Bioengineering models of cell signaling

In Vitro Self-Assembly of a Modified Diphenylalanine Peptide to Nanofibers Induced by the Eye Absent Enzyme and Alkaline Phosphatase and Its Activity against Breast Cancer Cell Proliferation

Drug-resistant breast cancers such as Triple negative breast cancer (TNBC) do not respond successfully to chemotherapy treatments because they lack the expression of receptor targets. Drug-resistant anti-cancer treatments require innovative approaches to target these cells without relying on the receptors. Intracellular self-assembly of small molecules induced by enzymes is a nanotechnology approach for inhibiting cancer cell growth. In this approach, enzymes will induce the self-assembly of small molecules to nanofibers, which leads to cell death. Here, we investigate the self-assembly of a modified small peptide induced by two different phosphatases: alkaline phosphatase (ALP) and eye absent tyrosine phosphatase (EYA). ALPs are expressed in many adult human tissues and are critical for many cellular functions. EYAs are embryonic enzymes that are over-expressed in drug-resistant breast cancers. We synthesized a small diphenylalanine-based peptide with a tyrosine phosphate end group as the substrate of phosphatase enzymes. Peptides were synthesized with solid phase techniques and were characterized by HPLC and MALDI-TOF. To characterize the self-assembly of peptides exposed to enzymes, different techniques were used such as scattering light intensity, microscopes, and phosphate detection kit. We then determined the toxicity effect of the peptide against normal breast cancer cells, MCF-7, and drug-resistant breast cancer cells, MDA-MB-231. The results showed that the EYA enzyme is able to initiate self-assembly at lower peptide concentration with higher self-assembling intensity compared to ALP. A significant decrease in the TNBC cell number was observed even with a low peptide concentration of 60 μM. These results collectively support the exploration of enzyme self-assembly to treat TNBC.

Molecule-to-Material-to-Bio Nanoarchitectonics with Biomedical Fullerene Nanoparticles

Nanoarchitectonics integrates nanotechnology with various other fields, with the goal of creating functional material systems from nanoscale units such as atoms, molecules, and nanomaterials. The concept bears strong similarities to the processes and functions seen in biological systems. Therefore, it is natural for materials designed through nanoarchitectonics to truly shine in bio-related applications. In this review, we present an overview of recent work exemplifying how nanoarchitectonics relates to biology and how it is being applied in biomedical research. First, we present nanoscale interactions being studied in basic biology and how they parallel nanoarchitectonics concepts. Then, we overview the state-of-the-art in biomedical applications pursuant to the nanoarchitectonics framework. On this basis, we take a deep dive into a particular building-block material frequently seen in nanoarchitectonics approaches: fullerene. We take a closer look at recent research on fullerene nanoparticles, paying special attention to biomedical applications in biosensing, gene delivery, and radical scavenging. With these subjects, we aim to illustrate the power of nanomaterials and biomimetic nanoarchitectonics when applied to bio-related applications, and we offer some considerations for future perspectives.

Biomimetic and Biological Nanoarchitectonics

A post-nanotechnology concept has been assigned to an emerging concept, nanoarchitectonics. Nanoarchitectonics aims to establish a discipline in which functional materials are fabricated from nano-scale components such as atoms, molecules, and nanomaterials using various techniques. Nanoarchitectonics opens ways to form a more unified paradigm by integrating nanotechnology with organic chemistry, supramolecular chemistry, material chemistry, microfabrication technology, and biotechnology. On the other hand, biological systems consist of rational organization of constituent molecules. Their structures have highly asymmetric and hierarchical features that allow for chained functional coordination, signal amplification, and vector-like energy and signal flow. The process of nanoarchitectonics is based on the premise of combining several different processes, which makes it easier to obtain a hierarchical structure. Therefore, nanoarchitectonics is a more suitable methodology for creating highly functional systems based on structural asymmetry and hierarchy like biosystems. The creation of functional materials by nanoarchitectonics is somewhat similar to the creation of functional systems in biological systems. It can be said that the goal of nanoarchitectonics is to create highly functional systems similar to those found in biological systems. This review article summarizes the synthesis of biomimetic and biological molecules and their functional structure formation from various viewpoints, from the molecular level to the cellular level. Several recent examples are arranged and categorized to illustrate such a trend with sections of (i) synthetic nanoarchitectonics for bio-related units, (ii) self-assembly nanoarchitectonics with bio-related units, (iii) nanoarchitectonics with nucleic acids, (iv) nanoarchitectonics with peptides, (v) nanoarchitectonics with proteins, and (vi) bio-related nanoarchitectonics in conjugation with materials.

A Lipid-Based Droplet Processor for Parallel Chemical Signals

A key goal of bottom-up synthetic biology is to construct cell- and tissue-like structures. Underpinning cellular life is the ability to process several external chemical signals, often in parallel. Until now, cell- and tissue-like structures have been constructed with no more than one signaling pathway. Many pathways rely on signal transport across membranes using protein nanopores. However, such systems currently suffer from the slow transport of molecules. We have optimized the application of these nanopores to permit fast molecular transport, which has allowed us to construct a processor for parallel chemical signals from the bottom up in a modular fashion. The processor comprises three aqueous droplet compartments connected by lipid bilayers and operates in an aqueous environment. It can receive two chemical signals from the external environment, process them orthogonally, and then produce a distinct output for each signal. It is suitable for both sensing and enzymatic processing of environmental signals, with fluorescence and molecular outputs. In the future, such processors could serve as smart drug delivery vehicles or as modules within synthetic tissues to control their behavior in response to external chemical signals.

Variable setpoint as a relaxing component in physiological control

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controller's ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.

Spatial pattern dynamics of 3D stem cell loss of pluripotency via rules-based computational modeling

Pluripotent embryonic stem cells (ESCs) have the unique ability to differentiate into cells from all germ lineages, making them a potentially robust cell source for regenerative medicine therapies, but difficulties in predicting and controlling ESC differentiation currently limit the development of therapies and applications from such cells. A common approach to induce the differentiation of ESCs in vitro is via the formation of multicellular aggregates known as embryoid bodies (EBs), yet cell fate specification within EBs is generally considered an ill-defined and poorly controlled process. Thus, the objective of this study was to use rules-based cellular modeling to provide insight into which processes influence initial cell fate transitions in 3-dimensional microenvironments. Mouse embryonic stem cells (D3 cell line) were differentiated to examine the temporal and spatial patterns associated with loss of pluripotency as measured through Oct4 expression. Global properties of the multicellular aggregates were accurately recapitulated by a physics-based aggregation simulation when compared to experimentally measured physical parameters of EBs. Oct4 expression patterns were analyzed by confocal microscopy over time and compared to simulated trajectories of EB patterns. The simulations demonstrated that loss of Oct4 can be modeled as a binary process, and that associated patterns can be explained by a set of simple rules that combine baseline stochasticity with intercellular communication. Competing influences between Oct4+ and Oct4- neighbors result in the observed patterns of pluripotency loss within EBs, establishing the utility of rules-based modeling for hypothesis generation of underlying ESC differentiation processes. Importantly, the results indicate that the rules dominate the emergence of patterns independent of EB structure, size, or cell division. In combination with strategies to engineer cellular microenvironments, this type of modeling approach is a powerful tool to predict stem cell behavior under a number of culture conditions that emulate characteristics of 3D stem cell niches.

Quantifying crosstalk among interferon-γ, interleukin-12, and tumor necrosis factor signaling pathways within a TH1 cell model

T helper (T(H)) cells integrate biochemical cues present in the tissue microenvironment and produce cytokines that orchestrate immune responses. Previous discoveries have revealed a qualitative understanding of how T(H) cells process this biochemical information; however, the lack of methods to quantify how well these depictions apply to a particular cell type limits our ability to translate our knowledge of the immune response from one biological system to another. We used model-based inference methods and quantitative flow cytometric analysis in mouse T(H)1 cells to determine the relative contributions of different putative branches in the signaling network that responds to the cytokine interleukin-12 (IL-12), which links innate and adaptive immunity. The response of T(H)1 cells to IL-12 exhibited hysteresis because it depended on both current and past exposure and engaged a positive feedback mechanism through the direct activation of signal transducer and activator of transcription 1. The hysteresis in the dose-response curve to IL-12 created a transient "memory" by sustaining cytokine secretion after the withdrawal of the stimulus. In summary, this combined experimental and computational approach illustrates how model-based inference can be used to better understand how cells process and act upon biochemical cues present in the tissue microenvironment.

Intercellular synchronization of diffusively coupled Ca(2+) oscillators

We examine the synchrony in the dynamics of localized [Ca(2 + )](i) oscillations among a group of cells exhibiting such complex Ca(2 + ) oscillations, connected in the form of long chain, via diffusing coupling where cytosolic Ca(2 + ) and inositol 1,4,5-triphosphate are coupling molecules. Based on our numerical results, we could able to identify three regimes, namely desynchronized, transition and synchronized regimes in the (T - k(e)) (time period-coupling constant) and (A - k(e)) (amplitude-coupling constant) spaces which are supported by phase plots (Δϕ verses time) and recurrence plots, respectively. We further show the increase of synchronization among the cells as the number of coupling molecules increases in the (T - k(e)) and (A - k(e)) spaces.

An integrated framework to model cellular phenotype as a component of biochemical networks

Identification of regulatory molecules in signaling pathways is critical for understanding cellular behavior. Given the complexity of the transcriptional gene network, the relationship between molecular expression and phenotype is difficult to determine using reductionist experimental methods. Computational models provide the means to characterize regulatory mechanisms and predict phenotype in the context of gene networks. Integrating gene expression data with phenotypic data in transcriptional network models enables systematic identification of critical molecules in a biological network. We developed an approach based on fuzzy logic to model cell budding in Saccharomyces cerevisiae using time series expression microarray data of the cell cycle. Cell budding is a phenotype of viable cells undergoing division. Predicted interactions between gene expression and phenotype reflected known biological relationships. Dynamic simulation analysis reproduced the behavior of the yeast cell cycle and accurately identified genes and interactions which are essential for cell viability.

Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of interleukin-12 (IL-12) signaling in naïve CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo-equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics.

Models at the single cell level

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks, and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

Studying adaptation and homeostatic behaviors of kinetic networks by using MATLAB

Organisms have the ability to counteract environmental perturbations and keep certain components within a cell homeostatically regulated. Closely related to homeostasis is the behavior of perfect adaptation where an organism responds to a step-wise perturbation by regulating some of its components, after a transient period, to their original pre-perturbation values. A particular interesting type of model relates to the so-called robust behavior where the homeostatic or perfect adaptation property is independent of the magnitude of the applied step-wise perturbation. It has been shown that this type of behavior is related to the control-theoretic concept of integral feedback (or integral control). Using downloadable MATLAB examples, we demonstrate how robust perfect adaptation sites can be identified in reaction kinetic networks by linearizing the system, applying the Laplace transform and inspecting the transfer function. We also show how the homeostatic set point in perfect adaptation is related to the presence of zero-order fluxes.

Effects of ionizing radiation on cell-to-cell communication

Cell-to-cell signaling has become a significant issue in radiation biology due to experimental evidence, accumulated primarily since the early 1990s, of radiation-induced bystander effects. Several candidate mediators involved in cell-to-cell communication have been investigated and proposed as being responsible for this phenomenon, but the current investigation techniques (both theoretical and experimental) of the mechanisms involved, due to the particular set-up of each experiment, result in experimental data that often are not directly comparable. In this study, a comprehensive approach was adopted to describe cell-to-cell communication (focusing on cytokine signaling) and its modulation by external agents such as ionizing radiation. The aim was also to provide integrated theoretical instruments and experimental data to help in understanding the peculiarities of in vitro experiments. Theoretical/modeling activities were integrated with experimental measurements by (1) redesigning a cybernetic model (proposed in its original form in the 1950s) to frame cell-to-cell communication processes, (2) implementing and developing a mathematical model, and (3) designing and carrying out experiments to quantify key parameters involved in intercellular signaling (focusing as a pilot study on the release and decay of IL-6 molecules and their modulation by radiation). This formalization provides an interpretative framework for understanding the intercellular signaling and in particular for focusing on the study of cell-to-cell communication in a "step-by-step" approach. Under this model, the complex phenomenon of signal transmission was reduced where possible into independent processes to investigate them separately, providing an evaluation of the role of cell communication to guarantee and maintain the robustness of the in vitro experimental systems against the effects of perturbations.

A multiscale systems perspective on cancer, immunotherapy, and Interleukin-12

Monoclonal antibodies represent some of the most promising molecular targeted immunotherapies. However, understanding mechanisms by which tumors evade elimination by the immune system of the host presents a significant challenge for developing effective cancer immunotherapies. The interaction of cancer cells with the host is a complex process that is distributed across a variety of time and length scales. The time scales range from the dynamics of protein refolding (i.e., microseconds) to the dynamics of disease progression (i.e., years). The length scales span the farthest reaches of the human body (i.e., meters) down to the range of molecular interactions (i.e., nanometers). Limited ranges of time and length scales are used experimentally to observe and quantify changes in physiology due to cancer. Translating knowledge obtained from the limited scales observed experimentally to predict patient response is an essential prerequisite for the rational design of cancer immunotherapies that improve clinical outcomes. In studying multiscale systems, engineers use systems analysis and design to identify important components in a complex system and to test conceptual understanding of the integrated system behavior using simulation. The objective of this review is to summarize interactions between the tumor and cell-mediated immunity from a multiscale perspective. Interleukin-12 and its role in coordinating antibody-dependent cell-mediated cytotoxicity is used illustrate the different time and length scale that underpin cancer immunoediting. An underlying theme in this review is the potential role that simulation can play in translating knowledge across scales.

Harmonic oscillations in homeostatic controllers: Dynamics of the p53 regulatory system

Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks.

Systematic calibration of a cell signaling network model

Background

Mathematical modeling is being applied to increasingly complex biological systems and datasets; however, the process of analyzing and calibrating against experimental data is often challenging and a rate limiting step in model development. To address this problem, we developed a systematic methodology for calibrating quantitative models of dynamic biological processes and illustrate its utility by validating a model of TRAIL (Tumor necrosis factor Related Apoptosis-Inducing Ligand)-induced cell death.

Results

We propose a serial framework integrating analysis and calibration modules and we compare various methods for global sensitivity analysis and global parameter estimation. First, adequacy of the network structure is checked by global sensitivity analysis to changes in concentrations of molecular species, validating that the model can reproduce qualitative features of the system behavior derived from experiments or literature surveys. Second, rate parameters are ranked by importance using gradient-based and variance-based sensitivity indices, and we systematically determine the optimal number of parameters to include in model calibration. Third, deterministic, stochastic and hybrid algorithms for global optimization are applied to estimate the values of the most important parameters by fitting to time series data. We compare the performance of these three optimization algorithms.

Conclusions

Our proposed framework covers the entire process from validating a proto-model to establishing a realistic model for in silico experiments and thereby provides a generalized workflow for the construction of predictive models of complex network systems.

Signal transduction networks in cancer: quantitative parameters influence network topology

Networks of fixed topology are used to summarize the collective understanding of the flow of signaling information within a cell (i.e., canonical signaling networks). Moreover, these canonical signaling networks are used to interpret how observed oncogenic changes in protein activity or expression alter information flow in cancer cells. However, creating a novel branch within a signaling network (i.e., a noncanonical edge) provides a mechanism for a cell to acquire the hallmark characteristics of cancer. The objective of this study was to assess the existence of a noncanonical edge within a receptor tyrosine kinase (RTK) signaling network based upon variation in protein expression alone, using a mathematical model of the early signaling events associated with epidermal growth factor receptor 1 (ErbB1) signaling network as an illustrative example. The abundance of canonical protein-RTK complexes (e.g., growth factor receptor bound protein 2-ErbB1 and Src homology 2 domain containing transforming protein 1-ErbB1) were used to establish a threshold that was correlated with ligand-dependent changes in cell proliferation. Given the available data, the uncertainty associated with this threshold was estimated using an empirical Bayesian approach. Using the variability in protein expression observed among a collection of breast cancer cell lines, this model was used to assess whether a noncanonical edge (e.g., Irs1-ErbB1) exceeds the threshold and to identify cell lines where this noncanonical edge is likely to be observed. Taken together, the simulations suggest that the topology of signal transduction networks within cells is influenced by quantitative parameters, such as protein expression and binding affinity. Moreover, forming this noncanonical pathway was not due solely to overexpression of the cell surface receptor but was influenced by overexpression of all members of the multiprotein complex. Multivariate alterations in expression of signaling proteins in cancer cells may activate noncanonical pathways and may rewire the signaling network within a cell.

An empirical Bayesian approach for model-based inference of cellular signaling networks

Background

A common challenge in systems biology is to infer mechanistic descriptions of biological process given limited observations of a biological system. Mathematical models are frequently used to represent a belief about the causal relationships among proteins within a signaling network. Bayesian methods provide an attractive framework for inferring the validity of those beliefs in the context of the available data. However, efficient sampling of high-dimensional parameter space and appropriate convergence criteria provide barriers for implementing an empirical Bayesian approach. The objective of this study was to apply an Adaptive Markov chain Monte Carlo technique to a typical study of cellular signaling pathways.

Results

As an illustrative example, a kinetic model for the early signaling events associated with the epidermal growth factor (EGF) signaling network was calibrated against dynamic measurements observed in primary rat hepatocytes. A convergence criterion, based upon the Gelman-Rubin potential scale reduction factor, was applied to the model predictions. The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters. The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies.

Conclusion

In summary, an empirical Bayesian approach was developed for inferring the confidence that one can place in a particular model that describes signal transduction mechanisms and for inferring inconsistencies in experimental measurements.

The control of the controller: molecular mechanisms for robust perfect adaptation and temperature compensation

Organisms have the property to adapt to a changing environment and keep certain components within a cell regulated at the same level (homeostasis). "Perfect adaptation" describes an organism's response to an external stepwise perturbation by regulating some of its variables/components precisely to their original preperturbation values. Numerous examples of perfect adaptation/homeostasis have been found, as for example, in bacterial chemotaxis, photoreceptor responses, MAP kinase activities, or in metal-ion homeostasis. Two concepts have evolved to explain how perfect adaptation may be understood: In one approach (robust perfect adaptation), the adaptation is a network property, which is mostly, but not entirely, independent of rate constant values; in the other approach (nonrobust perfect adaptation), a fine-tuning of rate constant values is needed. Here we identify two classes of robust molecular homeostatic mechanisms, which compensate for environmental variations in a controlled variable's inflow or outflow fluxes, and allow for the presence of robust temperature compensation. These two classes of homeostatic mechanisms arise due to the fact that concentrations must have positive values. We show that the concept of integral control (or integral feedback), which leads to robust homeostasis, is associated with a control species that has to work under zero-order flux conditions and does not necessarily require the presence of a physico-chemical feedback structure. There are interesting links between the two identified classes of homeostatic mechanisms and molecular mechanisms found in mammalian iron and calcium homeostasis, indicating that homeostatic mechanisms may underlie similar molecular control structures.

Predicting perfect adaptation motifs in reaction kinetic networks

Adaptation and compensation mechanisms are important to keep organisms fit in a changing environment. "Perfect adaptation" describes an organism's response to an external stepwise perturbation by resetting some of its variables precisely to their original preperturbation values. Examples of perfect adaptation are found in bacterial chemotaxis, photoreceptor responses, or MAP kinase activities. Two concepts have evolved for how perfect adaptation may be understood. In one approach, so-called "robust perfect adaptation", the adaptation is a network property (due to integral feedback control), which is independent of rate constant values. In the other approach, which we have termed "nonrobust perfect adaptation", a fine-tuning of rate constant values is needed to show perfect adaptation. Although integral feedback describes robust perfect adaptation in general terms, it does not directly show where in a network perfect adaptation may be observed. Using control theoretic methods, we are able to predict robust perfect adaptation sites within reaction kinetic networks and show that a prerequisite for robust perfect adaptation is that the network is open and irreversible. We applied the method on various reaction schemes and found that new (robust) perfect adaptation motifs emerge when considering suggested models of bacterial and eukaryotic chemotaxis.

Steady-state kinetic modeling constrains cellular resting states and dynamic behavior

A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y₁ signaling can cause widespread compensatory effects on cellular resting states.

Cells respond to extracellular signals through a complex coordination of interacting molecular components. Computational models can serve as powerful tools for prediction and analysis of signaling systems, but constructing large models typically requires extensive experimental datasets and computation. To facilitate the construction of complex signaling models, we present a strategy in which the models are built in a stepwise fashion, beginning with small “resting” networks that are combined to form larger models with complex time-dependent behaviors. Interestingly, we found that only a minor fraction of potential model configurations were compatible with resting behavior in an example signaling system. These reduced sets of configurations were used to limit the search for more complicated solutions that also captured the dynamic behavior of the system. Using an example model constructed by this approach, we show how a cell's resting behavior adjusts to changes in the kinetic rate processes of the system. This strategy offers a general and biologically intuitive framework for building large-scale kinetic models of steady-state cellular systems and their dynamics.

On the role of cell signaling models in cancer research

The main objective of this review is to emphasize the role and importance of the careful mathematical/computational modeling of signaling networks for the understanding of aberrant signaling in cancer and for the development of targeted therapies.

Integrating biosystem models using waveform relaxation

Modelling in systems biology often involves the integration of component models into larger composite models. How to do this systematically and efficiently is a significant challenge: coupling of components can be unidirectional or bidirectional, and of variable strengths. We adapt the waveform relaxation (WR) method for parallel computation of ODEs as a general methodology for computing systems of linked submodels. Four test cases are presented: (i) a cascade of unidirectionally and bidirectionally coupled harmonic oscillators, (ii) deterministic and stochastic simulations of calcium oscillations, (iii) single cell calcium oscillations showing complex behaviour such as periodic and chaotic bursting, and (iv) a multicellular calcium model for a cell plate of hepatocytes. We conclude that WR provides a flexible means to deal with multitime-scale computation and model heterogeneity. Global solutions over time can be captured independently of the solution techniques for the individual components, which may be distributed in different computing environments.

Pulsing cells: how fast is too fast?

Signal transduction pathways are complex coupled sets of biochemical reactions evolved to transmit and process information about the state of the immediate cell environment. Can we design experiments that would inform us about the properties and limitations of signal processing? Recent studies suggest that this indeed can be achieved by exciting a cell with carefully designed oscillatory stimuli. Although this analysis has its caveats, complex temporal stimulation of signal transduction networks can serve to rapidly advance our understanding of these information channels and ultimately create intelligent ways of controlling them.

Gene network dynamics controlling keratinocyte migration

Translation of large-scale data into a coherent model that allows one to simulate, predict and control cellular behavior is far from being resolved. Assuming that long-term cellular behavior is reflected in the gene expression kinetics, we infer a dynamic gene regulatory network from time-series measurements of DNA microarray data of hepatocyte growth factor-induced migration of primary human keratinocytes. Transferring the obtained interactions to the level of signaling pathways, we predict in silico and verify in vitro the necessary and sufficient time-ordered events that control migration. We show that pulse-like activation of the proto-oncogene receptor Met triggers a responsive state, whereas time sequential activation of EGF-R is required to initiate and maintain migration. Context information for enhancing, delaying or stopping migration is provided by the activity of the protein kinase A signaling pathway. Our study reveals the complex orchestration of multiple pathways controlling cell migration.

Mathematics of cell motility: have we got its number?

Mathematical and computational modeling is rapidly becoming an essential research technique complementing traditional experimental biological methods. However, lack of standard modeling methods, difficulties of translating biological phenomena into mathematical language, and differences in biological and mathematical mentalities continue to hinder the scientific progress. Here we focus on one area-cell motility-characterized by an unusually high modeling activity, largely due to a vast amount of quantitative, biophysical data, 'modular' character of motility, and pioneering vision of the area's experimental leaders. In this review, after brief introduction to biology of cell movements, we discuss quantitative models of actin dynamics, protrusion, adhesion, contraction, and cell shape and movement that made an impact on the process of biological discovery. We also comment on modeling approaches and open questions.

Biochemical basis for the functional switch that regulates hepatocyte growth factor receptor tyrosine kinase activation

Ligand-induced dimerization of receptor tyrosine kinases (RTKs) modulates a system of linked biochemical reactions, sharply switching the RTK from a quiescent state to an active state that becomes phosphorylated and triggers intracellular signaling pathways. To improve our understanding of this molecular switch, we developed a quantitative model for hepatocyte growth factor receptor (c-MET) activation using parameters derived in large part from c-MET kinetic and thermodynamic experiments. Our model accurately produces the qualitative and quantitative dynamic features of c-MET phosphorylation observed in cells following ligand binding, including a rapid transient buildup of phosphorylated c-MET at high ligand concentrations. In addition, our model predicts a slow buildup of phosphorylated c-MET under conditions of reduced phosphatase activity and no extracellular agonist. Significantly, this predicted response is observed in cells treated with phosphatase inhibitors, further validating our model. Parameter sensitivity studies clearly show that synergistic oligomerization-dependent changes in c-MET kinetic, thermodynamic, and dephosphorylation properties result in the selective activation of the dimeric receptor, confirming that this model can be used to accurately evaluate the relative importance of linked biochemical reactions important for c-MET activation. Our model suggests that the functional differences observed between c-MET monomers and dimers may have incrementally evolved to optimize cell surface signaling responses.

Modular cell biology: retroactivity and insulation

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input-output dynamic characteristics of transcriptional components, focusing on a property, which we call 'retroactivity', that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter-binding sites, or when the affinity of such binding sites is high. To attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation-dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast timescales of the phosphorylation and dephosphorylation reactions.

Biology by design: reduction and synthesis of cellular components and behaviour

Biological research is experiencing an increasing focus on the application of knowledge rather than on its generation. Thanks to the increased understanding of cellular systems and technological advances, biologists are more frequently asking not only 'how can I understand the structure and behaviour of this biological system?', but also 'how can I apply that knowledge to generate novel functions in different biological systems or in other contexts?' Active pursuit of the latter has nurtured the emergence of synthetic biology. Here, we discuss the motivation behind, and foundational technologies enabling, the development of this nascent field. We examine some early successes and applications while highlighting the challenges involved. Finally, we consider future directions and mention non-scientific considerations that can influence the field's growth.

Complexity in interpretation of embryonic epithelial-mesenchymal transition in response to transforming growth factor-beta signaling

Epithelial-mesenchymal transition (EMT) is a highly conserved and fundamental process that governs morphogenesis in development and may also contribute to cancer metastasis. Transforming growth factor (TGF-beta) is a potent inducer of EMT in various developmental and tumor systems. The analysis of TGF-beta signal transduction pathways is now considered a critically important area of biology, since many defects occur in these pathways in embryonic development. The complexity of TGF-beta signal transduction networks is overwhelming due to the large numbers of interacting constituents, complicated feedforward, feedback and crosstalk circuitry mechanisms that they involve in addition to the cellular kinetics and enzymatics that contribute to cell signaling. As a result of this complexity, apparently simple but highly important questions remain unanswered, that is, how do epithelial cells respond to such TGF-beta signals? System biology and cellular kinetics play a crucial role in cellular function; omissions of such a critical contributor may lead to inaccurate understanding of embryonic EMT. In this review, we identify and explain why certain conditions need to be considered for a true representation of TGF-beta signaling in vivo to better understand the controlled, yet delicate mechanism of embryonic EMT.

Both ligand- and cell-specific parameters control ligand agonism in a kinetic model of g protein-coupled receptor signaling

G protein–coupled receptors (GPCRs) exist in multiple dynamic states (e.g., ligand-bound, inactive, G protein–coupled) that influence G protein activation and ultimately response generation. In quantitative models of GPCR signaling that incorporate these varied states, parameter values are often uncharacterized or varied over large ranges, making identification of important parameters and signaling outcomes difficult to intuit. Here we identify the ligand- and cell-specific parameters that are important determinants of cell-response behavior in a dynamic model of GPCR signaling using parameter variation and sensitivity analysis. The character of response (i.e., positive/neutral/inverse agonism) is, not surprisingly, significantly influenced by a ligand's ability to bias the receptor into an active conformation. We also find that several cell-specific parameters, including the ratio of active to inactive receptor species, the rate constant for G protein activation, and expression levels of receptors and G proteins also dramatically influence agonism. Expressing either receptor or G protein in numbers several fold above or below endogenous levels may result in system behavior inconsistent with that measured in endogenous systems. Finally, small variations in cell-specific parameters identified by sensitivity analysis as significant determinants of response behavior are found to change ligand-induced responses from positive to negative, a phenomenon termed protean agonism. Our findings offer an explanation for protean agonism reported in β₂--adrenergic and α_2A-adrenergic receptor systems.

G protein–coupled receptors (GPCRs) are transmembrane proteins involved in physiological functions ranging from vasodilation and immune response to memory. The binding of both endogenous ligands (e.g., hormones, neurotransmitters) and exogenous ligands (e.g., pharmaceuticals) to these receptors initiates intracellular events that ultimately lead to cell responses. We describe a dynamic model for G protein activation, an immediate outcome of GPCR signaling, and use it together with efficient parameter variation and sensitivity analysis techniques to identify the key cell- and ligand-specific parameters that influence G protein activation. Our results show that although ligand-specific parameters do strongly influence cell response (either causing increases or decreases in G protein activation), cellular parameters may also dictate the magnitude and direction of G protein activation. We apply our findings to describe how protean agonism, a phenomenon in which the same ligand may induce both positive and negative responses, may result from changes in cell-specific parameters. These findings may be used to understand the molecular basis of different responses of cell types and tissues to pharmacological treatment. In addition, these methods may be applied generally to models of cellular signaling and will help guide experimental resources toward further characterization of the key parameters in these networks.

Biology by numbers: mathematical modelling in developmental biology

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

Role of sphingosine kinase in the expression of adhesion molecules on monocytes induced by tumor necrosis factor-alpha (relevant to atherosclerosis)

TNFα stimulates SPHK in the monocyte, which leads to the expression of adhesion molecules on the cell surface. The adhesion of leukocytes to the endothelium is one of the early stages of the onset of atherosclerosis. In this paper, we have delineated the TNFα-induced and SPHK-dependent signaling pathway. In addition, we have developed a biomathematical model to qualify the SPHK time-dependent activity at a specific site in the cell upon TNFα stimulation. Thus, this study provides a biochemical and mechanistic approaches to the understanding of leukocyte-endothelial attachment, so that measures could be designed to minimize the onset of atherosclerosis.

Decision tree modeling predicts effects of inhibiting contractility signaling on cell motility

BACKGROUND

Computational models of cell signaling networks typically are aimed at capturing dynamics of molecular components to derive quantitative insights from prior experimental data, and to make predictions concerning altered dynamics under different conditions. However, signaling network models have rarely been used to predict how cell phenotypic behaviors result from the integrated operation of these networks. We recently developed a decision tree model for how EGF-induced fibroblast cell motility across two-dimensional fibronectin-coated surfaces depends on the integrated activation status of five key signaling nodes, including a proximal regulator of transcellular contractile force generation, MLC (myosin light chain) [Hautaniemi et al, Bioinformatics 21: 2027 {2005}], but we have not previously attempted predictions of new experimental effects from this model.

RESULTS

In this new work, we construct an improved decision tree model for the combined influence of EGF and fibronectin on fibroblast cell migration based on a wider spectrum of experimental protein signaling and cell motility measurements, and directly test a significant and non-intuitive a priori prediction for the outcome of a targeted molecular intervention into the signaling network: that partially reducing activation of MLC would increase cell motility on moderately adhesive surfaces. This prediction was indeed confirmed experimentally: partial inhibition of the activating MLC kinase (MLCK) upstream using the pharmacologic agent ML-7 resulted in increased motility of NR6 fibroblasts. We further extended this exciting finding by showing that partial reduction of MLC activation similarly enhanced the transmigration of the human breast carcinoma cell line MDA-213 through a Matrigel barrier.

CONCLUSION

These findings specifically highlight a central regulatory role for transcellular contractility in governing cell motility, while at the same time demonstrating the value of a decision tree approach to a systems "signal-response" model in discerning non-intuitive behavior arising from integrated operation a cell signaling network.

Control of Streptococcus pyogenes virulence: modeling of the CovR/S signal transduction system

The CovR/S system in Streptococcus pyogenes (Group A Streptococcus, or GAS), a two-component signal transduction/transcription regulation system, controls the expression of major virulence factors. The presence of a negative feedback loop distinguishes the CovR/S system from the majority of bacterial two-component systems. We developed a deterministic model of the CovR/S system consisting of eight delay differential equations. Computational experiments showed that the system possessed a unique stable steady state. The dynamical behavior of the system showed a tendency for oscillations becoming more pronounced for longer but still biochemically realistic delays resulting from reductions in the rates of translation elongation. We have devised an efficient procedure for computing the system's steady state. Further, we have shown that the signal-response curves are hyperbolic for the default parameter values. However, in experiments with randomized parameters we demonstrated that sigmoidality of signal-response curves, implying a response threshold, is not only possible, but seems to be rather typical for CovR/S-like systems even when binding of the CovR response regulator protein to a promoter is non-cooperative. We used sensitivity analysis to simplify the model in order to make it analytically tractable. The existence and uniqueness of the steady state and hyperbolicity of signal-response curves for the majority of the variables was proved for the simplified model. Also, we found that provided CovS was active, the system was insensitive to changes in the concentration of any other phosphoryl donor such as acetyl phosphate.

Reduced-order modelling of biochemical networks: application to the GTPase-cycle signalling module

Biochemical systems embed complex networks and hence development and analysis of their detailed models pose a challenge for computation. Coarse-grained biochemical models, called reduced-order models (ROMs), consisting of essential biochemical mechanisms are more useful for computational analysis and for studying important features of a biochemical network. The authors present a novel method to model-reduction by identifying potentially important parameters using multidimensional sensitivity analysis. A ROM is generated for the GTPase-cycle module of m1 muscarinic acetylcholine receptor, Gq, and regulator of G-protein signalling 4 (a GTPase-activating protein or GAP) starting from a detailed model of 48 reactions. The resulting ROM has only 17 reactions. The ROM suggested that complexes of G-protein coupled receptor (GPCR) and GAP--which were proposed in the detailed model as a hypothesis--are required to fit the experimental data. Models previously published in the literature are also simulated and compared with the ROM. Through this comparison, a minimal ROM, that also requires complexes of GPCR and GAP, with just 15 parameters is generated. The proposed reduced-order modelling methodology is scalable to larger networks and provides a general framework for the reduction of models of biochemical systems.

Synthetic multivalent ligands as probes of signal transduction

Cell-surface receptors acquire information from the extracellular environment and coordinate intracellular responses. Many receptors do not operate as individual entities, but rather as part of dimeric or oligomeric complexes. Coupling the functions of multiple receptors may endow signaling pathways with the sensitivity and malleability required to govern cellular responses. Moreover, multireceptor signaling complexes may provide a means of spatially segregating otherwise degenerate signaling cascades. Understanding the mechanisms, extent, and consequences of receptor co-localization and interreceptor communication is critical; chemical synthesis can provide compounds to address the role of receptor assembly in signal transduction. Multivalent ligands can be generated that possess a variety of sizes, shapes, valencies, orientations, and densities of binding elements. This Review focuses on the use of synthetic multivalent ligands to characterize receptor function.

Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations

Bimolecular reactions in the plasma membrane, such as receptor dimerization, are a key signaling step for many signaling systems. For receptors to dimerize, they must first diffuse until a collision happens, upon which a dimerization reaction may occur. Therefore, study of the dynamics of cell signaling on the membrane may require the use of a spatial modeling framework. Despite the availability of spatial simulation methods, e.g., stochastic spatial Monte Carlo (MC) simulation and partial differential equation (PDE) based approaches, many biological models invoke well-mixed assumptions without completely evaluating the importance of spatial organization. Whether one is to utilize a spatial or non-spatial simulation framework is therefore an important decision. In order to evaluate the importance of spatial effects a priori, i.e., without performing simulations, we have assessed the applicability of a dimensionless number, known as second Damköhler number (Da), defined here as the ratio of time scales of collision and reaction, for 2-dimensional bimolecular reactions. Our study shows that dimerization reactions in the plasma membrane with Da approximately >0.1 (tested in the receptor density range of 10(2)-10(5)/microm(2)) require spatial modeling. We also evaluated the effective reaction rate constants of MC and simple deterministic PDEs. Our simulations show that the effective reaction rate constant decreases with time due to time dependent changes in the spatial distribution of receptors. As a result, the effective reaction rate constant of simple PDEs can differ from that of MC by up to two orders of magnitude. Furthermore, we show that the fluctuations in the number of copies of signaling proteins (noise) may also depend on the diffusion properties of the system. Finally, we used the spatial MC model to explore the effect of plasma membrane heterogeneities, such as receptor localization and reduced diffusivity, on the dimerization rate. Interestingly, our simulations show that localization of epidermal growth factor receptor (EGFR) can cause the diffusion limited dimerization rate to be up to two orders of magnitude higher at higher average receptor densities reported for cancer cells, as compared to a normal cell.

Stimulus-frequency otoacoustic emissions measured with amplitude-modulated suppressor tones (L)

Stimulus-frequency otoacoustic emissions (SFOAEs) are typically derived as the difference in sound pressure in the ear canal with and without a suppressor tone added to the probe tone. A novel variation of this method applies a sinusoidal amplitude modulation (AM) to the suppressor tone, which causes the SFOAE to also be modulated. The AM-SFOAE can be separated from the probe frequency using spectral methods. AM-SFOAE measurements are described for four normal-hearing subjects using 6-Hz AM. Because the suppressor modulation is at a higher rate, the AM-SFOAE technique avoids the confounding influence of heartbeat, which also modulates the probe tone.

Algebraic dependency models of protein signal transduction networks from time-series data

Signal transduction networks are crucial for inter- and intra-cellular signaling. Signals are often transmitted via covalent modification of protein structure, with phosphorylation/dephosphorylation as the primary example. In this paper, we apply a recently described method of computational algebra to the modeling of signaling networks, based on time-course protein modification data. Computational algebraic techniques are employed to construct next-state functions. A Monte Carlo method is used to approximate the Deegan-Packel Index of Power corresponding to the respective variables. The Deegan-Packel Index of Power is used to conjecture dependencies in the cellular signaling networks. We apply this method to two examples of protein modification time-course data available in the literature. These experiments identified protein carbonylation upon exposure of cells to sub-lethal concentrations of copper. We demonstrate that this method can identify protein dependencies that might correspond to regulatory mechanisms to shut down glycolysis in a reverse, step-wise fashion in response to copper-induced oxidative stress in yeast. These examples show that the computational algebra approach can identify dependencies that may outline signaling networks involved in the response of glycolytic enzymes to the oxidative stress caused by copper.

Model identification of signal transduction networks from data using a state regulator problem

Advances in molecular biology provide an opportunity to develop detailed models of biological processes that can be used to obtain an integrated understanding of the system. However, development of useful models from the available knowledge of the system and experimental observations still remains a daunting task. In this work, a model identification strategy for complex biological networks is proposed. The approach includes a state regulator problem (SRP) that provides estimates of all the component concentrations and the reaction rates of the network using the available measurements. The full set of the estimates is utilised for model parameter identification for the network of known topology. An a priori model complexity test that indicates the feasibility of performance of the proposed algorithm is developed. Fisher information matrix (FIM) theory is used to address model identifiability issues. Two signalling pathway case studies, the caspase function in apoptosis and the MAP kinase cascade system, are considered. The MAP kinase cascade, with measurements restricted to protein complex concentrations, fails the a priori test and the SRP estimates are poor as expected. The apoptosis network structure used in this work has moderate complexity and is suitable for application of the proposed tools. Using a measurement set of seven protein concentrations, accurate estimates for all unknowns are obtained. Furthermore, the effects of measurement sampling frequency and quality of information in the measurement set on the performance of the identified model are described.