Decoupling of receptor and downstream signals in the Akt pathway by its low-pass filter characteristics

The physical basis of analog-to-digital signal processing in the EGFR system-Delving into the role of the endoplasmic reticulum

Receptor tyrosine kinases exhibit ligand-induced activity and uptake into cells via endocytosis. In the case of epidermal growth factor (EGF) receptor (EGFR), the resulting endosomes are trafficked to the perinuclear region, where dephosphorylation of receptors occurs, which are subsequently directed to degradation. Traveling endosomes bearing phosphorylated EGFRs are subjected to the activity of cytoplasmic phosphatases as well as interactions with the endoplasmic reticulum (ER). The peri-nuclear region harbors ER-embedded phosphatases, a component of the EGFR-bearing endosome-ER contact site. The ER is also emerging as a central player in spatiotemporal control of endosomal motility, positioning, tubulation, and fission. Past studies strongly suggest that the physical interaction between the ER and endosomes forms a reaction "unit" for EGFR dephosphorylation. Independently, endosomes have been implicated to enable quantization of EGFR signals by modulation of the phosphorylation levels. Here, we review the distinct mechanisms by which endosomes form the logistical means for signal quantization and speculate on the role of the ER.

Applications of model simulation in pharmacological fields and the problems of theoretical reliability

The use of mathematical models has become increasingly prevalent in pharmacological fields, particularly in drug development processes. These models are instrumental in tasks such as designing clinical trials and assessing factors like efficacy, toxicity, and clinical practice. Various types of models have been developed and documented. Nevertheless, emphasizing the reliability of parameter values is crucial, as they play a pivotal role in shaping the behavior of the system. In some instances, parameter values reported previously are treated as fixed values, which can lead to convergence towards values that deviate substantially from those found in actual biological systems. This is especially true when parameter values are determined through fitting to limited observations. To mitigate this risk, the reuse of parameter values from previous reports should be approached with a critical evaluation of their validity. Currently, there is a proposal for a simultaneous search for plausible values for all parameters using comprehensive search algorithms in both pharmacokinetic and pharmacodynamic or systems pharmacological models. Implementing these methodologies can help address issues related to parameter determination. Furthermore, integrating these approaches with methods developed in the field of machine-learning field has the potential to enhance the reliability of parameter values and the resulting model outputs.

Phenotypic consequences of logarithmic signaling in MAPK stress response

How cells respond to dynamic environmental changes is crucial for understanding fundamental biological processes and cell physiology. In this study, we developed an experimental and quantitative analytical framework to explore how dynamic stress gradients that change over time regulate cellular volume, signaling activation, and growth phenotypes. Our findings reveal that gradual stress conditions substantially enhance cell growth compared to conventional acute stress. This growth advantage correlates with a minimal reduction in cell volume dependent on the dynamic of stress. We explain the growth phenotype with our finding of a logarithmic signal transduction mechanism in the yeast Mitogen-Activated Protein Kinase (MAPK) osmotic stress response pathway. These insights into the interplay between gradual environments, cell volume change, dynamic cell signaling, and growth, advance our understanding of fundamental cellular processes in gradual stress environments.

Controllability and accessibility analysis of nonlinear biosystems

BACKGROUND

We address the problem of determining the controllability and accessibility of nonlinear biosystems. We consider models described by affine-in-inputs ordinary differential equations, which are adequate for a wide array of biological processes. Roughly speaking, the controllability of a dynamical system determines the possibility of steering it from an initial state to any point in its neighbourhood; accessibility is a weaker form of controllability.

METHODS

While the methodology for analysing the controllability of linear systems is well established, its generalization to the nonlinear case has proven elusive. Thus, a number of related but different properties - including different versions of accessibility, reachability or weak local controllability - have been defined to approach its study, and several partial results exist in lieu of a general test. Here, leveraging the applicable results from differential geometric control theory, we source sufficient conditions to assess nonlinear controllability, as well as a necessary and sufficient condition for accessibility.

RESULTS

We develop an algorithmic procedure to evaluate these conditions efficiently, and we provide its open source implementation. Using this software tool, we analyse the accessibility and controllability of a number of models of biomedical interest. While some of them are fully controllable, we find others that are not, as is the case of some models of EGF and NFκB signalling networks.

CONCLUSIONS

The contributions in this paper facilitate the accessibility and controllability analysis of nonlinear models, not only in biomedicine but also in other areas in which they have been rarely performed to date.

Posterior marginalization accelerates Bayesian inference for dynamical models of biological processes

Bayesian inference is an important method in the life and natural sciences for learning from data. It provides information about parameter and prediction uncertainties. Yet, generating representative samples from the posterior distribution is often computationally challenging. Here, we present an approach that lowers the computational complexity of sample generation for dynamical models with scaling, offset, and noise parameters. The proposed method is based on the marginalization of the posterior distribution. We provide analytical results for a broad class of problems with conjugate priors and show that the method is suitable for a large number of applications. Subsequently, we demonstrate the benefit of the approach for applications from the field of systems biology. We report an improvement up to 50 times in the effective sample size per unit of time. As the scheme is broadly applicable, it will facilitate Bayesian inference in different research fields.

PI3K signaling through a biochemical systems lens

Following 3 decades of extensive research into PI3K signaling, it is now evidently clear that the underlying network does not equate to a simple ON/OFF switch. This is best illustrated by the multifaceted nature of the many diseases associated with aberrant PI3K signaling, including common cancers, metabolic disease, and rare developmental disorders. However, we are still far from a complete understanding of the fundamental control principles that govern the numerous phenotypic outputs that are elicited by activation of this well-characterized biochemical signaling network, downstream of an equally diverse set of extrinsic inputs. At its core, this is a question on the role of PI3K signaling in cellular information processing and decision making. Here, we review the determinants of accurate encoding and decoding of growth factor signals and discuss outstanding questions in the PI3K signal relay network. We emphasize the importance of quantitative biochemistry, in close integration with advances in single-cell time-resolved signaling measurements and mathematical modeling.

Deterministic early endosomal maturations emerge from a stochastic trigger-and-convert mechanism

Endosomal maturation is critical for robust and timely cargo transport to specific cellular compartments. The most prominent model of early endosomal maturation involves a phosphoinositide-driven gain or loss of specific proteins on individual endosomes, emphasising an autonomous and stochastic description. However, limitations in fast, volumetric imaging long hindered direct whole cell-level measurements of absolute numbers of maturation events. Here, we use lattice light-sheet imaging and bespoke automated analysis to track individual very early (APPL1-positive) and early (EEA1-positive) endosomes over the entire population, demonstrating that direct inter-endosomal contact drives maturation between these populations. Using fluorescence lifetime, we show that this endosomal interaction is underpinned by asymmetric binding of EEA1 to very early and early endosomes through its N- and C-termini, respectively. In combination with agent-based simulation which supports a 'trigger-and-convert' model, our findings indicate that APPL1- to EEA1-positive maturation is driven not by autonomous events but by heterotypic EEA1-mediated interactions, providing a mechanism for temporal and population-level control of maturation.

An optogenetic-phosphoproteomic study reveals dynamic Akt1 signaling profiles in endothelial cells

The serine/threonine kinase AKT is a central node in cell signaling. While aberrant AKT activation underlies the development of a variety of human diseases, how different patterns of AKT-dependent phosphorylation dictate downstream signaling and phenotypic outcomes remains largely enigmatic. Herein, we perform a systems-level analysis that integrates methodological advances in optogenetics, mass spectrometry-based phosphoproteomics, and bioinformatics to elucidate how different intensity, duration, and pattern of Akt1 stimulation lead to distinct temporal phosphorylation profiles in vascular endothelial cells. Through the analysis of ~35,000 phosphorylation sites across multiple conditions precisely controlled by light stimulation, we identify a series of signaling circuits activated downstream of Akt1 and interrogate how Akt1 signaling integrates with growth factor signaling in endothelial cells. Furthermore, our results categorize kinase substrates that are preferably activated by oscillating, transient, and sustained Akt1 signals. We validate a list of phosphorylation sites that covaried with Akt1 phosphorylation across experimental conditions as potential Akt1 substrates. Our resulting dataset provides a rich resource for future studies on AKT signaling and dynamics.

Rate thresholds in cell signaling have functional and phenotypic consequences in non-linear time-dependent environments

All cells employ signal transduction pathways to respond to physiologically relevant extracellular cytokines, stressors, nutrient levels, hormones, morphogens, and other stimuli that vary in concentration and rate in healthy and diseased states. A central unsolved fundamental question in cell signaling is whether and how cells sense and integrate information conveyed by changes in the rate of extracellular stimuli concentrations, in addition to the absolute difference in concentration. We propose that different environmental changes over time influence cell behavior in addition to different signaling molecules or different genetic backgrounds. However, most current biomedical research focuses on acute environmental changes and does not consider how cells respond to environments that change slowly over time. As an example of such environmental change, we review cell sensitivity to environmental rate changes, including the novel mechanism of rate threshold. A rate threshold is defined as a threshold in the rate of change in the environment in which a rate value below the threshold does not activate signaling and a rate value above the threshold leads to signal activation. We reviewed p38/Hog1 osmotic stress signaling in yeast, chemotaxis and stress response in bacteria, cyclic adenosine monophosphate signaling in Amoebae, growth factors signaling in mammalian cells, morphogen dynamics during development, temporal dynamics of glucose and insulin signaling, and spatio-temproral stressors in the kidney. These reviewed examples from the literature indicate that rate thresholds are widespread and an underappreciated fundamental property of cell signaling. Finally, by studying cells in non-linear environments, we outline future directions to understand cell physiology better in normal and pathophysiological conditions.

Multiscale modeling of collective cell migration elucidates the mechanism underlying tumor-stromal interactions in different spatiotemporal scales

Metastasis is the pathogenic spread of cancer cells from a primary tumor to a secondary site which happens at the late stages of cancer. It is caused by a variety of biological, chemical, and physical processes, such as molecular interactions, intercellular communications, and tissue-level activities. Complex interactions of cancer cells with their microenvironment components such as cancer associated fibroblasts (CAFs) and extracellular matrix (ECM) cause them to adopt an invasive phenotype that promotes tumor growth and migration. This paper presents a multiscale model for integrating a wide range of time and space interactions at the molecular, cellular, and tissue levels in a three-dimensional domain. The modeling procedure starts with presenting nonlinear dynamics of cancer cells and CAFs using ordinary differential equations based on TGFβ, CXCL12, and LIF signaling pathways. Unknown kinetic parameters in these models are estimated using hybrid unscented Kalman filter and the models are validated using experimental data. Then, the principal role of CAFs on metastasis is revealed by spatial-temporal modeling of circulating signals throughout the TME. At this stage, the model has evolved into a coupled ODE-PDE system that is capable of determining cancer cells' status in one of the quiescent, proliferating or migratory conditions due to certain metastasis factors and ECM characteristics. At the tissue level, we consider a force-based framework to model the cancer cell proliferation and migration as the final step towards cancer cell metastasis. The ability of the multiscale model to depict cancer cells' behavior in different levels of modeling is confirmed by comparing its outputs with the results of RT PCR and wound scratch assay techniques. Performance evaluation of the model indicates that the proposed multiscale model can pave the way for improving the efficiency of therapeutic methods in metastasis prevention.

Utility of constraints reflecting system stability on analyses for biological models

Simulating complex biological models consisting of multiple ordinary differential equations can aid in the prediction of the pharmacological/biological responses; however, they are often hampered by the availability of reliable kinetic parameters. In the present study, we aimed to discover the properties of behaviors without determining an optimal combination of kinetic parameter values (parameter set). The key idea was to collect as many parameter sets as possible. Given that many systems are biologically stable and resilient (BSR), we focused on the dynamics around the steady state and formulated objective functions for BSR by partial linear approximation of the focused region. Using the objective functions and modified global cluster Newton method, we developed an algorithm for a thorough exploration of the allowable parameter space for biological systems (TEAPS). We first applied TEAPS to the NF-κB signaling model. This system shows a damped oscillation after stimulation and seems to fit the BSR constraint. By applying TEAPS, we found several directions in parameter space which stringently determines the BSR property. In such directions, the experimentally fitted parameter values were included in the range of the obtained parameter sets. The arachidonic acid metabolic pathway model was used as a model related to pharmacological responses. The pharmacological effects of nonsteroidal anti-inflammatory drugs were simulated using the parameter sets obtained by TEAPS. The structural properties of the system were partly extracted by analyzing the distribution of the obtained parameter sets. In addition, the simulations showed inter-drug differences in prostacyclin to thromboxane A2 ratio such that aspirin treatment tends to increase the ratio, while rofecoxib treatment tends to decrease it. These trends are comparable to the clinical observations. These results on real biological models suggest that the parameter sets satisfying the BSR condition can help in finding biologically plausible parameter sets and understanding the properties of biological systems.

We propose a new method to analyze the properties of biological dynamic models, which we named TEAPS (Thorough Exploration of Allowable Parameter Space). TEAPS can thoroughly determine combinations of parameter values for ordinary differential equations with which an initial state in a certain range converges to a particular fixed point. This stable and resilient behavior is a characteristic shared with many biological systems, including metabolic systems and intracellular signaling systems. Therefore, this thorough search outlined the possible parameter space as biological systems for target models, which helps to understand the system constraints when the target systems behave dynamically. The obtained parameter space can be used as an initial space for parameter tuning. For models that include a large number of parameters, the parameter space to be searched in the parameter tuning process is too large; therefore, narrowing down the space by TEAPS potentially contributes to the analysis of the dynamics of complicated biological models. Thus, our approach can partly overcome the current problem in parameter tuning and can advance the computational dynamic analyses of biological systems.

Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to study biochemical reactions in cellular networks since they effectively describe the temporal evolution of these networks using mass action kinetics. The parameters of these models are rarely known a priori and must instead be estimated by calibration using experimental data. Optimization-based calibration of ODE models on is often challenging, even for low-dimensional problems. Multiple hypotheses have been advanced to explain why biochemical model calibration is challenging, including non-identifiability of model parameters, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking. Nonetheless, reliable model calibration is essential for uncertainty analysis, model comparison, and biological interpretation. We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving a variety of Hessian approximation schemes. We evaluated fides on a recently developed corpus of biologically realistic benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same mathematical instructions (algorithms). Analysis of possible sources of poor optimizer performance identified limitations in the widely used Gauss-Newton, BFGS and SR1 Hessian approximation schemes. We addressed these drawbacks with a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. When applied to the corpus of test models, we found that fides was on average more reliable and efficient than existing methods using a variety of criteria. We expect fides to be broadly useful for ODE constrained optimization problems in biochemical models and to be a foundation for future methods development.

A protocol for dynamic model calibration

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Mini-batch optimization enables training of ODE models on large-scale datasets

Quantitative dynamic models are widely used to study cellular signal processing. A critical step in modelling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. Mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark mini-batch optimization for ordinary differential equation (ODE) models, thereby establishing a direct link between dynamic modelling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modelling of even larger and more complex systems than what is currently possible.

A Modular Workflow for Model Building, Analysis, and Parameter Estimation in Systems Biology and Neuroscience

Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. Here we focus on the scale of biochemical pathways, which is one of the main objects of study in systems biology. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB® scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.

Continuous variable responses and signal gating form kinetic bases for pulsatile insulin signaling and emergence of resistance

Evolutionarily conserved insulin signaling is central to nutrient sensing, storage, and utilization across tissues. Dysfunctional insulin signaling is associated with metabolic disorders, cancer, and aging. Hence, the pathway components have emerged as key targets for pharmacological interventions in addition to insulin administration itself. Despite this, activation–inactivation dynamics of individual components, which exert regulatory control in a physiological context, is poorly understood. Now, with our systems-based approach, we reveal kinetic parameters, which define the flow of information through both metabolic and growth-factor arms and thus determine signaling architecture. We also provide a kinetic basis for 1) the advantage of pulsatile-fasted insulin signaling that enables fed-insulin response and 2) the detrimental impact of repeat fed-insulin inputs that causes resistance.

Understanding kinetic control of biological processes is as important as identifying components that constitute pathways. Insulin signaling is central for almost all metazoans, and its perturbations are associated with various developmental disorders, metabolic diseases, and aging. While temporal phosphorylation changes and kinetic constants have provided some insights, constant or variable parameters that establish and maintain signal topology are poorly understood. Here, we report kinetic parameters that encode insulin concentration and nutrient-dependent flow of information using iterative experimental and mathematical simulation-based approaches. Our results illustrate how dynamics of distinct phosphorylation events collectively contribute to selective kinetic gating of signals and maximum connectivity of the signaling cascade under normo-insulinemic but not hyper-insulinemic states. In addition to identifying parameters that provide predictive value for maintaining the balance between metabolic and growth-factor arms, we posit a kinetic basis for the emergence of insulin resistance. Given that pulsatile insulin secretion during a fasted state precedes a fed response, our findings reveal rewiring of insulin signaling akin to memory and anticipation, which was hitherto unknown. Striking disparate temporal behavior of key phosphorylation events that destroy the topology under hyper-insulinemic states underscores the importance of unraveling regulatory components that act as bandwidth filters. In conclusion, besides providing fundamental insights, our study will help in identifying therapeutic strategies that conserve coupling between metabolic and growth-factor arms, which is lost in diseases and conditions of hyper-insulinemia.

Finding new edges: systems approaches to MTOR signaling

Cells have evolved highly intertwined kinase networks to finely tune cellular homeostasis to the environment. The network converging on the mechanistic target of rapamycin (MTOR) kinase constitutes a central hub that integrates metabolic signals and adapts cellular metabolism and functions to nutritional changes and stress. Feedforward and feedback loops, crosstalks and a plethora of modulators finely balance MTOR-driven anabolic and catabolic processes. This complexity renders it difficult — if not impossible — to intuitively decipher signaling dynamics and network topology. Over the last two decades, systems approaches have emerged as powerful tools to simulate signaling network dynamics and responses. In this review, we discuss the contribution of systems studies to the discovery of novel edges and modulators in the MTOR network in healthy cells and in disease.

A rate threshold mechanism regulates MAPK stress signaling and survival

Cells are exposed to changes in extracellular stimulus concentration that vary as a function of rate. However, how cells integrate information conveyed from stimulation rate along with concentration remains poorly understood. Here, we examined how varying the rate of stress application alters budding yeast mitogen-activated protein kinase (MAPK) signaling and cell behavior at the single-cell level. We show that signaling depends on a rate threshold that operates in conjunction with stimulus concentration to determine the timing of MAPK signaling during rate-varying stimulus treatments. We also discovered that the stimulation rate threshold and stimulation rate-dependent cell survival are sensitive to changes in the expression levels of the Ptp2 phosphatase, but not of another phosphatase that similarly regulates osmostress signaling during switch-like treatments. Our results demonstrate that stimulation rate is a regulated determinant of cell behavior and provide a paradigm to guide the dissection of major stimulation rate dependent mechanisms in other systems.

Diverse Cell Stimulation Kinetics Identify Predictive Signal Transduction Models

Computationally understanding the molecular mechanisms that give rise to cell signaling responses upon different environmental, chemical, and genetic perturbations is a long-standing challenge that requires models that fit and predict quantitative responses for new biological conditions. Overcoming this challenge depends not only on good models and detailed experimental data but also on the rigorous integration of both. We propose a quantitative framework to perturb and model generic signaling networks using multiple and diverse changing environments (hereafter "kinetic stimulations") resulting in distinct pathway activation dynamics. We demonstrate that utilizing multiple diverse kinetic stimulations better constrains model parameters and enables predictions of signaling dynamics that would be impossible using traditional dose-response or individual kinetic stimulations. To demonstrate our approach, we use experimentally identified models to predict signaling dynamics in normal, mutated, and drug-treated conditions upon multitudes of kinetic stimulations and quantify which proteins and reaction rates are most sensitive to which extracellular stimulations.

Benchmark problems for dynamic modeling of intracellular processes

Motivation

Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A multitude of computational approaches, e.g. for parameter estimation or uncertainty analysis have been developed within recent years. However, many of these approaches lack proper testing in application settings because a comprehensive set of benchmark problems is yet missing.

Results

We present a collection of 20 benchmark problems in order to evaluate new and existing methodologies, where an ODE model with corresponding experimental data is referred to as problem. In addition to the equations of the dynamical system, the benchmark collection provides observation functions as well as assumptions about measurement noise distributions and parameters. The presented benchmark models comprise problems of different size, complexity and numerical demands. Important characteristics of the models and methodological requirements are summarized, estimated parameters are provided, and some example studies were performed for illustrating the capabilities of the presented benchmark collection.

Availability and implementation

The models are provided in several standardized formats, including an easy-to-use human readable form and machine-readable SBML files. The data is provided as Excel sheets. All files are available at https://github.com/Benchmarking-Initiative/Benchmark-Models, including step-by-step explanations and MATLAB code to process and simulate the models.

Supplementary information

Supplementary data are available at Bioinformatics online.

Model-based analysis of response and resistance factors of cetuximab treatment in gastric cancer cell lines

Targeted cancer therapies are powerful alternatives to chemotherapies or can be used complementary to these. Yet, the response to targeted treatments depends on a variety of factors, including mutations and expression levels, and therefore their outcome is difficult to predict. Here, we develop a mechanistic model of gastric cancer to study response and resistance factors for cetuximab treatment. The model captures the EGFR, ERK and AKT signaling pathways in two gastric cancer cell lines with different mutation patterns. We train the model using a comprehensive selection of time and dose response measurements, and provide an assessment of parameter and prediction uncertainties. We demonstrate that the proposed model facilitates the identification of causal differences between the cell lines. Furthermore, our study shows that the model provides predictions for the responses to different perturbations, such as knockdown and knockout experiments. Among other results, the model predicted the effect of MET mutations on cetuximab sensitivity. These predictive capabilities render the model a basis for the assessment of gastric cancer signaling and possibly for the development and discovery of predictive biomarkers.

Unraveling the causal differences between drug responders and non-responders is an important challenge. The information can help to understand molecular mechanisms and to guide the selection and design of targeted therapies. Here, we approach this problem for cetuximab treatment for gastric cancer using mechanistic mathematical modeling. The proposed model describes responder and non-responder gastric cancer cell lines and can predict the response in several validation experiments. Our analysis provides a differentiated view on mutations and explains, for instance, the relevance of MET mutations and the insignificance of PIK3CA mutation in the considered cell lines. The model might potentially provide the basis for understanding the recent failure of several clinical studies.

Organization at criticality enables processing of time-varying signals by receptor networks

How cells utilize surface receptors for chemoreception is a recurrent question spanning between physics and biology over the past few decades. However, the dynamical mechanism for processing time-varying signals is still unclear. Using dynamical systems formalism to describe criticality in non-equilibrium systems, we propose generic principle for temporal information processing through phase space trajectories using dynamic transient memory. In contrast to short-term memory, dynamic memory generated via "ghost" attractor enables signal integration depending on stimulus history and thereby uniquely promotes integrating and interpreting complex temporal growth factor signals. We argue that this is a generic feature of receptor networks, the first layer of the cell that senses the changing environment. Using the experimentally established epidermal growth factor sensing system, we propose how recycling could provide self-organized maintenance of the critical receptor concentration at the plasma membrane through a simple, fluctuation-sensing mechanism. Processing of non-stationary signals, a feature previously attributed only to neural networks, thus uniquely emerges for receptor networks organized at criticality.

Cracking the context-specific PI3K signaling code

Specificity in signal transduction is determined by the ability of cells to "encode" and subsequently "decode" different environmental signals. Akin to computer software, this "signaling code" governs context-dependent execution of cellular programs through modulation of signaling dynamics and can be corrupted by disease-causing mutations. Class IA phosphoinositide 3-kinase (PI3K) signaling is critical for normal growth and development and is dysregulated in human disorders such as benign overgrowth syndromes, cancer, primary immune deficiency, and metabolic syndrome. Despite decades of PI3K research, understanding of context-dependent regulation of the PI3K pathway and of the underlying signaling code remains rudimentary. Here, we review current knowledge on context-specific PI3K signaling and how technological advances now make it possible to move from a qualitative to quantitative understanding of this pathway. Insight into how cellular PI3K signaling is encoded or decoded may open new avenues for rational pharmacological targeting of PI3K-associated diseases. The principles of PI3K context-dependent signal encoding and decoding described here are likely applicable to most, if not all, major cell signaling pathways.

Serine 474 phosphorylation is essential for maximal Akt2 kinase activity in adipocytes

The Ser/Thr protein kinase Akt regulates essential biological processes such as cell survival, growth, and metabolism. Upon growth factor stimulation, Akt is phosphorylated at Ser⁴⁷⁴; however, how this phosphorylation contributes to Akt activation remains controversial. Previous studies, which induced loss of Ser⁴⁷⁴ phosphorylation by ablating its upstream kinase mTORC2, have implicated Ser⁴⁷⁴ phosphorylation as a driver of Akt substrate specificity. Here we directly studied the role of Akt2 Ser⁴⁷⁴ phosphorylation in 3T3-L1 adipocytes by preventing Ser⁴⁷⁴ phosphorylation without perturbing mTORC2 activity. This was achieved by utilizing a chemical genetics approach, where ectopically expressed S474A Akt2 was engineered with a W80A mutation to confer resistance to the Akt inhibitor MK2206, and thus allow its activation independent of endogenous Akt. We found that insulin-stimulated phosphorylation of four bona fide Akt substrates (TSC2, PRAS40, FOXO1/3a, and AS160) was reduced by ∼50% in the absence of Ser⁴⁷⁴ phosphorylation. Accordingly, insulin-stimulated mTORC1 activation, protein synthesis, FOXO nuclear exclusion, GLUT4 translocation, and glucose uptake were attenuated upon loss of Ser⁴⁷⁴ phosphorylation. We propose a model where Ser⁴⁷⁴ phosphorylation is required for maximal Akt2 kinase activity in adipocytes.

Generating kinetic environments to study dynamic cellular processes in single cells

Cells of any organism are consistently exposed to changes over time in their environment. The kinetics by which these changes occur are critical for the cellular response and fate decision. It is therefore important to control the temporal changes of extracellular stimuli precisely to understand biological mechanisms in a quantitative manner. Most current cell culture and biochemical studies focus on instant changes in the environment and therefore neglect the importance of kinetic environments. To address these shortcomings, we developed two experimental methodologies to precisely control the environment of single cells. These methodologies are compatible with standard biochemistry, molecular, cell and quantitative biology assays. We demonstrate applicability by obtaining time series and time point measurements in both live and fixed cells. We demonstrate the feasibility of the methodology in yeast and mammalian cell culture in combination with widely used assays such as flow cytometry, time-lapse microscopy and single-molecule RNA Fluorescent in-situ Hybridization (smFISH). Our experimental methodologies are easy to implement in most laboratory settings and allows the study of kinetic environments in a wide range of assays and different cell culture conditions.

Short-term cellular memory tunes the signaling responses of the chemokine receptor CXCR4

The chemokine receptor CXCR4 regulates fundamental processes in development, normal physiology, and diseases, including cancer. Small subpopulations of CXCR4-positive cells drive the local invasion and dissemination of malignant cells during metastasis, emphasizing the need to understand the mechanisms controlling responses at the single-cell level to receptor activation by the chemokine ligand CXCL12. Using single-cell imaging, we discovered that short-term cellular memory of changes in environmental conditions tuned CXCR4 signaling to Akt and ERK, two kinases activated by this receptor. Conditioning cells with growth stimuli before CXCL12 exposure increased the number of cells that initiated CXCR4 signaling and the amplitude of Akt and ERK activation. Data-driven, single-cell computational modeling revealed that growth factor conditioning modulated CXCR4-dependent activation of Akt and ERK by decreasing extrinsic noise (preexisting cell-to-cell differences in kinase activity) in PI3K and mTORC1. Modeling established mTORC1 as critical for tuning single-cell responses to CXCL12-CXCR4 signaling. Our single-cell model predicted how combinations of extrinsic noise in PI3K, Ras, and mTORC1 superimposed on different driver mutations in the ERK and/or Akt pathways to bias CXCR4 signaling. Computational experiments correctly predicted that selected kinase inhibitors used for cancer therapy shifted subsets of cells to states that were more permissive to CXCR4 activation, suggesting that such drugs may inadvertently potentiate pro-metastatic CXCR4 signaling. Our work establishes how changing environmental inputs modulate CXCR4 signaling in single cells and provides a framework to optimize the development and use of drugs targeting this signaling pathway.

Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer

We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detection of clusters of data in the presence of structural requirements which we encode as algebraic constraints in a linear program. Our clustering method is general and can be tailored to a variety of applications in science and industry. We illustrate our method on a collection of experiments measuring the response of genetically diverse breast cancer cell lines to an array of ligands. Each experiment consists of a cell line–ligand combination, and contains time-course measurements of the early signalling kinases MAPK and AKT at two different ligand dose levels. By imposing appropriate structural constraints and respecting the multi-indexed structure of the data, the analysis of clusters can be optimized for biological interpretation and therapeutic understanding. We then perform a systematic, large-scale exploration of mechanistic models of MAPK–AKT crosstalk for each cluster. This analysis allows us to quantify the heterogeneity of breast cancer cell subtypes, and leads to hypotheses about the signalling mechanisms that mediate the response of the cell lines to ligands.

Sialic Acids in Neurology

Sialic acid (Sia) is involved in many biological activities and commonly occurs as a monosialyl residue at the nonreducing terminal end of glycoconjugates. The loss of activity of UDP-GlcNAc2-epimerase/ManNAc kinase, which is a key enzyme in Sia biosynthesis, is lethal to the embryo, which clearly indicates the importance of Sia in embryogenesis. Occasionally, oligo/polymeric Sia structures such as disialic acid (diSia), oligosialic acid (oligoSia), and polysialic acid (polySia) occur in glycoconjugates. In particular, polySia, a well-known epitope that commonly occurs in neuroinvasive bacteria and vertebrate brains, is one of the most well-known and biologically/neurologically important glycotopes in vertebrates. The biological effects of polySia, especially on neural cell-adhesion molecules, have been well studied, and in-depth knowledge regarding polySia has been accumulated. In addition, the importance of diSia and oligoSia epitopes has been reported. In this chapter, the recent advances in the study of diSia, oligoSia, and polySia residues in glycoproteins in neurology, and their history, definition, occurrence, analytical methods, biosynthesis, and biological functions evaluated by phenotypes of gene-targeted mice, biochemical features, and related diseases are described.

Modulators of Redox Metabolism in Head and Neck Cancer

SIGNIFICANCE

Head and neck squamous cell cancer (HNSCC) is a complex disease characterized by high genetic and metabolic heterogeneity. Radiation therapy (RT) alone or combined with systemic chemotherapy is widely used for treatment of HNSCC as definitive treatment or as adjuvant treatment after surgery. Antibodies against epidermal growth factor receptor are used in definitive or palliative treatment. Recent Advances: Emerging targeted therapies against other proteins of interest as well as programmed cell death protein 1 and programmed death-ligand 1 immunotherapies are being explored in clinical trials.

CRITICAL ISSUES

The disease heterogeneity, invasiveness, and resistance to standard of care RT or chemoradiation therapy continue to constitute significant roadblocks for treatment and patients' quality of life (QOL) despite improvements in treatment modality and the emergence of new therapies over the past two decades.

FUTURE DIRECTIONS

As reviewed here, alterations in redox metabolism occur at all stages of HNSCC management, providing opportunities for improved prevention, early detection, response to therapies, and QOL. Bioinformatics and computational systems biology approaches are key to integrate redox effects with multiomics data from cells and clinical specimens and to identify redox modifiers or modifiable target proteins to achieve improved clinical outcomes. Antioxid. Redox Signal.

Model-based Inference of a Directed Network of Circadian Neurons

The suprachiasmatic nucleus (SCN) is the master clock of the brain. It is a network of neurons that behave like biological oscillators, capable of synchronizing and maintaining daily rhythms. The detailed structure of this network is still unknown, and the role that the connectivity pattern plays in the network’s ability to generate robust oscillations has yet to be fully elucidated. In recent work, we used an information theory–based technique to infer the structure of the functional network for synchronization, from bioluminescence reporter data. Here, we propose a computational method to determine the directionality of the connections between the neurons. We find that most SCN neurons have a similar number of incoming connections, but the number of outgoing connections per neuron varies widely, with the most highly connected neurons residing preferentially in the core.

Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

Insulin plays a central role in glucose homeostasis, and impairment of insulin action causes glucose intolerance and leads to type 2 diabetes mellitus (T2DM). A decrease in the transient peak and sustained increase of circulating insulin following an infusion of glucose accompany T2DM pathogenesis. However, the mechanism underlying this abnormal temporal pattern of circulating insulin concentration remains unknown. Here we show that changes in opposite direction of hepatic and peripheral insulin clearance characterize this abnormal temporal pattern of circulating insulin concentration observed in T2DM. We developed a mathematical model using a hyperglycemic and hyperinsulinemic-euglycemic clamp in 111 subjects, including healthy normoglycemic and diabetic subjects. The hepatic and peripheral insulin clearance significantly increase and decrease, respectively, from healthy to borderline type and T2DM. The increased hepatic insulin clearance reduces the amplitude of circulating insulin concentration, whereas the decreased peripheral insulin clearance changes the temporal patterns of circulating insulin concentration from transient to sustained. These results provide further insight into the pathogenesis of T2DM, and thus may contribute to develop better treatment of this condition.

Type 2 diabetes mellitus (T2DM) is one of the fastest growing public health problems, characterized by chronic hyperglycemia with the failure of glucose homeostasis. Evaluating alteration in biological functions regulating circulating glucose concentration is complicated due to the mutual relation between circulating glucose and insulin. A team led by Wataru Ogawa at Kobe University designed clinical experiments for breaking such feedback relations, and a team led by Shinya Kuroda at University of Tokyo developed mathematical models for specifically quantifying the functions from the clinical data. The estimated model parameters revealed the significant increase in hepatic and decrease in peripheral insulin clearance, which occur before and after insulin delivery into systemic circulation, respectively, from healthy to T2DM subjects. Model analysis suggested these insulin clearances centrally regulate the dynamics of circulating insulin concentration in the glucose-insulin regulatory system.

Long negative feedback loop enhances period tunability of biological oscillators

Oscillatory phenomena play a major role in organisms. In some biological oscillations such as cell cycles and heartbeats, the period can be tuned without significant changes in the amplitude. This property is called (period) tunability, one of the prominent features of biological oscillations. However, how biological oscillators produce tunable oscillations remains largely unexplored. We tackle this question using computational experiments. It has been reported that positive-plus-negative feedback oscillators produce tunable oscillations through the hysteresis-based mechanism. First, in this study, we confirmed that positive-plus-negative feedback oscillators generate tunable oscillations. Second, we found that tunability is positively correlated with the dynamic range of oscillations. Third, we showed that long negative feedback oscillators without any additional positive feedback loops can produce tunable oscillations. Finally, we computationally demonstrated that by lengthening the negative feedback loop, the Repressilator, known as a non-tunable synthetic gene oscillator, can be converted into a tunable oscillator. This work provides synthetic biologists with clues to design tunable gene oscillators.

Understanding the mTOR signaling pathway via mathematical modeling

The mechanistic target of rapamycin (mTOR) is a central regulatory pathway that integrates a variety of environmental cues to control cellular growth and homeostasis by intricate molecular feedbacks. In spite of extensive knowledge about its components, the molecular understanding of how these function together in space and time remains poor and there is a need for Systems Biology approaches to perform systematic analyses. In this work, we review the recent progress how the combined efforts of mathematical models and quantitative experiments shed new light on our understanding of the mTOR signaling pathway. In particular, we discuss the modeling concepts applied in mTOR signaling, the role of multiple feedbacks and the crosstalk mechanisms of mTOR with other signaling pathways. We also discuss the contribution of principles from information and network theory that have been successfully applied in dissecting design principles of the mTOR signaling network. We finally propose to classify the mTOR models in terms of the time scale and network complexity, and outline the importance of the classification toward the development of highly comprehensive and predictive models. WIREs Syst Biol Med 2017, 9:e1379. doi: 10.1002/wsbm.1379 For further resources related to this article, please visit the WIREs website.

Model-based control of the temporal patterns of intracellular signaling in silico

The functions of intracellular signal transduction systems are determined by the temporal behavior of intracellular molecules and their interactions. Of the many dynamical properties of the system, the relationship between the dynamics of upstream molecules and downstream molecules is particularly important. A useful tool in understanding this relationship is a methodology to control the dynamics of intracellular molecules with an extracellular stimulus. However, this is a difficult task because the relationship between the levels of upstream molecules and those of downstream molecules is often not only stochastic, but also time-inhomogeneous, nonlinear, and not one-to-one. In this paper, we present an easy-to-implement model-based control method that makes the target downstream molecule to trace a desired time course by changing the concentration of a controllable upstream molecule. Our method uses predictions from Monte Carlo simulations of the model to decide the strength of the stimulus, while using a particle-based approach to make inferences regarding unobservable states. We applied our method to in silico control problems of insulin-dependent AKT pathway model and EGF-dependent Akt pathway model with system noise. We show that our method can robustly control the dynamics of the intracellular molecules against unknown system noise of various strengths, even in the absence of complete knowledge of the true model of the target system.

Robustness of MEK-ERK Dynamics and Origins of Cell-to-Cell Variability in MAPK Signaling

Cellular signaling processes can exhibit pronounced cell-to-cell variability in genetically identical cells. This affects how individual cells respond differentially to the same environmental stimulus. However, the origins of cell-to-cell variability in cellular signaling systems remain poorly understood. Here, we measure the dynamics of phosphorylated MEK and ERK across cell populations and quantify the levels of population heterogeneity over time using high-throughput image cytometry. We use a statistical modeling framework to show that extrinsic noise, particularly that from upstream MEK, is the dominant factor causing cell-to-cell variability in ERK phosphorylation, rather than stochasticity in the phosphorylation/dephosphorylation of ERK. We furthermore show that without extrinsic noise in the core module, variable (including noisy) signals would be faithfully reproduced downstream, but the within-module extrinsic variability distorts these signals and leads to a drastic reduction in the mutual information between incoming signal and ERK activity.

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Active MEK and ERK levels differ profoundly among genetically identical cells

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A statistical framework is developed to identify the causes of this variability

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Analysis shows that extrinsic noise upstream MEK-ERK module causes cell variability

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Within-module extrinsic variability distorts signals

Functional network inference of the suprachiasmatic nucleus

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.

Challenges in horizontal model integration

Background

Systems Biology has motivated dynamic models of important intracellular processes at the pathway level, for example, in signal transduction and cell cycle control. To answer important biomedical questions, however, one has to go beyond the study of isolated pathways towards the joint study of interacting signaling pathways or the joint study of signal transduction and cell cycle control. Thereby the reuse of established models is preferable, as it will generally reduce the modeling effort and increase the acceptance of the combined model in the field.

Results

Obtaining a combined model can be challenging, especially if the submodels are large and/or come from different working groups (as is generally the case, when models stored in established repositories are used). To support this task, we describe a semi-automatic workflow based on established software tools. In particular, two frequent challenges are described: identification of the overlap and subsequent (re)parameterization of the integrated model.

Conclusions

The reparameterization step is crucial, if the goal is to obtain a model that can reproduce the data explained by the individual models. For demonstration purposes we apply our workflow to integrate two signaling pathways (EGF and NGF) from the BioModels Database.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0266-3) contains supplementary material, which is available to authorized users.

Glucose Homeostatic Law: Insulin Clearance Predicts the Progression of Glucose Intolerance in Humans

Homeostatic control of blood glucose is regulated by a complex feedback loop between glucose and insulin, of which failure leads to diabetes mellitus. However, physiological and pathological nature of the feedback loop is not fully understood. We made a mathematical model of the feedback loop between glucose and insulin using time course of blood glucose and insulin during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps in 113 subjects with variety of glucose tolerance including normal glucose tolerance (NGT), impaired glucose tolerance (IGT) and type 2 diabetes mellitus (T2DM). We analyzed the correlation of the parameters in the model with the progression of glucose intolerance and the conserved relationship between parameters. The model parameters of insulin sensitivity and insulin secretion significantly declined from NGT to IGT, and from IGT to T2DM, respectively, consistent with previous clinical observations. Importantly, insulin clearance, an insulin degradation rate, significantly declined from NGT, IGT to T2DM along the progression of glucose intolerance in the mathematical model. Insulin clearance was positively correlated with a product of insulin sensitivity and secretion assessed by the clamp analysis or determined with the mathematical model. Insulin clearance was correlated negatively with postprandial glucose at 2h after oral glucose tolerance test. We also inferred a square-law between the rate constant of insulin clearance and a product of rate constants of insulin sensitivity and secretion in the model, which is also conserved among NGT, IGT and T2DM subjects. Insulin clearance shows a conserved relationship with the capacity of glucose disposal among the NGT, IGT and T2DM subjects. The decrease of insulin clearance predicts the progression of glucose intolerance.

Band-pass processing in a GPCR signaling pathway selects for NFAT transcription factor activation

Many biological processes are rhythmic and proper timing is increasingly appreciated as being critical for development and maintenance of physiological functions. To understand how temporal modulation of an input signal influences downstream responses, we employ microfluidic pulsatile stimulation of a G-protein coupled receptor, the muscarinic M3 receptor, in single cells with simultaneous real-time imaging of both intracellular calcium and NFAT nuclear localization. Interestingly, we find that reduced stimulation with pulses of ligand can give more efficient transcription factor activation, if stimuli are timed appropriately. Our experiments and computational analyses show that M3 receptor-induced calcium oscillations form a low pass filter while calcium-induced NFAT translocation forms a high pass filter. The combination acts as a band-pass filter optimized for intermediate frequencies of stimulation. We demonstrate that receptor desensitization and NFAT translocation rates determine critical features of the band-pass filter and that the band-pass may be shifted for different receptors or NFAT dynamics. As an example, we show that the two NFAT isoforms (NFAT4 and NFAT1) have shifted band-pass windows for the same receptor. While we focus specifically on the M3 muscarinic receptor and NFAT translocation, band-pass processing is expected to be a general theme that applies to multiple signaling pathways.

An optogenetic system for interrogating the temporal dynamics of Akt

The dynamic activity of the serine/threonine kinase Akt is crucial for the regulation of diverse cellular functions, but the precise spatiotemporal control of its activity remains a critical issue. Herein, we present a photo-activatable Akt (PA-Akt) system based on a light-inducible protein interaction module of Arabidopsis thaliana cryptochrome2 (CRY2) and CIB1. Akt fused to CRY2phr, which is a minimal light sensitive domain of CRY2 (CRY2-Akt), is reversibly activated by light illumination in several minutes within a physiological dynamic range and specifically regulates downstream molecules and inducible biological functions. We have generated a computational model of CRY2-Akt activation that allows us to use PA-Akt to control the activity quantitatively. The system provides evidence that the temporal patterns of Akt activity are crucial for generating one of the downstream functions of the Akt-FoxO pathway; the expression of a key gene involved in muscle atrophy (Atrogin-1). The use of an optical module with computational modeling represents a general framework for interrogating the temporal dynamics of biomolecules by predictive manipulation of optogenetic modules.

A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems

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We propose the dQSSA model as a novel way of modelling complex biological networks.

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No low enzyme concentration assumption, covering more biological settings.

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Reduces the number of parameters, which simplifies optimisation.

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dQSSA was validated both in silico and in vitro.

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Both biochemical and signalling pathways can be modelled accurately and simply.

Quasi steady-state enzyme kinetic models are increasingly used in systems modelling. The Michaelis Menten model is popular due to its reduced parameter dimensionality, but its low-enzyme and irreversibility assumption may not always be valid in the in vivo context. Whilst the total quasi-steady state assumption (tQSSA) model eliminates the reactant stationary assumptions, its mathematical complexity is increased. Here, we propose the differential quasi-steady state approximation (dQSSA) kinetic model, which expresses the differential equations as a linear algebraic equation. It eliminates the reactant stationary assumptions of the Michaelis Menten model without increasing model dimensionality. The dQSSA was found to be easily adaptable for reversible enzyme kinetic systems with complex topologies and to predict behaviour consistent with mass action kinetics in silico. Additionally, the dQSSA was able to predict coenzyme inhibition in the reversible lactate dehydrogenase enzyme, which the Michaelis Menten model failed to do. Whilst the dQSSA does not account for the physical and thermodynamic interactions of all intermediate enzyme-substrate complex states, it is proposed to be suitable for modelling complex enzyme mediated biochemical systems. This is due to its simpler application, reduced parameter dimensionality and improved accuracy.

Quantitative analysis of receptor tyrosine kinase-effector coupling at functionally relevant stimulus levels

A major goal of current signaling research is to develop a quantitative understanding of how receptor activation is coupled to downstream signaling events and to functional cellular responses. Here, we measure how activation of the RET receptor tyrosine kinase on mouse neuroblastoma cells by the neurotrophin artemin (ART) is quantitatively coupled to key downstream effectors. We show that the efficiency of RET coupling to ERK and Akt depends strongly on ART concentration, and it is highest at the low (∼100 pM) ART levels required for neurite outgrowth. Quantitative discrimination between ERK and Akt pathway signaling similarly is highest at this low ART concentration. Stimulation of the cells with 100 pM ART activated RET at the rate of ∼10 molecules/cell/min, leading at 5-10 min to a transient peak of ∼150 phospho-ERK (pERK) molecules and ∼50 pAkt molecules per pRET, after which time the levels of these two signaling effectors fell by 25-50% while the pRET levels continued to slowly rise. Kinetic experiments showed that signaling effectors in different pathways respond to RET activation with different lag times, such that the balance of signal flux among the different pathways evolves over time. Our results illustrate that measurements using high, super-physiological growth factor levels can be misleading about quantitative features of receptor signaling. We propose a quantitative model describing how receptor-effector coupling efficiency links signal amplification to signal sensitization between receptor and effector, thereby providing insight into design principles underlying how receptors and their associated signaling machinery decode an extracellular signal to trigger a functional cellular outcome.

Quantitative Analysis of Robustness of Dynamic Response and Signal Transfer in Insulin mediated PI3K/AKT Pathway

Robustness is a critical feature of signaling pathways ensuring signal propagation with high fidelity in the event of perturbations. Here we present a detailed quantitative analysis of robustness in insulin mediated PI3K/AKT pathway, a critical signaling pathway maintaining self-renewal in human embryonic stem cells. Using global sensitivity analysis, we identified robustness promoting mechanisms that ensure (1) maintenance of a first order or overshoot dynamics of self-renewal molecule, p-AKT and (2) robust transfer of signals from oscillatory insulin stimulus to p-AKT in the presence of noise. Our results indicate that negative feedback controls the robustness to most perturbations. Faithful transfer of signal from the stimulating ligand to p-AKT occurs even in the presence of noise, albeit with signal attenuation and high frequency cut-off. Negative feedback contributes to signal attenuation, while positive regulators upstream of PIP₃ contribute to signal amplification. These results establish precise mechanisms to modulate self-renewal molecules like p-AKT.

Three level signal transduction cascades lead to reliably timed switches

Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades.

Polysialic acid: biosynthesis, novel functions and applications

As an anti-adhesive, a reservoir for key biological molecules, and a modulator of signaling, polysialic acid (polySia) is critical for nervous system development and maintenance, promotes cancer metastasis, tissue regeneration and repair, and is implicated in psychiatric diseases. In this review, we focus on the biosynthesis and functions of mammalian polySia, and the use of polySia in therapeutic applications. PolySia modifies a small subset of mammalian glycoproteins, with the neural cell adhesion molecule, NCAM, serving as its major carrier. Studies show that mammalian polysialyltransferases employ a unique recognition mechanism to limit the addition of polySia to a select group of proteins. PolySia has long been considered an anti-adhesive molecule, and its impact on cell adhesion and signaling attributed directly to this property. However, recent studies have shown that polySia specifically binds neurotrophins, growth factors, and neurotransmitters and that this binding depends on chain length. This work highlights the importance of considering polySia quality and quantity, and not simply its presence or absence, as its various roles are explored. The capsular polySia of neuroinvasive bacteria allows these organisms to evade the host immune response. While this "stealth" characteristic has made meningitis vaccine development difficult, it has also made polySia a worthy replacement for polyetheylene glycol in the generation of therapeutic proteins with low immunogenicity and improved circulating half-lives. Bacterial polysialyltransferases are more promiscuous than the protein-specific mammalian enzymes, and new studies suggest that these enzymes have tremendous therapeutic potential, especially for strategies aimed at neural regeneration and tissue repair.

The EGFR demonstrates linear signal transmission

Cells sense information encoded in extracellular ligand concentrations and process it using intracellular signalling cascades. Using mathematical modelling and high-throughput imaging of individual cells, we studied how a transient extracellular growth factor signal is sensed by the epidermal growth factor receptor system, processed by downstream signalling, and transmitted to the nucleus. We found that transient epidermal growth factor signals are linearly translated into an activated epidermal growth factor receptor integrated over time. This allows us to generate a simplified model of receptor signaling where the receptor acts as a perfect sensor of extracellular information, while the nonlinear input-output relationship of EGF-EGFR triggered signalling is a consequence of the downstream MAPK cascade alone.

Information theory and signal transduction systems: from molecular information processing to network inference

Sensing and responding to the environment are two essential functions that all biological organisms need to master for survival and successful reproduction. Developmental processes are marshalled by a diverse set of signalling and control systems, ranging from systems with simple chemical inputs and outputs to complex molecular and cellular networks with non-linear dynamics. Information theory provides a powerful and convenient framework in which such systems can be studied; but it also provides the means to reconstruct the structure and dynamics of molecular interaction networks underlying physiological and developmental processes. Here we supply a brief description of its basic concepts and introduce some useful tools for systems and developmental biologists. Along with a brief but thorough theoretical primer, we demonstrate the wide applicability and biological application-specific nuances by way of different illustrative vignettes. In particular, we focus on the characterisation of biological information processing efficiency, examining cell-fate decision making processes, gene regulatory network reconstruction, and efficient signal transduction experimental design.

S-Fms signalobody enhances myeloid cell growth and migration

Since receptor tyrosine kinases (RTKs) control various cell fates in many types of cells, mimicry of RTK functions is promising for artificial control of cell fates. We have previously developed single-chain Fv (scFv)/receptor chimeras named signalobodies that can mimic receptor signaling in response to a specific antigen. While the RTK-based signalobodies enabled us to control cell growth and migration, further extension of applicability in another cell type would underlie the impact of the RTK-based signalobodies. In this study, we applied the scFv-c-Fms (S-Fms) signalobody in a murine myeloid progenitor cell line, FDC-P1. S-Fms transduced a fluorescein-conjugated BSA (BSA-FL)-dependent growth signal and activated downstream signaling molecules including MEK, ERK, Akt, and STAT3, which are major constituents of Ras/MAPK, PI3K/Akt, and JAK/STAT signaling pathways. In addition, S-Fms transduced a migration signal as demonstrated by the transwell-based migration assay. Direct real-time observation of the cells further confirmed that FDC/S-Fms cells underwent directional cell migration toward a positive gradient of BSA-FL. These results demonstrated the utility of the S-Fms signalobody for controlling growth and migration of myeloid cells. Further extension of our approach includes economical large-scale production of practically relevant blood cells as well as artificial control of cell migration for tissue regeneration and immune response.