometries, which enable direct comparison with imaging data. These models address questions regarding the regulatory capability arising from spatial organization of the cell. Examples are provided of studies that have successfully exploited the Virtual Cell software to address the spatial contribution to signaling.

Modeling of spatially-restricted intracellular signaling

Understanding the signaling capabilities of a cell presents a major challenge, not only due to the number of molecules involved, but also because of the complex network connectivity of intracellular signaling. Recently, the proliferation of quantitative imaging techniques has led to the discovery of the vast spatial organization of intracellular signaling. Computational modeling has emerged as a powerful tool for understanding how inhomogeneous signaling originates and is maintained. This article covers the current imaging techniques used to obtain quantitative spatial data and the mathematical approaches used to model spatial cell biology. Modeling-derived hypotheses have been experimentally tested and the integration of modeling and imaging approaches has led to non-intuitive mechanistic insights.

Computational modeling of mammalian signaling networks

One of the most exciting developments in signal transduction research has been the proliferation of studies in which a biological discovery was initiated by computational modeling. In this study, we review the major efforts that enable such studies. First, we describe the experimental technologies that are generally used to identify the molecular components and interactions in, and dynamic behavior exhibited by, a network of interest. Next, we review the mathematical approaches that are used to model signaling network behavior. Finally, we focus on three specific instances of 'model-driven discovery': cases in which computational modeling of a signaling network has led to new insights that have been verified experimentally.

Cytosolic H+ microdomain developed around AE1 during AE1-mediated Cl-/HCO3- exchange

Microdomains, regions of discontinuous cytosolic solute concentration enhanced by rapid solute transport and slow diffusion rates, have many cellular roles. pH-regulatory membrane transporters, like the Cl−/HCO3− exchanger AE1, could develop H+ microdomains since AE1 has a rapid transport rate and cytosolic H+ diffusion is slow. We examined whether the pH environment surrounding AE1 differs from other cellular locations. As AE1 drives Cl−/HCO3− exchange, differences in pH, near and remote from AE1, were monitored by confocal microscopy using two pH-sensitive fluorescent proteins: deGFP4 (GFP) and mNectarine (mNect). Plasma membrane (PM) pH (defined as ∼1 μm region around the cell periphery) was monitored by GFP fused to AE1 (GFP.AE1), and mNect fused to an inactive mutant of the Na+-coupled nucleoside co-transporter, hCNT3 (mNect.hCNT3). GFP.AE1 to mNect.hCNT3 distance was varied by co-expression of different amounts of the two proteins in HEK293 cells. As the GFP.AE1–mNect.hCNT3 distance increased, mNect.hCNT3 detected the Cl−/HCO3− exchange-associated cytosolic pH change with a time delay and reduced rate of pH change compared to GFP.AE1. We found that a H+ microdomain 0.3 μm in diameter forms around GFP.AE1 during physiological HCO3− transport. Carbonic anhydrase isoform II inhibition prevented H+ microdomain formation. We also measured the rate of H+ movement from PM GFP.AE1 to endoplasmic reticulum (ER), using mNect fused to the cytosolic face of ER-resident calnexin (CNX.mNect). The rate of H+ diffusion through cytosol was 60-fold faster than along the cytosolic surface of the plasma membrane. The pH environment surrounding pH regulatory transport proteins may differ as a result of H+ microdomain formation, which will affect nearby pH-sensitive processes.

Reporting from the field: genetically encoded fluorescent reporters uncover signaling dynamics in living biological systems

Real-time visualization of a wide range of biochemical processes in living systems is being made possible through the development and application of genetically encoded fluorescent reporters. These versatile biosensors have proven themselves tailor-made to the study of signal transduction, and in this review, we discuss some of the unique insights that they continue to provide regarding the spatial organization and dynamic regulation of intracellular signaling networks. In addition, we explore the more recent push to expand the scope of biological phenomena that can be monitored using these reporters, while also considering the potential to integrate this highly adaptable technology with a number of emerging techniques that may significantly broaden our view of how networks of biochemical processes shape larger biological phenomena.

Signalling ballet in space and time

Although we have amassed extensive catalogues of signalling network components, our understanding of the spatiotemporal control of emergent network structures has lagged behind. Dynamic behaviour is starting to be explored throughout the genome, but analysis of spatial behaviours is still confined to individual proteins. The challenge is to reveal how cells integrate temporal and spatial information to determine specific biological functions. Key findings are the discovery of molecular signalling machines such as Ras nanoclusters, spatial activity gradients and flexible network circuitries that involve transcriptional feedback. They reveal design principles of spatiotemporal organization that are crucial for network function and cell fate decisions.

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.