Quantitative cell biology with the Virtual Cell

Technologies for whole-cell modeling: Genome-wide reconstruction of a cell in silico

With advances in high-throughput, large-scale in vivo measurement and genome modification techniques at the single-nucleotide level, there is an increasing demand for the development of new technologies for the flexible design and control of cellular systems. Computer-aided design is a powerful tool to design new cells. Whole-cell modeling aims to integrate various cellular subsystems, determine their interactions and cooperative mechanisms, and predict comprehensive cellular behaviors by computational simulations on a genome-wide scale. It has been applied to prokaryotes, yeasts, and higher eukaryotic cells, and utilized in a wide range of applications, including production of valuable substances, drug discovery, and controlled differentiation. Whole-cell modeling, consisting of several thousand elements with diverse scales and properties, requires innovative model construction, simulation, and analysis techniques. Furthermore, whole-cell modeling has been extended to multiple scales, including high-resolution modeling at the single-nucleotide and single-amino acid levels and multicellular modeling of tissues and organs. This review presents an overview of the current state of whole-cell modeling, discusses the novel computational and experimental technologies driving it, and introduces further developments toward multihierarchical modeling on a whole-genome scale.

Quantification of energy-converting protein complexes in plant thylakoid membranes

Knowledge about the exact abundance and ratio of photosynthetic protein complexes in thylakoid membranes is central to understanding structure-function relationships in energy conversion. Recent modeling approaches for studying light harvesting and electron transport reactions rely on quantitative information on the constituent complexes in thylakoid membranes. Over the last decades several quantitative methods have been established and refined, enabling precise stoichiometric information on the five main energy-converting building blocks in the thylakoid membrane: Light-harvesting complex II (LHCII), Photosystem II (PSII), Photosystem I (PSI), cytochrome b₆f complex (cyt b₆f complex), and ATPase. This paper summarizes a few quantitative spectroscopic and biochemical methods that are currently available for quantification of plant thylakoid protein complexes. Two new methods are presented for quantification of LHCII and the cyt b₆f complex, which agree well with established methods. In addition, recent improvements in mass spectrometry (MS) allow deeper compositional information on thylakoid membranes. The comparison between mass spectrometric and more classical protein quantification methods shows similar quantities of complexes, confirming the potential of thylakoid protein complex quantification by MS. The quantitative information on PSII, PSI, and LHCII reveal that about one third of LHCII must be associated with PSI for a balanced light energy absorption by the two photosystems.

A multifarious exploration of synaptic tagging and capture hypothesis in synaptic plasticity: Development of an integrated mathematical model and computational experiments

The synaptic tagging and capture (STC) hypothesis not only explain the integration and association of synaptic activities, but also the formation of learning and memory. The synaptic pathways involved in the synaptic tagging and capture phenomenon are called STC pathways. The STC hypothesis provides a potential explanation of the neuronal and synaptic processes underlying the synaptic consolidation of memories. Several mechanisms and molecules have been proposed to explain the process of memory allocation and synaptic tags, respectively. However, a clear link between the STC hypothesis and memory allocation is still missing because the encoding of memories in neural circuits is mainly associated with strongly recurrently connected groups of neurons. To explore the mechanisms of potential synaptic tagging candidates and their involvement in the process of memory allocation, we develop a mathematical model for a single dendritic spine based on five essential criteria of a synaptic tag. By developing a mathematical model, we attempt to understand the roles of the potentially critical molecular networks underlying the STC and the essential attributes of a synaptic tag. We include essential memory molecules in the STC model that have been identified in earlier studies as crucial for STC pathways. CaMKII activation is critical for the setting of the initial tag; however, coordinated activities with other kinases and the biochemical pathways are necessary for the tag to be stable. PKA modulates NMDAR-mediated Ca²⁺ signalling. Similarly, PKA and ERK crosstalk is essential for Ca²⁺ - mediated protein synthesis during l-LTP. Our theoretical model explains the quantitative contribution of Tags and protein synthesis during l-LTP in synaptic strength.

Methodology for development of single cell dendritic spine (SCDS) synaptic tagging and capture model using Virtual Cell (VCell)

Single cell dendritic spine modelling methodology has been adopted to explain structural plasticity and respective change in the neuronal volume previously. However, the single cell dendrite methodology has not been employed previously to explain one of the important aspects of memory allocation i.e., Synaptic tagging and Capture (STC) hypothesis. It is difficult to relate the physical properties of STC pathways to structural changes and synaptic strength. We create a mathematical model based on earlier reported synaptic tagging networks. We built the model using Virtual Cell (VCell) software and used it to interpret experimental data and investigate the behavior and characteristics of known Synaptic tagging candidates.•We investigate processes associated with synaptic tagging candidates and compare them to the assumptions based on the STC hypothesis.•We assess the behavior of several reported synaptic tagging candidates against the requirements outlined in the synaptic tagging hypothesis.

Understanding the functional role of membrane confinements in TNF-mediated signaling by multiscale simulations

The interaction between TNFα and TNFR1 is essential in maintaining tissue development and immune responses. While TNFR1 is a cell surface receptor, TNFα exists in both soluble and membrane-bound forms. Interestingly, it was found that the activation of TNFR1-mediated signaling pathways is preferentially through the soluble form of TNFα, which can also induce the clustering of TNFR1 on plasma membrane of living cells. We developed a multiscale simulation framework to compare receptor clustering induced by soluble and membrane-bound ligands. Comparing with the freely diffusive soluble ligands, we hypothesize that the conformational dynamics of membrane-bound ligands are restricted, which affects the clustering of ligand-receptor complexes at cell-cell interfaces. Our simulation revealed that only small clusters can form if TNFα is bound on cell surface. In contrast, the clustering triggered by soluble TNFα is more dynamic, and the size of clusters is statistically larger. We therefore demonstrated the impact of membrane-bound ligand on dynamics of receptor clustering. Moreover, considering that larger TNFα-TNFR1 clusters is more likely to provide spatial platform for downstream signaling pathway, our studies offer new mechanistic insights about why the activation of TNFR1-mediated signaling pathways is not preferred by membrane-bound form of TNFα.

Tryptophan Production Maximization in a Fed-Batch Bioreactor with Modified E. coli Cells, by Optimizing Its Operating Policy Based on an Extended Structured Cell Kinetic Model

Hybrid kinetic models, linking structured cell metabolic processes to the dynamics of macroscopic variables of the bioreactor, are more and more used in engineering evaluations to derive more precise predictions of the process dynamics under variable operating conditions. Depending on the cell model complexity, such a math tool can be used to evaluate the metabolic fluxes in relation to the bioreactor operating conditions, thus suggesting ways to genetically modify the microorganism for certain purposes. Even if development of such an extended dynamic model requires more experimental and computational efforts, its use is advantageous. The approached probative example refers to a model simulating the dynamics of nanoscale variables from several pathways of the central carbon metabolism (CCM) of Escherichia coli cells, linked to the macroscopic state variables of a fed-batch bioreactor (FBR) used for the tryptophan (TRP) production. The used E. coli strain was modified to replace the PTS system for glucose (GLC) uptake with a more efficient one. The study presents multiple elements of novelty: (i) the experimentally validated modular model itself, and (ii) its efficiency in computationally deriving an optimal operation policy of the FBR.

Mechanistic dissection of spatial organization in NF-κB signaling pathways by hybrid simulations

The nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) is one of the most important transcription factors involved in the regulation of inflammatory signaling pathways. Inappropriate activation of these pathways has been linked to autoimmunity and cancers. Emerging experimental evidences have been showing the existence of elaborate spatial organizations for various molecular components in the pathways. One example is the scaffold protein tumor necrosis factor receptor associated factor (TRAF). While most TRAF proteins form trimeric quaternary structure through their coiled-coil regions, the N-terminal region of some members in the family can further be dimerized. This dimerization of TRAF trimers can drive them into higher-order clusters as a response to receptor stimulation, which functions as a spatial platform to mediate the downstream poly-ubiquitination. However, the molecular mechanism underlying the TRAF protein clustering and its functional impacts are not well-understood. In this article, we developed a hybrid simulation method to tackle this problem. The assembly of TRAF-based signaling platform at the membrane-proximal region is modeled with spatial resolution, while the dynamics of downstream signaling network, including the negative feedbacks through various signaling inhibitors, is simulated as stochastic chemical reactions. These two algorithms are further synchronized under a multiscale simulation framework. Using this computational model, we illustrated that the formation of TRAF signaling platform can trigger an oscillatory NF-κB response. We further demonstrated that the temporal patterns of downstream signal oscillations are closely regulated by the spatial factors of TRAF clustering, such as the geometry and energy of dimerization between TRAF trimers. In general, our study sheds light on the basic mechanism of NF-κB signaling pathway and highlights the functional importance of spatial regulation within the pathway. The simulation framework also showcases its potential of application to other signaling pathways in cells.

A multiscale study on the mechanisms of spatial organization in ligand-receptor interactions on cell surfaces

The binding of cell surface receptors with extracellular ligands triggers distinctive signaling pathways, leading into the corresponding phenotypic variation of cells. It has been found that in many systems, these ligand-receptor complexes can further oligomerize into higher-order structures. This ligand-induced oligomerization of receptors on cell surfaces plays an important role in regulating the functions of cell signaling. The underlying mechanism, however, is not well understood. One typical example is proteins that belong to the tumor necrosis factor receptor (TNFR) superfamily. Using a generic multiscale simulation platform that spans from atomic to subcellular levels, we compared the detailed physical process of ligand-receptor oligomerization for two specific members in the TNFR superfamily: the complex formed between ligand TNFα and receptor TNFR1 versus the complex formed between ligand TNFβ and receptor TNFR2. Interestingly, although these two systems share high similarity on the tertiary and quaternary structural levels, our results indicate that their oligomers are formed with very different dynamic properties and spatial patterns. We demonstrated that the changes of receptor’s conformational fluctuations due to the membrane confinements are closely related to such difference. Consistent to previous experiments, our simulations also showed that TNFR can preassemble into dimers prior to ligand binding, while the introduction of TNF ligands induced higher-order oligomerization due to a multivalent effect. This study, therefore, provides the molecular basis to TNFR oligomerization and reveals new insights to TNFR-mediated signal transduction. Moreover, our multiscale simulation framework serves as a prototype that paves the way to study higher-order assembly of cell surface receptors in many other bio-systems.

A computational study of co-inhibitory immune complex assembly at the interface between T cells and antigen presenting cells

The activation and differentiation of T-cells are mainly directly by their co-regulatory receptors. T lymphocyte-associated protein-4 (CTLA-4) and programed cell death-1 (PD-1) are two of the most important co-regulatory receptors. Binding of PD-1 and CTLA-4 with their corresponding ligands programed cell death-ligand 1 (PD-L1) and B7 on the antigen presenting cells (APC) activates two central co-inhibitory signaling pathways to suppress T cell functions. Interestingly, recent experiments have identified a new cis-interaction between PD-L1 and B7, suggesting that a crosstalk exists between two co-inhibitory receptors and the two pairs of ligand-receptor complexes can undergo dynamic oligomerization. Inspired by these experimental evidences, we developed a coarse-grained model to characterize the assembling of an immune complex consisting of CLTA-4, B7, PD-L1 and PD-1. These four proteins and their interactions form a small network motif. The temporal dynamics and spatial pattern formation of this network was simulated by a diffusion-reaction algorithm. Our simulation method incorporates the membrane confinement of cell surface proteins and geometric arrangement of different binding interfaces between these proteins. A wide range of binding constants was tested for the interactions involved in the network. Interestingly, we show that the CTLA-4/B7 ligand-receptor complexes can first form linear oligomers, while these oligomers further align together into two-dimensional clusters. Similar phenomenon has also been observed in other systems of cell surface proteins. Our test results further indicate that both co-inhibitory signaling pathways activated by B7 and PD-L1 can be down-regulated by the new cis-interaction between these two ligands, consistent with previous experimental evidences. Finally, the simulations also suggest that the dynamic and the spatial properties of the immune complex assembly are highly determined by the energetics of molecular interactions in the network. Our study, therefore, brings new insights to the co-regulatory mechanisms of T cell activation.

The activation of a T cell can be regulated by the receptors on its surface, such as CTLA-4 and PD-1. People used to think that these two receptors inhibit T cell activation through distinct pathways. However, recent experiments discovered that the ligands of these two receptors, B7 and PD-L1, can interact with each other on the same surface of antigen presenting cells. Here we utilized computational simulations to investigate functional roles of this newly discovered interaction in T cell coregulation. The specific environment of interface between T cell and antigen presenting cell has been taken into account of our model. Ligand and receptors randomly diffuse within this interface area. They further involve in different types of interactions, with each other from the same side or the opposite side of cell surface. Using this method, we found ligands and receptors can not only form complexes, but also aggregate into large-scale clusters. We also demonstrated that the engagement between B7 and PD-L1 can reduce the interactions with their corresponding receptors. This study, therefore, offers new insights to our understanding of signal regulation in T cells.

Understand the Functions of Scaffold Proteins in Cell Signaling by a Mesoscopic Simulation Method

Scaffold proteins are central players in regulating the spatial-temporal organization of many important signaling pathways in cells. They offer physical platforms to downstream signaling proteins so that their transient interactions in a crowded and heterogeneous environment of cytosol can be greatly facilitated. However, most scaffold proteins tend to simultaneously bind more than one signaling molecule, which leads to the spatial assembly of multimeric protein complexes. The kinetics of these protein oligomerizations are difficult to quantify by traditional experimental approaches. To understand the functions of scaffold proteins in cell signaling, we developed a, to our knowledge, new hybrid simulation algorithm in which both spatial organization and binding kinetics of proteins were implemented. We applied this new technique to a simple network system that contains three molecules. One molecule in the network is a scaffold protein, whereas the other two are its binding targets in the downstream signaling pathway. Each of the three molecules in the system contains two binding motifs that can interact with each other and are connected by a flexible linker. By applying the new simulation method to the model, we show that the scaffold proteins will promote not only thermodynamics but also kinetics of cell signaling given the premise that the interaction between the two signaling molecules is transient. Moreover, by changing the flexibility of the linker between two binding motifs, our results suggest that the conformational fluctuations in a scaffold protein play a positive role in recruiting downstream signaling molecules. In summary, this study showcases the capability of computational simulation in understanding the general principles of scaffold protein functions.

Two MYB Proteins in a Self-Organizing Activator-Inhibitor System Produce Spotted Pigmentation Patterns

Many organisms exhibit visually striking spotted or striped pigmentation patterns. Developmental models predict that such spatial patterns can form when a local autocatalytic feedback loop and a long-range inhibitory feedback loop interact. At its simplest, this self-organizing network only requires one self-activating activator that also activates a repressor, which inhibits the activator and diffuses to neighboring cells. However, the molecular activators and inhibitors fully fitting this versatile model remain elusive in pigmentation systems. Here, we characterize an R2R3-MYB activator and an R3-MYB repressor in monkeyflowers (Mimulus). Through experimental perturbation and mathematical modeling, we demonstrate that the properties of these two proteins correspond to an activator-inhibitor pair in a two-component, reaction-diffusion system, explaining the formation of dispersed anthocyanin spots in monkeyflower petals. Notably, disrupting this pattern impacts pollinator visitation. Thus, subtle changes in simple activator-inhibitor systems are likely essential contributors to the evolution of the remarkable diversity of pigmentation patterns in flowers.

A computational model for understanding the oligomerization mechanisms of TNF receptor superfamily

By recognizing members in the tumor necrosis factor (TNF) receptor superfamily, TNF ligand proteins function as extracellular cytokines to activate various signaling pathways involved in inflammation, proliferation, and apoptosis. Most ligands in TNF superfamily are trimeric and can simultaneously bind to three receptors on cell surfaces. It has been experimentally observed that the formation of these molecular complexes further triggers the oligomerization of TNF receptors, which in turn regulate the intracellular signaling processes by providing transient compartmentalization in the membrane proximal regions of cytoplasm. In order to decode the molecular mechanisms of oligomerization in TNF receptor superfamily, we developed a new computational method that can physically simulate the spatial-temporal process of binding between TNF ligands and their receptors. The simulations show that the TNF receptors can be organized into hexagonal oligomers. The formation of this spatial pattern is highly dependent not only on the molecular properties such as the affinities of trans and cis binding, but also on the cellular factors such as the concentration of TNF ligands in the extracellular area or the density of TNF receptors on cell surfaces. Moreover, our model suggests that if TNF receptors are pre-organized into dimers before ligand binding, these lateral interactions between receptor monomers can play a positive role in stabilizing the ligand-receptor interactions, as well as in regulating the kinetics of receptor oligomerization. Altogether, this method throws lights on the mechanisms of TNF ligand-receptor interactions in cellular environments.

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.

A multi-state model of the CaMKII dodecamer suggests a role for calmodulin in maintenance of autophosphorylation

Ca2+/calmodulin-dependent protein kinase II (CaMKII) accounts for up to 2 percent of all brain protein and is essential to memory function. CaMKII activity is known to regulate dynamic shifts in the size and signaling strength of neuronal connections, a process known as synaptic plasticity. Increasingly, computational models are used to explore synaptic plasticity and the mechanisms regulating CaMKII activity. Conventional modeling approaches may exclude biophysical detail due to the impractical number of state combinations that arise when explicitly monitoring the conformational changes, ligand binding, and phosphorylation events that occur on each of the CaMKII holoenzyme's subunits. To manage the combinatorial explosion without necessitating bias or loss in biological accuracy, we use a specialized syntax in the software MCell to create a rule-based model of a twelve-subunit CaMKII holoenzyme. Here we validate the rule-based model against previous experimental measures of CaMKII activity and investigate molecular mechanisms of CaMKII regulation. Specifically, we explore how Ca2+/CaM-binding may both stabilize CaMKII subunit activation and regulate maintenance of CaMKII autophosphorylation. Noting that Ca2+/CaM and protein phosphatases bind CaMKII at nearby or overlapping sites, we compare model scenarios in which Ca2+/CaM and protein phosphatase do or do not structurally exclude each other's binding to CaMKII. Our results suggest a functional mechanism for the so-called "CaM trapping" phenomenon, wherein Ca2+/CaM may structurally exclude phosphatase binding and thereby prolong CaMKII autophosphorylation. We conclude that structural protection of autophosphorylated CaMKII by Ca2+/CaM may be an important mechanism for regulation of synaptic plasticity.

A predictive computational model reveals that GIV/girdin serves as a tunable valve for EGFR-stimulated cyclic AMP signals

Cellular levels of the versatile second messenger cyclic (c)AMP are regulated by the antagonistic actions of the canonical G protein → adenylyl cyclase pathway that is initiated by G-protein–coupled receptors (GPCRs) and attenuated by phosphodiesterases (PDEs). Dysregulated cAMP signaling drives many diseases; for example, its low levels facilitate numerous sinister properties of cancer cells. Recently, an alternative paradigm for cAMP signaling has emerged in which growth factor–receptor tyrosine kinases (RTKs; e.g., EGFR) access and modulate G proteins via a cytosolic guanine-nucleotide exchange modulator (GEM), GIV/girdin; dysregulation of this pathway is frequently encountered in cancers. In this study, we present a network-based compartmental model for the paradigm of GEM-facilitated cross-talk between RTKs and G proteins and how that impacts cellular cAMP. Our model predicts that cross-talk between GIV, Gα_s, and Gα_i proteins dampens ligand-stimulated cAMP dynamics. This prediction was experimentally verified by measuring cAMP levels in cells under different conditions. We further predict that the direct proportionality of cAMP concentration as a function of receptor number and the inverse proportionality of cAMP concentration as a function of PDE concentration are both altered by GIV levels. Taking these results together, our model reveals that GIV acts as a tunable control valve that regulates cAMP flux after growth factor stimulation. For a given stimulus, when GIV levels are high, cAMP levels are low, and vice versa. In doing so, GIV modulates cAMP via mechanisms distinct from the two most often targeted classes of cAMP modulators, GPCRs and PDEs.

InterCells: A Generic Monte-Carlo Simulation of Intercellular Interfaces Captures Nanoscale Patterning at the Immune Synapse

Molecular interactions across intercellular interfaces serve to convey information between cells and to trigger appropriate cell functions. Examples include cell development and growth in tissues, neuronal and immune synapses (ISs). Here, we introduce an agent-based Monte-Carlo simulation of user-defined cellular interfaces. The simulation allows for membrane molecules, embedded at intercellular contacts, to diffuse and interact, while capturing the topography and energetics of the plasma membranes of the interface. We provide a detailed example related to pattern formation in the early IS. Using simulation predictions and three-color single molecule localization microscopy (SMLM), we detected the intricate mutual patterning of T cell antigen receptors (TCRs), integrins and glycoproteins in early T cell contacts with stimulating coverslips. The simulation further captures the dynamics of the patterning under the experimental conditions and at the IS with antigen presenting cells (APCs). Thus, we provide a generic tool for simulating realistic cell-cell interfaces, which can be used for critical hypothesis testing and experimental design in an iterative manner.

Multiscale smeared finite element model for mass transport in biological tissue: From blood vessels to cells and cellular organelles

One of the basic and vital processes in living organisms is mass exchange, which occurs on several levels: it goes from blood vessels to cells and organelles within cells. On that path, molecules, as oxygen, metabolic products, drugs, etc. Traverse different macro and micro environments - blood, extracellular/intracellular space, and interior of organelles; and also biological barriers such as walls of blood vessels and membranes of cells and organelles. Many aspects of this mass transport remain unknown, particularly the biophysical mechanisms governing drug delivery. The main research approach relies on laboratory and clinical investigations. In parallel, considerable efforts have been directed to develop computational tools for additional insight into the intricate process of mass exchange and transport. Along these lines, we have recently formulated a composite smeared finite element (CSFE) which is composed of the smeared continuum pressure and concentration fields of the capillary and lymphatic system, and of these fields within tissue. The element offers an elegant and simple procedure which opens up new lines of inquiry and can be applied to large systems such as organs and tumors models. Here, we extend this concept to a multiscale scheme which concurrently couples domains that span from large blood vessels, capillaries and lymph, to cell cytosol and further to organelles of nanometer size. These spatial physical domains are coupled by the appropriate connectivity elements representing biological barriers. The composite finite element has "degrees of freedom" which include pressures and concentrations of all compartments of the vessels-tissue assemblage. The overall model uses the standard, measurable material properties of the continuum biological environments and biological barriers. It can be considered as a framework into which we can incorporate various additional effects (such as electrical or biochemical) for transport through membranes or within cells. This concept and the developed FE software within our package PAK offers a computational tool that can be applied to whole-organ systems, while also including specific domains such as tumors. The solved examples demonstrate the accuracy of this model and its applicability to large biological systems.

Fission yeast Myo2: Molecular organization and diffusion in the cytoplasm

Myosin-II is required for the assembly and constriction of cytokinetic contractile rings in fungi and animals. We used electron microscopy, fluorescence recovery after photobleaching (FRAP), and fluorescence correlation spectroscopy (FCS) to characterize the physical properties of Myo2 from fission yeast Schizosaccharomyces pombe. By electron microscopy, Myo2 has two heads and a coiled-coiled tail like myosin-II from other species. The first 65 nm of the tail is a stiff rod, followed by a flexible, less-ordered region up to 30 nm long. Myo2 sediments as a 7 S molecule in high salt, but aggregates rather than forming minifilaments at lower salt concentrations; this is unaffected by heavy chain phosphorylation. We used FRAP and FCS to observe the dynamics of Myo2 in live S. pombe cells and in cell extracts at different salt concentrations; both show that Myo2 with an N-terminal mEGFP tag has a diffusion coefficient of ∼ 3 µm² s^-1 in the cytoplasm of live cells during interphase and mitosis. Photon counting histogram analysis of the FCS data confirmed that Myo2 diffuses as doubled-headed molecules in the cytoplasm. FCS measurements on diluted cell extracts showed that mEGFP-Myo2 has a diffusion coefficient of ∼ 30 µm² s^-1 in 50 to 400 mM KCl concentrations.

Src homology 2 domains enhance tyrosine phosphorylation in vivo by protecting binding sites in their target proteins from dephosphorylation

Phosphotyrosine (pTyr)-dependent signaling is critical for many cellular processes. It is highly dynamic, as signal output depends not only on phosphorylation and dephosphorylation rates but also on the rates of binding and dissociation of effectors containing phosphotyrosine-dependent binding modules such as Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains. Previous in vitro studies suggested that binding of SH2 and PTB domains can enhance protein phosphorylation by protecting the sites bound by these domains from phosphatase-mediated dephosphorylation. To test whether this occurs in vivo, we used the binding of growth factor receptor bound 2 (GRB2) to phosphorylated epidermal growth factor receptor (EGFR) as a model system. We analyzed the effects of SH2 domain overexpression on protein tyrosine phosphorylation by quantitative Western and far-Western blotting, mass spectrometry, and computational modeling. We found that SH2 overexpression results in a significant, dose-dependent increase in EGFR tyrosine phosphorylation, particularly of sites corresponding to the binding specificity of the overexpressed SH2 domain. Computational models using experimentally determined EGFR phosphorylation and dephosphorylation rates, and pTyr-EGFR and GRB2 concentrations, recapitulated the experimental findings. Surprisingly, both modeling and biochemical analyses suggested that SH2 domain overexpression does not result in a major decrease in the number of unbound phosphorylated SH2 domain-binding sites. Our results suggest that signaling via SH2 domain binding is buffered over a relatively wide range of effector concentrations and that SH2 domain proteins with overlapping binding specificities are unlikely to compete with one another for phosphosites in vivo.

A Computational Model for Kinetic Studies of Cadherin Binding and Clustering

Cadherin is a cell-surface transmembrane receptor that mediates calcium-dependent cell-cell adhesion and is a major component of adhesive junctions. The formation of intercellular adhesive junctions is initiated by trans binding between cadherins on adjacent cells, which is followed by the clustering of cadherins via the formation of cis interactions between cadherins on the same cell membranes. Moreover, classical cadherins have multiple glycosylation sites along their extracellular regions. It was found that aberrant glycosylation affects the adhesive function of cadherins and correlates with metastatic phenotypes of several cancers. However, a mechanistic understanding of cadherin clustering during cell adhesion and the role of glycosylation in this process is still lacking. Here, we designed a kinetic model that includes multistep reaction pathways for cadherin clustering. We further applied a diffusion-reaction algorithm to numerically simulate the clustering process using a recently developed coarse-grained model. Using experimentally measured rates of trans binding between soluble E-cadherin extracellular domains, we conducted simulations of cadherin-mediated cell-cell binding kinetics, and the results are quantitatively comparable to experimental data from micropipette experiments. In addition, we show that incorporating cadherin clustering via cis interactions further increases intercellular binding. Interestingly, a two-phase kinetic profile was derived under the assumption that glycosylation regulates the kinetic rates of cis interactions. This two-phase profile is qualitatively consistent with experimental results from micropipette measurements. Therefore, our computational studies provide new, to our knowledge, insights into the molecular mechanism of cadherin-based cell adhesion.

Understanding the Functional Roles of Multiple Extracellular Domains in Cell Adhesion Molecules with a Coarse-Grained Model

Intercellular contacts in multicellular organisms are maintained by membrane receptors called cell adhesion molecules (CAMs), which are expressed on cell surfaces. One interesting feature of CAMs is that almost all of their extracellular regions contain repeating copies of structural domains. It is not clear why so many extracellular domains need to be evolved through natural selection. We tackled this problem by computational modeling. A generic model of CAMs was constructed based on the domain organization of neuronal CAM, which is engaged in maintaining neuron-neuron adhesion in central nervous system. By placing these models on a cell-cell interface, we developed a Monte-Carlo simulation algorithm that incorporates both molecular factors including conformational changes of CAMs and cellular factor including fluctuations of plasma membranes to approach the physical process of CAM-mediated adhesion. We found that the presence of multiple domains at the extracellular region of a CAM plays a positive role in regulating its trans-interaction with other CAMs from the opposite side of cell surfaces. The trans-interaction can further be facilitated by the intramolecular contacts between different extracellular domains of a CAM. Finally, if more than one CAM is introduced on each side of cell surfaces, the lateral binding (cis-interactions) between these CAMs will positively correlate with their trans-interactions only within a small energetic range, suggesting that cell adhesion is an elaborately designed process in which both trans- and cis-interactions are fine-tuned collectively by natural selection. In short, this study deepens our general understanding of the molecular mechanisms of cell adhesion.

SpringSaLaD: A Spatial, Particle-Based Biochemical Simulation Platform with Excluded Volume

We introduce Springs, Sites, and Langevin Dynamics (SpringSaLaD), a comprehensive software platform for spatial, stochastic, particle-based modeling of biochemical systems. SpringSaLaD models biomolecules in a coarse-grained manner as a group of linked spherical sites with excluded volume. This mesoscopic approach bridges the gap between highly detailed molecular dynamics simulations and the various methods used to study network kinetics and diffusion at the cellular level. SpringSaLaD is a standalone tool that supports model building, simulation, visualization, and data analysis, all through a user-friendly graphical user interface that should make it more accessible than tools built into more comprehensive molecular dynamics infrastructures. Importantly, for bimolecular reactions we derive an exact expression relating the macroscopic on-rate to the various microscopic parameters with the inclusion of excluded volume; this makes SpringSaLaD more accurate than other tools, which rely on approximate relationships between these parameters.

Simulation of diffusion using a modular cell dynamic simulation system

A variety of mathematical models is used to describe and simulate the multitude of natural processes examined in life sciences. In this paper we present a scalable and adjustable foundation for the simulation of natural systems. Based on neighborhood relations in graphs and the complex interactions in cellular automata, the model uses recurrence relations to simulate changes on a mesoscopic scale. This implicit definition allows for the manipulation of every aspect of the model even during simulation. The definition of value rules ω facilitates the accumulation of change during time steps. Those changes may result from different physical, chemical or biological phenomena. Value rules can be combined into modules, which in turn can be used to create baseline models. Exemplarily, a value rule for the diffusion of chemical substances was designed and its applicability is demonstrated. Finally, the stability and accuracy of the solutions is analyzed.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Regulation of quantal currents determines synaptic strength at neuromuscular synapses in larval Drosophila

Studies of synaptic homeostasis during muscle fiber (MF) growth in Drosophila larvae have focused on the regulation of the quantal content of transmitter release. However, early studies in crayfish and frog suggested that regulation of quantal current size may be an integral mechanism in synaptic homeostasis. To examine this further in Drosophila, we compared the electrical properties, miniature excitatory postsynaptic potentials (minEPSPs) and miniature excitatory postsynaptic currents (minEPSCs) in different-sized MFs in third-instar larvae and for a single MF during larval growth. The third-instar MFs showed differences in input resistance due to differences in size and specific membrane resistance. We found that electrical coupling between MFs did not contribute substantially to the electrical properties; however, the electrode leak conductance and a slower developing increase in membrane conductance can influence the electrical recordings from these MFs. Our results demonstrated that larger MFs had larger minEPSCs to compensate for changes in MF electrical properties. This was most clearly seen for MF4 during larval growth from the second to third instar. During a predicted 80 % decrease in MF input resistance, the minEPSCs showed a 35 % increase in amplitude and 165 % increase in duration. Simulations demonstrated that the increase in minEPSC size resulted in a 129 % increase in minEPSP amplitude for third-instar larvae; this was mainly due to the increase in minEPSC duration. We also found that MFs with common innervation had similar-sized minEPSCs suggesting that MF innervation influences minEPSC size. Overall, the results showed that increased quantal content and quantal current size contribute equally to synaptic homeostasis during MF growth.

PASMet: a web-based platform for prediction, modelling and analyses of metabolic systems

PASMet (Prediction, Analysis and Simulation of Metabolic networks) is a web-based platform for proposing and verifying mathematical models to understand the dynamics of metabolism. The advantages of PASMet include user-friendliness and accessibility, which enable biologists and biochemists to easily perform mathematical modelling. PASMet offers a series of user-functions to handle the time-series data of metabolite concentrations. The functions are organised into four steps: (i) Prediction of a probable metabolic pathway and its regulation; (ii) Construction of mathematical models; (iii) Simulation of metabolic behaviours; and (iv) Analysis of metabolic system characteristics. Each function contains various statistical and mathematical methods that can be used independently. Users who may not have enough knowledge of computing or programming can easily and quickly analyse their local data without software downloads, updates or installations. Users only need to upload their files in comma-separated values (CSV) format or enter their model equations directly into the website. Once the time-series data or mathematical equations are uploaded, PASMet automatically performs computation on server-side. Then, users can interactively view their results and directly download them to their local computers. PASMet is freely available with no login requirement at http://pasmet.riken.jp/ from major web browsers on Windows, Mac and Linux operating systems.

Elucidating the Functional Roles of Spatial Organization in Cross-Membrane Signal Transduction by a Hybrid Simulation Method

The ligand-binding of membrane receptors on cell surfaces initiates the dynamic process of cross-membrane signal transduction. It is an indispensable part of the signaling network for cells to communicate with external environments. Recent experiments revealed that molecular components in signal transduction are not randomly mixed, but spatially organized into distinctive patterns. These patterns, such as receptor clustering and ligand oligomerization, lead to very different gene expression profiles. However, little is understood about the molecular mechanisms and functional impacts of this spatial-temporal regulation in cross-membrane signal transduction. In order to tackle this problem, we developed a hybrid computational method that decomposes a model of signaling network into two simulation modules. The physical process of binding between receptors and ligands on cell surfaces are simulated by a diffusion-reaction algorithm, while the downstream biochemical reactions are modeled by stochastic simulation of Gillespie algorithm. These two processes are coupled together by a synchronization framework. Using this method, we tested the dynamics of a simple signaling network in which the ligand binding of cell surface receptors triggers the phosphorylation of protein kinases, and in turn regulates the expression of target genes. We found that spatial aggregation of membrane receptors at cellular interfaces is able to either amplify or inhibit downstream signaling outputs, depending on the details of clustering mechanism. Moreover, by providing higher binding avidity, the co-localization of ligands into multi-valence complex modulates signaling in very different ways that are closely related to the binding affinity between ligand and receptor. We also found that the temporal oscillation of the signaling pathway that is derived from genetic feedback loops can be modified by the spatial clustering of membrane receptors. In summary, our method demonstrates the functional importance of spatial organization in cross-membrane signal transduction. The method can be applied to any specific signaling pathway in cells.

Elucidating the general principles of cell adhesion with a coarse-grained simulation model

Coarse-grained simulation of interplay between cell adhesion and cell signaling.

Programmatic access to logical models in the Cell Collective modeling environment via a REST API

Cell Collective (www.cellcollective.org) is a web-based interactive environment for constructing, simulating and analyzing logical models of biological systems. Herein, we present a Web service to access models, annotations, and simulation data in the Cell Collective platform through the Representational State Transfer (REST) Application Programming Interface (API). The REST API provides a convenient method for obtaining Cell Collective data through almost any programming language. To ensure easy processing of the retrieved data, the request output from the API is available in a standard JSON format.

AVAILABILITY AND IMPLEMENTATION

The Cell Collective REST API is freely available at http://thecellcollective.org/tccapi. All public models in Cell Collective are available through the REST API. For users interested in creating and accessing their own models through the REST API first need to create an account in Cell Collective (http://thecellcollective.org).

CONTACT

thelikar2@unl.edu.

SUPPLEMENTARY INFORMATION

Technical user documentation: https://goo.gl/U52GWo.

Mechanistic modeling confronts the complexity of molecular cell biology

Mechanistic modeling has the potential to transform how cell biologists contend with the inescapable complexity of modern biology. I am a physiologist–electrical engineer–systems biologist who has been working at the level of cell biology for the past 24 years. This perspective aims 1) to convey why we build models, 2) to enumerate the major approaches to modeling and their philosophical differences, 3) to address some recurrent concerns raised by experimentalists, and then 4) to imagine a future in which teams of experimentalists and modelers build—and subject to exhaustive experimental tests—models covering the entire spectrum from molecular cell biology to human pathophysiology. There is, in my view, no technical obstacle to this future, but it will require some plasticity in the biological research mind-set.

Multiscale reaction-diffusion simulations with Smoldyn

Summary: Smoldyn is a software package for stochastic modelling of spatial biochemical networks and intracellular systems. It was originally developed with an accurate off-lattice particle-based model at its core. This has recently been enhanced with the addition of a computationally efficient on-lattice model, which can be run stand-alone or coupled together for multiscale simulations using both models in regions where they are most required, increasing the applicability of Smoldyn to larger molecule numbers and spatial domains. Simulations can switch between models with only small additions to their configuration file, enabling users with existing Smoldyn configuration files to run the new on-lattice model with any reaction, species or surface descriptions they might already have.

Availability and Implementation: Source code and binaries freely available for download at www.smoldyn.org, implemented in C/C++ and supported on Linux, Mac OSX and MS Windows.

Contact:martin.robinson@maths.ox.ac.uk

Supplementary Information: Supplementary data are available at Bioinformatics online and include additional details on model specification and modelling of surfaces, as well as the Smoldyn configuration file used to generate Figure 1.

A coarse-grained model for the simulations of biomolecular interactions in cellular environments

The interactions of bio-molecules constitute the key steps of cellular functions. However, in vivo binding properties differ significantly from their in vitro measurements due to the heterogeneity of cellular environments. Here we introduce a coarse-grained model based on rigid-body representation to study how factors such as cellular crowding and membrane confinement affect molecular binding. The macroscopic parameters such as the equilibrium constant and the kinetic rate constant are calibrated by adjusting the microscopic coefficients used in the numerical simulations. By changing these model parameters that are experimentally approachable, we are able to study the kinetic and thermodynamic properties of molecular binding, as well as the effects caused by specific cellular environments. We investigate the volumetric effects of crowded intracellular space on bio-molecular diffusion and diffusion-limited reactions. Furthermore, the binding constants of membrane proteins are currently difficult to measure. We provide quantitative estimations about how the binding of membrane proteins deviates from soluble proteins under different degrees of membrane confinements. The simulation results provide biological insights to the functions of membrane receptors on cell surfaces. Overall, our studies establish a connection between the details of molecular interactions and the heterogeneity of cellular environments.

Basic features of a cell electroporation model: illustrative behavior for two very different pulses

Science increasingly involves complex modeling. Here we describe a model for cell electroporation in which membrane properties are dynamically modified by poration. Spatial scales range from cell membrane thickness (5 nm) to a typical mammalian cell radius (10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μm), and can be used with idealized and experimental pulse waveforms. The model consists of traditional passive components and additional active components representing nonequilibrium processes. Model responses include measurable quantities: transmembrane voltage, membrane electrical conductance, and solute transport rates and amounts for the representative “long” and “short” pulses. The long pulse—1.5 kV/cm, 100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μs—evolves two pore subpopulations with a valley at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim}$$\end{document}∼5 nm, which separates the subpopulations that have peaks at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim}$$\end{document}∼1.5 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim}$$\end{document}∼12 nm radius. Such pulses are widely used in biological research, biotechnology, and medicine, including cancer therapy by drug delivery and nonthermal physical tumor ablation by causing necrosis. The short pulse—40 kV/cm, 10 ns—creates 80-fold more pores, all small (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<$$\end{document}<3 nm; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}∼1 nm peak). These nanosecond pulses ablate tumors by apoptosis. We demonstrate the model’s responses by illustrative electrical and poration behavior, and transport of calcein and propidium. We then identify extensions for expanding modeling capability. Structure-function results from MD can allow extrapolations that bring response specificity to cell membranes based on their lipid composition. After a pulse, changes in pore energy landscape can be included over seconds to minutes, by mechanisms such as cell swelling and pulse-induced chemical reactions that slowly alter pore behavior.

Synaptic excitation is regulated by the postsynaptic dSK channel at the Drosophila larval NMJ

In the mammalian central nervous system, the postsynaptic small-conductance Ca(2+)-dependent K(+) (SK) channel has been shown to reduce postsynaptic depolarization and limit Ca(2+) influx through N-methyl-d-aspartate receptors. To examine further the role of the postsynaptic SK channel in synaptic transmission, we studied its action at the Drosophila larval neuromuscular junction (NMJ). Repetitive synaptic stimulation produced an increase in postsynaptic membrane conductance leading to depression of excitatory postsynaptic potential amplitude and hyperpolarization of the resting membrane potential (RMP). This reduction in synaptic excitation was due to the postsynaptic Drosophila SK (dSK) channel; synaptic depression, increased membrane conductance and RMP hyperpolarization were reduced in dSK mutants or after expressing a Ca(2+) buffer in the muscle. Ca(2+) entering at the postsynaptic membrane was sufficient to activate dSK channels based upon studies in which the muscle membrane was voltage clamped to prevent opening voltage-dependent Ca(2+) channels. Increasing external Ca(2+) produced an increase in resting membrane conductance and RMP that was not seen in dSK mutants or after adding the glutamate-receptor blocker philanthotoxin. Thus it appeared that dSK channels were also activated by spontaneous transmitter release and played a role in setting membrane conductance and RMP. In mammals, dephosphorylation by protein phosphatase 2A (PP2A) increased the Ca(2+) sensitivity of the SK channel; PP2A appeared to increase the sensitivity of the dSK channel since PP2A inhibitors reduced activation of the dSK channel by evoked synaptic activity or increased external Ca(2+). It is proposed that spontaneous and evoked transmitter release activate the postsynaptic dSK channel to limit synaptic excitation and stabilize synapses.

The delicate bistability of CaMKII

Calcium/calmodulin-dependent protein kinase II (CaMKII) is a synaptic, autophosphorylating kinase that is essential for learning and memory. Previous models have suggested that CaMKII functions as a bistable switch that could be the molecular correlate of long-term memory, but experiments have failed to validate these predictions. These models involved significant approximations to overcome the combinatorial complexity inherent in a multisubunit, multistate system. Here, we develop a stochastic particle-based model of CaMKII activation and dynamics that overcomes combinatorial complexity without significant approximations. We report four major findings. First, the CaMKII model system is never bistable at resting calcium concentrations, which suggests that CaMKII activity does not function as the biochemical switch underlying long-term memory. Second, the steady-state activation curves are either laserlike or steplike. Both are characterized by a well-defined threshold for activation, which suggests that thresholding is a robust feature of this system. Third, transiently activated CaMKII can maintain its activity over the time course of many experiments, and such slow deactivation may account for the few reports of bistability in the literature. And fourth, under in vivo conditions, increases in phosphatase activity can increase CaMKII activity. This is a surprising and counterintuitive effect, as dephosphorylation is generally associated with CaMKII deactivation.

In-silico models of stem cell and developmental systems

Understanding how developmental systems evolve over time is a key question in stem cell and developmental biology research. However, due to hurdles of existing experimental techniques, our understanding of these systems as a whole remains partial and coarse. In recent years, we have been constructing in-silico models that synthesize experimental knowledge using software engineering tools. Our approach integrates known isolated mechanisms with simplified assumptions where the knowledge is limited. This has proven to be a powerful, yet underutilized, tool to analyze the developmental process. The models provide a means to study development in-silico by altering the model’s specifications, and thereby predict unforeseen phenomena to guide future experimental trials. To date, three organs from diverse evolutionary organisms have been modeled: the mouse pancreas, the C. elegans gonad, and partial rodent brain development. Analysis and execution of the models recapitulated the development of the organs, anticipated known experimental results and gave rise to novel testable predictions. Some of these results had already been validated experimentally. In this paper, I review our efforts in realistic in-silico modeling of stem cell research and developmental biology and discuss achievements and challenges. I envision that in the future, in-silico models as presented in this paper would become a common and useful technique for research in developmental biology and related research fields, particularly regenerative medicine, tissue engineering and cancer therapeutics.

ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments

We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.

There is more than one way to model an elephant. Experiment-driven modeling of the actin cytoskeleton

Mathematical modeling has established its value for investigating the interplay of biochemical and mechanical mechanisms underlying actin-based motility. Because of the complex nature of actin dynamics and its regulation, many of these models are phenomenological or conceptual, providing a general understanding of the physics at play. But the wealth of carefully measured kinetic data on the interactions of many of the players in actin biochemistry cries out for the creation of more detailed and accurate models that could permit investigators to dissect interdependent roles of individual molecular components. Moreover, no human mind can assimilate all of the mechanisms underlying complex protein networks; so an additional benefit of a detailed kinetic model is that the numerous binding proteins, signaling mechanisms, and biochemical reactions can be computationally organized in a fully explicit, accessible, visualizable, and reusable structure. In this review, we will focus on how comprehensive and adaptable modeling allows investigators to explain experimental observations and develop testable hypotheses on the intracellular dynamics of the actin cytoskeleton.

Hybrid spatial Gillespie and particle tracking simulation

Motivation: Cellular signal transduction involves spatial–temporal dynamics and often stochastic effects due to the low particle abundance of some molecular species. Others can, however, be of high abundances. Such a system can be simulated either with the spatial Gillespie/Stochastic Simulation Algorithm (SSA) or Brownian/Smoluchowski dynamics if space and stochasticity are important. To combine the accuracy of particle-based methods with the superior performance of the SSA, we suggest a hybrid simulation.

Results: The proposed simulation allows an interactive or automated switching for regions or species of interest in the cell. Especially we see an application if for instance receptor clustering at the membrane is modeled in detail and the transport through the cytoplasm is included as well. The results show the increase in performance of the overall simulation, and the limits of the approach if crowding is included. Future work will include the development of a GUI to improve control of the simulation.

Availability of Implementation:www.bison.ethz.ch/research/spatial_simulations.

Contact:mklann@ee.ethz.ch or koeppl@ethz.ch

Supplementary/Information:Supplementary data are available at Bioinformatics online.

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.

Leveraging modeling approaches: reaction networks and rules

We have witnessed an explosive growth in research involving mathematical models and computer simulations of intracellular molecular interactions, ranging from metabolic pathways to signaling and gene regulatory networks. Many software tools have been developed to aid in the study of such biological systems, some of which have a wealth of features for model building and visualization, and powerful capabilities for simulation and data analysis. Novel high-resolution and/or high-throughput experimental techniques have led to an abundance of qualitative and quantitative data related to the spatiotemporal distribution of molecules and complexes, their interactions kinetics, and functional modifications. Based on this information, computational biology researchers are attempting to build larger and more detailed models. However, this has proved to be a major challenge. Traditionally, modeling tools require the explicit specification of all molecular species and interactions in a model, which can quickly become a major limitation in the case of complex networks - the number of ways biomolecules can combine to form multimolecular complexes can be combinatorially large. Recently, a new breed of software tools has been created to address the problems faced when building models marked by combinatorial complexity. These have a different approach for model specification, using reaction rules and species patterns. Here we compare the traditional modeling approach with the new rule-based methods. We make a case for combining the capabilities of conventional simulation software with the unique features and flexibility of a rule-based approach in a single software platform for building models of molecular interaction networks.

Compartmentalization and metabolic channeling for multienzymatic biosynthesis: practical strategies and modeling approaches

: The construction of efficient enzyme complexes for multienzymatic biosynthesis is of increasing interest in order to achieve maximum yield and to minimize the interference due to shortcomings that are typical for straightforward one-pot multienzyme catalysis. These include product or intermediate feedback inhibition, degeneration, and diffusive losses of reaction intermediates, consumption of co-factors, and others. The main mechanisms in nature to tackle these effects in transient or stable protein associations are the formation of metabolic channeling and microcompartments, processes that are desirable also for multienzymatic biosynthesis in vitro. This chapter provides an overview over two main aspects. First, numerous recent strategies for establishing compartmentalized multienzyme associations and constructed synthetic enzyme complexes are reviewed. Second, the computational methods at hand to investigate and optimize such associations systematically, especially with focus on large multienzyme complexes and metabolic channeling, are discussed. Perspectives on future studies of multienzymatic biosynthesis concerning compartmentalization and metabolic channeling are presented.

Mathematical simulation of membrane protein clustering for efficient signal transduction

Initiation and propagation of cell signaling depend on productive interactions among signaling proteins at the plasma membrane. These diffusion-limited interactions can be influenced by features of the membrane that introduce barriers, such as cytoskeletal corrals, or microdomains that transiently confine both transmembrane receptors and membrane-tethered peripheral proteins. Membrane topographical features can lead to clustering of receptors and other membrane components, even under very dynamic conditions. This review considers the experimental and mathematical evidence that protein clustering impacts cell signaling in complex ways. Simulation approaches used to consider these stochastic processes are discussed.

Qualitative translation of relations from BioPAX to SBML qual

Motivation: The biological pathway exchange language (BioPAX) and the systems biology markup language (SBML) belong to the most popular modeling and data exchange languages in systems biology. The focus of SBML is quantitative modeling and dynamic simulation of models, whereas the BioPAX specification concentrates mainly on visualization and qualitative analysis of pathway maps. BioPAX describes reactions and relations. In contrast, SBML core exclusively describes quantitative processes such as reactions. With the SBML qualitative models extension (qual), it has recently also become possible to describe relations in SBML. Before the development of SBML qual, relations could not be properly translated into SBML. Until now, there exists no BioPAX to SBML converter that is fully capable of translating both reactions and relations.

Results: The entire nature pathway interaction database has been converted from BioPAX (Level 2 and Level 3) into SBML (Level 3 Version 1) including both reactions and relations by using the new qual extension package. Additionally, we present the new webtool BioPAX2SBML for further BioPAX to SBML conversions. Compared with previous conversion tools, BioPAX2SBML is more comprehensive, more robust and more exact.

Availability: BioPAX2SBML is freely available at http://webservices.cs.uni-tuebingen.de/ and the complete collection of the PID models is available at http://www.cogsys.cs.uni-tuebingen.de/downloads/Qualitative-Models/.

Contact:finja.buechel@uni-tuebingen.de

Supplementary Information:Supplementary data are available at Bioinformatics online.

Reduction of dynamical biochemical reactions networks in computational biology

Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state (QSS) and quasi-equilibrium approximations (QE), and provide practical recipes for model reduction of linear and non-linear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques.