Dynamical modeling and multi-experiment fitting with PottersWheel

Transcriptomics-inferred dynamics of SARS-CoV-2 interactions with host epithelial cells

Virus-host interactions can reveal potentially effective and selective therapeutic targets for treating infection. Here, we performed an integrated analysis of the dynamics of virus replication and the host cell transcriptional response to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection using human Caco-2 colon cancer cells as a model. Time-resolved RNA sequencing revealed that, upon infection, cells immediately transcriptionally activated genes associated with inflammatory pathways that mediate the antiviral response, which was followed by an increase in the expression of genes involved in ribosome and mitochondria function, thus suggesting rapid alterations in protein production and cellular energy supply. At later stages, between 24 and 48 hours after infection, the expression of genes involved in metabolic processes-in particular, those related to xenobiotic metabolism-was decreased. Mathematical modeling incorporating SARS-CoV-2 replication suggested that SARS-CoV-2 proteins inhibited the host antiviral response and that virus transcripts exceeded the translation capacity of the host cells. Targeting kinase-dependent pathways that exhibited increases in transcription in host cells was as effective as a virus-targeted inhibitor at repressing viral replication. Our findings in this model system delineate a sequence of SARS-CoV-2 virus-host interactions that may facilitate the identification of druggable host pathways to suppress infection.

Physiologically Based Pharmacokinetic Modeling of Nanoparticle Biodistribution: A Review of Existing Models, Simulation Software, and Data Analysis Tools

Cancer treatment and pharmaceutical development require targeted treatment and less toxic therapeutic intervention to achieve real progress against this disease. In this scenario, nanomedicine emerged as a reliable tool to improve drug pharmacokinetics and to translate to the clinical biologics based on large molecules. However, the ability of our body to recognize foreign objects together with carrier transport heterogeneity derived from the combination of particle physical and chemical properties, payload and surface modification, make the designing of effective carriers very difficult. In this scenario, physiologically based pharmacokinetic modeling can help to design the particles and eventually predict their ability to reach the target and treat the tumor. This effort is performed by scientists with specific expertise and skills and familiarity with artificial intelligence tools such as advanced software that are not usually in the "cords" of traditional medical or material researchers. The goal of this review was to highlight the advantages that computational modeling could provide to nanomedicine and bring together scientists with different background by portraying in the most simple way the work of computational developers through the description of the tools that they use to predict nanoparticle transport and tumor targeting in our body.

Modulation of signaling cross-talk between pJNK and pAKT generates optimal apoptotic response

Tumor necrosis factor alpha (TNFα) is a well-known modulator of apoptosis by maintaining a balance between proliferation and cell-death in normal cells. Cancer cells often evade apoptotic response following TNFα stimulation by altering signaling cross-talks. Thus, varying the extent of signaling cross-talk could enable optimal TNFα mediated apoptotic dynamics. Herein, we use an experimental data-driven mathematical modeling to quantitate the extent of synergistic signaling cross-talk between the intracellular entities phosphorylated JNK (pJNK) and phosphorylated AKT (pAKT) that orchestrate the phenotypic apoptosis level by modulating the activated Caspase3 dynamics. Our study reveals that this modulation is orchestrated by the distinct dynamic nature of the synergism at early and late phases. We show that this synergism in signal flow is governed by branches originating from either TNFα receptor and NFκB, which facilitates signaling through survival pathways. We demonstrate that the experimentally quantified apoptosis levels semi-quantitatively correlates with the model simulated Caspase3 transients. Interestingly, perturbing pJNK and pAKT transient dynamics fine-tunes this accumulated Caspase3 guided apoptotic response. Thus, our study offers useful insights for identifying potential targeted therapies for optimal apoptotic response.

Optimization of synthetic molecular reporters for a mesenchymal glioblastoma transcriptional program by integer programing

MOTIVATION

A recent approach to perform genetic tracing of complex biological problems involves the generation of synthetic deoxyribonucleic acid (DNA) probes that specifically mark cells with a phenotype of interest. These synthetic locus control regions (sLCRs), in turn, drive the expression of a reporter gene, such as fluorescent protein. To build functional and specific sLCRs, it is critical to accurately select multiple bona fide cis-regulatory elements from the target cell phenotype cistrome. This selection occurs by maximizing the number and diversity of transcription factors (TFs) within the sLCR, yet the size of the final sLCR should remain limited.

RESULTS

In this work, we discuss how optimization, in particular integer programing, can be used to systematically address the construction of a specific sLCR and optimize pre-defined properties of the sLCR. Our presented instance of a linear optimization problem maximizes the activation potential of the sLCR such that its size is limited to a pre-defined length and a minimum number of all TFs deemed sufficiently characteristic for the phenotype of interest is covered. We generated an sLCR to trace the mesenchymal glioblastoma program in patients by solving our corresponding linear program with the software optimizer Gurobi. Considering the binding strength of transcription factor binding sites (TFBSs) with their TFs as a proxy for activation potential, the optimized sLCR scores similarly to an sLCR experimentally validated in vivo, and is smaller in size while having the same coverage of TFBSs.

AVAILABILITY AND IMPLEMENTATION

We provide a Python implementation of the presented framework in the Supplementary Material with which an optimal selection of cis-regulatory elements can be calculated once the target set of TFs and their binding strength with their TFBSs is known.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A modular systems biological modelling framework studies cyclic nucleotide signaling in platelets

BACKGROUND

The cyclic nucleotides cAMP and cGMP inhibit platelet activation. Different platelet signaling modules work together. We develop here a modelling framework to integrate different signaling modules and apply it to platelets.

RESULTS

We introduce a novel standardized bilinear coupling mechanism allowing sub model debugging and standardization of coupling with optimal data driven modelling by methods from optimization. Besides cAMP signaling our model considers specific cGMP effects including external stimuli by drugs. Moreover, the output of the cGMP module serves as input for a modular model of VASP phosphorylation and for the activity of cAMP and cGMP pathways in platelets. Experimental data driven modeling allows us to design models with quantitative output. We use the condensed information about involved regulation and system responses for modeling drug effects and obtaining optimal experimental settings. Stepwise further validation of our model is given by direct experimental data.

CONCLUSIONS

We present a general framework for model integration using modules and their stimulus responses. We demonstrate it by a multi-modular model for platelet signaling focusing on cGMP and VASP phosphorylation. Moreover, this allows to estimate drug action on any of the inhibitory cyclic nucleotide pathways (cGMP, cAMP) and is supported by experimental data.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

Temporal control of the integrated stress response by a stochastic molecular switch

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

GAMES: A Dynamic Model Development Workflow for Rigorous Characterization of Synthetic Genetic Systems

Mathematical modeling is invaluable for advancing understanding and design of synthetic biological systems. However, the model development process is complicated and often unintuitive, requiring iteration on various computational tasks and comparisons with experimental data. Ad hoc model development can pose a barrier to reproduction and critical analysis of the development process itself, reducing the potential impact and inhibiting further model development and collaboration. To help practitioners manage these challenges, we introduce the Generation and Analysis of Models for Exploring Synthetic Systems (GAMES) workflow, which includes both automated and human-in-the-loop processes. We systematically consider the process of developing dynamic models, including model formulation, parameter estimation, parameter identifiability, experimental design, model reduction, model refinement, and model selection. We demonstrate the workflow with a case study on a chemically responsive transcription factor. The generalizable workflow presented in this tutorial can enable biologists to more readily build and analyze models for various applications.

Relationship Between Dimensionality and Convergence of Optimization Algorithms: A Comparison Between Data-Driven Normalization and Scaling Factor-Based Methods Using PEPSSBI

Ordinary differential equation models are used to represent intracellular signaling pathways in silico, aiding and guiding biological experiments to elucidate intracellular regulation. To construct such quantitative and predictive models of intracellular interactions, unknown parameters need to be estimated. Most of biological data are expressed in relative or arbitrary units, raising the question of how to compare model simulations with data. It has recently been shown that for models with large number of unknown parameters, fitting algorithms using a data-driven normalization of the simulations (DNS) performs best in terms of the convergence time and parameter identifiability. DNS approach compares model simulations and corresponding data both normalized by the same normalization procedure, without requiring additional parameters to be estimated, as necessary for widely used scaling factor-based methods. However, currently there is no parameter estimation software that directly supports DNS. In this chapter, we show how to apply DNS to dynamic models of systems and synthetic biology using PEPSSBI (Parameter Estimation Pipeline for Systems and Synthetic Biology). PEPSSBI is the first software that supports DNS, through algorithmically supported data normalization and objective function construction. PEPSSBI also supports model import using SBML and repeated parameter estimation runs executed in parallel either on a personal computer or a multi-CPU cluster.

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.

A generic approach to decipher the mechanistic pathway of heterogeneous protein aggregation kinetics

Amyloid formation is a generic property of many protein/polypeptide chains. A broad spectrum of proteins, despite having diversity in the inherent precursor sequence and heterogeneity present in the mechanism of aggregation produces a common cross β-spine structure that is often associated with several human diseases. However, a general modeling framework to interpret amyloid formation remains elusive. Herein, we propose a data-driven mathematical modeling approach that elucidates the most probable interaction network for the aggregation of a group of proteins (α-synuclein, Aβ42, Myb, and TTR proteins) by considering an ensemble set of network models, which include most of the mechanistic complexities and heterogeneities related to amyloidogenesis. The best-fitting model efficiently quantifies various timescales involved in the process of amyloidogenesis and explains the mechanistic basis of the monomer concentration dependency of amyloid-forming kinetics. Moreover, the present model reconciles several mutant studies and inhibitor experiments for the respective proteins, making experimentally feasible non-intuitive predictions, and provides further insights about how to fine-tune the various microscopic events related to amyloid formation kinetics. This might have an application to formulate better therapeutic measures in the future to counter unwanted amyloidogenesis. Importantly, the theoretical method used here is quite general and can be extended for any amyloid-forming protein.

An effective model of endogenous clocks and external stimuli determining circadian rhythms

Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/ .

Modeling the Nonlinear Dynamics of Intracellular Signaling Networks

This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.

Intricate Genetic Programs Controlling Dormancy in Mycobacterium tuberculosis

Mycobacterium tuberculosis (MTB) displays the remarkable ability to transition in and out of dormancy, a hallmark of the pathogen’s capacity to evade the immune system and exploit susceptible individuals. Uncovering the gene regulatory programs that underlie the phenotypic shifts in MTB during disease latency and reactivation has posed a challenge. We develop an experimental system to precisely control dissolved oxygen levels in MTB cultures in order to capture the transcriptional events that unfold as MTB transitions into and out of hypoxia-induced dormancy. Using a comprehensive genome-wide transcription factor binding map and insights from network topology analysis, we identify regulatory circuits that deterministically drive sequential transitions across six transcriptionally and functionally distinct states encompassing more than three-fifths of the MTB genome. The architecture of the genetic programs explains the transcriptional dynamics underlying synchronous entry of cells into a dormant state that is primed to infect the host upon encountering favorable conditions.

Mycobacterium tuberculosis (MTB) persists within the host by counteracting disparate stressors including hypoxia. Peterson et al. report a transcriptional program that coordinates sequential state transitions to drive MTB in and out of hypoxia-induced dormancy. Among varied properties, this program encodes advanced preparedness to infect the host in favorable conditions.

Benchmarking of numerical integration methods for ODE models of biological systems

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

Simple Kinetic Models in Molecular Chronobiology

Circadian rhythms are constituted by a complex dynamical system with intertwined feedback loops, molecular switches, and self-sustained oscillations. Mathematical modeling supports understanding available heterogeneous kinetic data, highlights basic mechanisms, and can guide experimental research. Here, we introduce the basic steps from a biological question to simple models providing insight into gene-regulatory mechanisms. We illustrate the general approach by three examples: modeling decay processes, clock-controlled genes, and self-sustained oscillations.

Modeling COVID-19 epidemic in Heilongjiang province, China

The Coronavirus Disease 2019 (COVID-19) surges worldwide. However, massive imported patients especially into Heilongjiang Province in China recently have been an alert for local COVID-19 outbreak. We collected data from January 23 to March 25 from Heilongjiang province and trained an ordinary differential equation model to fit the epidemic data. We extended the simulation using this trained model to characterize the effect of an imported 'escaper'. We showed that an imported 'escaper' was responsible for the newly confirmed COVID-19 infections from Apr 9 to Apr 19 in Heilongjiang province. Stochastic simulations further showed that significantly increased local contacts among imported 'escaper', its epidemiologically associated cases and susceptible populations greatly contributed to the local outbreak of COVID-19. Meanwhile, we further found that the reported number of asymptomatic patients was markedly lower than model predictions implying a large asymptomatic pool which was not identified. We further forecasted the effect of implementing strong interventions immediately to impede COVID-19 outbreak for Heilongjiang province. Implementation of stronger interventions to lower mutual contacts could accelerate the complete recovery from coronavirus infections in Heilongjiang province. Collectively, our model has characterized the epidemic of COVID-19 in Heilongjiang province and implied that strongly controlled measured should be taken for infected and asymptomatic patients to minimize total infections.

Estimating the effects of asymptomatic and imported patients on COVID-19 epidemic using mathematical modeling

The epidemic of Coronavirus Disease 2019 has been a serious threat to public health worldwide. Data from 23 January to 31 March at Jiangsu and Anhui provinces in China were collected. We developed an adjusted model with two novel features: the asymptomatic population and threshold behavior in recovery. Unbiased parameter estimation identified faithful model fitting. Our model predicted that the epidemic for asymptomatic patients (ASP) was similar in both provinces. The latent periods and outbreak sizes are extremely sensitive to strongly controlled interventions such as isolation and quarantine for both asymptomatic and imported cases. We predicted that ASP serve as a more severe factor with faster outbreaks and larger outbreak sizes compared with imported patients. Therefore, we argued that the currently strict interventions should be continuously implemented, and unraveling the asymptomatic pool is critically important before preventive strategy such as vaccines.

A mathematical model with threshold behavior in recovery and asymptomatic patients.

Asymptomatic infections may trigger faster outbreak with larger outbreak size.

COVID‐19 outbreak size and latent period are sensitive to mutual contacts.

Strict interventions should be implemented to restrict potential outbreak.

A multi-inverse approach for a holistic understanding of applied animal science systems

Technological and mathematical advances have provided opportunities to investigate new approaches for the holistic quantification of complex biological systems. One objective of these approaches, including the multi-inverse deterministic approach proposed in this paper, is to deepen the understanding of biological systems through the structural development of a useful, best-fitted inverse mechanistic model. The objective of the present work was to evaluate the capacity of a deterministic approach, that is, the multi-inverse approach (MIA), to yield meaningful quantitative nutritional information. To this end, a case study addressing the effect of diet composition on sheep weight was performed using data from a previous experiment on saccharina (a sugarcane byproduct), and an inverse deterministic model (named Paracoa) was developed. The MIA successfully revealed an increase in the final weight of sheep with an increase in the percentage of corn in the diet. Although the soluble fraction also increased with increasing corn percentage, the effective nonsoluble degradation increased fourfold, indicating that the increased weight gain resulted from the nonsoluble substrate. A profile likelihood analysis showed that the potential best-fitted model had identifiable parameters, and that the parameter relationships were affected by the type of data, number of parameters and model structure. It is necessary to apply the MIA to larger and/or more complex datasets to obtain a clearer understanding of its potential.

Coupling Cas9 to artificial inhibitory domains enhances CRISPR-Cas9 target specificity

The limited target specificity of CRISPR-Cas nucleases poses a challenge with respect to their application in research and therapy. Here, we present a simple and original strategy to enhance the specificity of CRISPR-Cas9 genome editing by coupling Cas9 to artificial inhibitory domains. Applying a combination of mathematical modeling and experiments, we first determined how CRISPR-Cas9 activity profiles relate to Cas9 specificity. We then used artificially weakened anti-CRISPR (Acr) proteins either coexpressed with or directly fused to Cas9 to fine-tune its activity toward selected levels, thereby achieving an effective kinetic insulation of ON- and OFF-target editing events. We demonstrate highly specific genome editing in mammalian cells using diverse single-guide RNAs prone to potent OFF-targeting. Last, we show that our strategy is compatible with different modes of delivery, including transient transfection and adeno-associated viral vectors. Together, we provide a highly versatile approach to reduce CRISPR-Cas OFF-target effects via kinetic insulation.

Intestinal Fish Cell Barrier Model to Assess Transfer of Organic Chemicals in Vitro: An Experimental and Computational Study

We studied the role of the fish intestine as a barrier for organic chemicals using the epithelial barrier model built on the rainbow trout (Oncorhynchus mykiss) intestinal cell line, RTgutGC and the newly developed exposure chamber, TransFEr, specifically designed to work with hydrophobic and volatile chemicals. Testing 11 chemicals with a range of physicochemical properties (logK_OW: 2.2 to 6.3, logHLC: 6.1 to 2.3) and combining the data with a mechanistic kinetic model enabled the determination of dominant processes underlying the transfer experiments and the derivation of robust transfer rates. Against the current assumption in chemical uptake modeling, chemical transfer did not strictly depend on the logK_OW but resulted from chemical-specific intracellular accumulation and biotransformation combined with paracellular and active transport. Modeling also identified that conducting elaborate measurements of the plastic parts, including the polystyrene insert and the PET filter, is unnecessary and that stirring in the TransFEr chamber reduced the stagnant water layers compared to theoretical predictions. Aside from providing insights into chemical uptake via the intestinal epithelium, this system can easily be transferred to other cell-based barrier systems, such as the fish gill or mammalian intestinal models and may improve in vitro-in vivo extrapolation and prediction of chemical bioaccumulation into organisms.

Estrogen receptors promote NSCLC progression by modulating the membrane receptor signaling network: a systems biology perspective

Background

Estrogen receptors (ERs) are thought to play an important role in non-small cell lung cancer (NSCLC). However, the effect of ERs in NSCLC is still controversial and needs further investigation. A new consideration is that ERs may affect NSCLC progression through complicated molecular signaling networks rather than individual targets. Therefore, this study aims to explore the effect of ERs in NSCLC from the perspective of cancer systems biology.

Methods

The gene expression profile of NSCLC samples in TCGA dataset was analyzed by bioinformatics method. Variations of cell behaviors and protein expression were detected in vitro. The kinetic process of molecular signaling network was illustrated by a systemic computational model. At last, immunohistochemical (IHC) and survival analysis was applied to evaluate the clinical relevance and prognostic effect of key receptors in NSCLC.

Results

Bioinformatics analysis revealed that ERs might affect many cancer-related molecular events and pathways in NSCLC, particularly membrane receptor activation and signal transduction, which might ultimately lead to changes in cell behaviors. Experimental results confirmed that ERs could regulate cell behaviors including cell proliferation, apoptosis, invasion and migration; ERs also regulated the expression or activation of key members in membrane receptor signaling pathways such as epidermal growth factor receptor (EGFR), Notch1 and Glycogen synthase kinase-3β/β-Catenin (GSK3β/β-Catenin) pathways. Modeling results illustrated that the promotive effect of ERs in NSCLC was implemented by modulating the signaling network composed of EGFR, Notch1 and GSK3β/β-Catenin pathways; ERs maintained and enhanced the output of oncogenic signals by adding redundant and positive-feedback paths into the network. IHC results echoed that high expression of ERs, EGFR and Notch1 had a synergistic effect on poor prognosis of advanced NSCLC.

Conclusions

This study indicated that ERs were likely to promote NSCLC progression by modulating the integrated membrane receptor signaling network composed of EGFR, Notch1 and GSK3β/β-Catenin pathways and then affecting tumor cell behaviors. It also complemented the molecular mechanisms underlying the progression of NSCLC and provided new opportunities for optimizing therapeutic scheme of NSCLC.

Systems NMR: single-sample quantification of RNA, proteins and metabolites for biomolecular network analysis

Cellular behavior is controlled by the interplay of diverse biomolecules. Most experimental methods, however, can only monitor a single molecule class or reaction type at a time. We developed an in vitro nuclear magnetic resonance spectroscopy (NMR) approach, which permitted dynamic quantification of an entire 'heterotypic' network-simultaneously monitoring three distinct molecule classes (metabolites, proteins and RNA) and all elementary reaction types (bimolecular interactions, catalysis, unimolecular changes). Focusing on an eight-reaction co-transcriptional RNA folding network, in a single sample we recorded over 35 time points with over 170 observables each, and accurately determined five core reaction constants in multiplex. This reconstruction revealed unexpected cross-talk between the different reactions. We further observed dynamic phase-separation in a system of five distinct RNA-binding domains in the course of the RNA transcription reaction. Our Systems NMR approach provides a deeper understanding of biological network dynamics by combining the dynamic resolution of biochemical assays and the multiplexing ability of 'omics'.

Identifying important parameters in the inflammatory process with a mathematical model of immune cell influx and macrophage polarization

In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage polarization, with the simplifying assumption that macrophages can be classified as M1 or M2. With this model, we were able to reproduce the expected timing of sequential influx of immune cells and mediators in a general inflammatory setting. We then fit this model to in vivo experimental data obtained from a mouse peritonitis model of inflammation, which is widely used to evaluate endogenous processes in response to an inflammatory stimulus. Model robustness is explored with local structural and practical identifiability of the proposed model a posteriori. Additionally, we perform sensitivity analysis that identifies the population of apoptotic neutrophils as a key driver of the inflammatory process. Finally, we simulate a selection of proposed therapies including points of intervention in the case of delayed neutrophil apoptosis, which our model predicts will result in a sustained inflammatory response. Our model can therefore provide hypothesis testing for therapeutic interventions that target macrophage phenotype and predict outcomes to be validated by subsequent experimentation.

Using experimental data and mathematical analysis, we develop a model for the inflammatory response that includes macrophage polarization between M1 and M2 phenotypes. Dysfunction of this phenotypic switch can disrupt the timely influx and egress of immune cells during the healing process and lead to chronic wounds or disease. The modulation of macrophage population has been suggested as a strategy to dampen inflammation in diseases that feature chronic inflammation, such as diabetes and atherosclerosis. It is therefore important that we learn more about which components of the system drive the population level switch in phenotype. Our model is able to reproduce the expected timing of sequential influx of neutrophils and macrophages in response to an inflammatory stimulus. Model parameters were estimated with weighted least squares fitting to in vivo experimental data from a mouse model of peritonitis while considering identifiability of parameter sets. We perform sensitivity analysis that identifies primary drivers of the system, and predict the effects of variations in these key parameters on immune cell populations.

How to Steer and Control ERK and the ERK Signaling Cascade Exemplified by Looking at Cardiac Insufficiency

Mathematical optimization framework allows the identification of certain nodes within a signaling network. In this work, we analyzed the complex extracellular-signal-regulated kinase 1 and 2 (ERK1/2) cascade in cardiomyocytes using the framework to find efficient adjustment screws for this cascade that is important for cardiomyocyte survival and maladaptive heart muscle growth. We modeled optimal pharmacological intervention points that are beneficial for the heart, but avoid the occurrence of a maladaptive ERK1/2 modification, the autophosphorylation of ERK at threonine 188 (ERK Thr 188 phosphorylation), which causes cardiac hypertrophy. For this purpose, a network of a cardiomyocyte that was fitted to experimental data was equipped with external stimuli that model the pharmacological intervention points. Specifically, two situations were considered. In the first one, the cardiomyocyte was driven to a desired expression level with different treatment strategies. These strategies were quantified with respect to beneficial effects and maleficent side effects and then which one is the best treatment strategy was evaluated. In the second situation, it was shown how to model constitutively activated pathways and how to identify drug targets to obtain a desired activity level that is associated with a healthy state and in contrast to the maleficent expression pattern caused by the constitutively activated pathway. An implementation of the algorithms used for the calculations is also presented in this paper, which simplifies the application of the presented framework for drug targeting, optimal drug combinations and the systematic and automatic search for pharmacological intervention points. The codes were designed such that they can be combined with any mathematical model given by ordinary differential equations.

Community-driven roadmap for integrated disease maps

The Disease Maps Project builds on a network of scientific and clinical groups that exchange best practices, share information and develop systems biomedicine tools. The project aims for an integrated, highly curated and user-friendly platform for disease-related knowledge. The primary focus of disease maps is on interconnected signaling, metabolic and gene regulatory network pathways represented in standard formats. The involvement of domain experts ensures that the key disease hallmarks are covered and relevant, up-to-date knowledge is adequately represented. Expert-curated and computer readable, disease maps may serve as a compendium of knowledge, allow for data-supported hypothesis generation or serve as a scaffold for the generation of predictive mathematical models. This article summarizes the 2nd Disease Maps Community meeting, highlighting its important topics and outcomes. We outline milestones on the roadmap for the future development of disease maps, including creating and maintaining standardized disease maps; sharing parts of maps that encode common human disease mechanisms; providing technical solutions for complexity management of maps; and Web tools for in-depth exploration of such maps. A dedicated discussion was focused on mathematical modeling approaches, as one of the main goals of disease map development is the generation of mathematically interpretable representations to predict disease comorbidity or drug response and to suggest drug repositioning, altogether supporting clinical decisions.

Misinterpretation risks of global stochastic optimisation of kinetic models revealed by multiple optimisation runs

One of use cases for metabolic network optimisation of biotechnologically applied microorganisms is the in silico design of new strains with an improved distribution of metabolic fluxes. Global stochastic optimisation methods (genetic algorithms, evolutionary programing, particle swarm and others) can optimise complicated nonlinear kinetic models and are friendly for unexperienced user: they can return optimisation results with default method settings (population size, number of generations and others) and without adaptation of the model. Drawbacks of these methods (stochastic behaviour, undefined duration of optimisation, possible stagnation and no guaranty of reaching optima) cause optimisation result misinterpretation risks considering the very diverse educational background of the systems biology and synthetic biology research community. Different methods implemented in the COPASI software package are tested in this study to determine their ability to find feasible solutions and assess the convergence speed to the best value of the objective function. Special attention is paid to the potential misinterpretation of results. Optimisation methods are tested with additional constraints that can be introduced to ensure the biological feasibility of the resulting optimised design: (1) total enzyme activity constraint (called also amino acid pool constraint) to limit the sum of enzyme concentrations and (2) homeostatic constraint limiting steady state metabolite concentration corridor around the steady state concentrations of metabolites in the original model. Impact of additional constraints on the performance of optimisation methods and misinterpretation risks is analysed.

Unraveling mitotic protein networks by 3D multiplexed epitope drug screening

Three-dimensional protein localization intricately determines the functional coordination of cellular processes. The complex spatial context of protein landscape has been assessed by multiplexed immunofluorescent staining or mass spectrometry, applied to 2D cell culture with limited physiological relevance or tissue sections. Here, we present 3D SPECS, an automated technology for 3D Spatial characterization of Protein Expression Changes by microscopic Screening. This workflow comprises iterative antibody staining, high-content 3D imaging, and machine learning for detection of mitoses. This is followed by mapping of spatial protein localization into a spherical, cellular coordinate system, a basis for model-based prediction of spatially resolved affinities of proteins. As a proof-of-concept, we mapped twelve epitopes in 3D-cultured spheroids and investigated the network effects of twelve mitotic cancer drugs. Our approach reveals novel insights into spindle fragility and chromatin stress, and predicts unknown interactions between proteins in specific mitotic pathways. 3D SPECS's ability to map potential drug targets by multiplexed immunofluorescence in 3D cell culture combined with our automated high-content assay will inspire future functional protein expression and drug assays.

Modelling and simulation of biased agonism dynamics at a G protein-coupled receptor

Theoretical models of G protein-coupled receptor (GPCR) concentration-response relationships often assume an agonist producing a single functional response via a single active state of the receptor. These models have largely been analysed assuming steady-state conditions. There is now much experimental evidence to suggest that many GPCRs can exist in multiple receptor conformations and elicit numerous functional responses, with ligands having the potential to activate different signalling pathways to varying extents-a concept referred to as biased agonism, functional selectivity or pluri-dimensional efficacy. Moreover, recent experimental results indicate a clear possibility for time-dependent bias, whereby an agonist's bias with respect to different pathways may vary dynamically. Efforts towards understanding the implications of temporal bias by characterising and quantifying ligand effects on multiple pathways will clearly be aided by extending current equilibrium binding and biased activation models to include G protein activation dynamics. Here, we present a new model of time-dependent biased agonism, based on ordinary differential equations for multiple cubic ternary complex activation models with G protein cycle dynamics. This model allows simulation and analysis of multi-pathway activation bias dynamics at a single receptor for the first time, at the level of active G protein (αGTP), towards the analysis of dynamic functional responses. The model is generally applicable to systems with NG G proteins and N* active receptor states. Numerical simulations for NG=N*=2 reveal new insights into the effects of system parameters (including cooperativities, and ligand and receptor concentrations) on bias dynamics, highlighting new phenomena including the dynamic inter-conversion of bias direction. Further, we fit this model to 'wet' experimental data for two competing G proteins (Gi and Gs) that become activated upon stimulation of the adenosine A1 receptor with adenosine derivative compounds. Finally, we show that our model can qualitatively describe the temporal dynamics of this competing G protein activation.

Correlated receptor transport processes buffer single-cell heterogeneity

Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system.

Cell surface receptors translate extracellular ligand concentrations to intracellular responses. Receptor transport between the plasma membrane and other cellular compartments regulates the number of accessible receptors at the plasma membrane that determines the strength of downstream pathway activation at a given ligand concentration. In cell populations, pathway activation strength and cellular responses vary between cells. Understanding origins of cell-to-cell variability is highly relevant for cancer research, motivated by the problem of fractional killing by chemotherapies and development of resistance in subpopulations of tumor cells. The erythropoietin receptor (EpoR) is a characteristic example of a receptor system that strongly depends on receptor transport processes. It is involved in several cellular processes, such as differentiation or proliferation, regulates the renewal of erythrocytes, and is expressed in several tumors. To investigate the involvement of receptor transport processes in cell-to-cell variability, we quantitatively characterized trafficking of EpoR in individual cells by combining live-cell imaging with mathematical modeling. Thereby, we found that EpoR dynamics was strongly dependent on rapid receptor transport and turnover. Interestingly, although transport processes largely differed between individual cells, receptor concentrations in cellular compartments were robust to variability in trafficking processes due to the correlated kinetics of opposing transport processes.

A modeling approach to evaluate the balance between bioactivation and detoxification of MeIQx in human hepatocytes

BACKGROUND

Heterocyclic aromatic amines (HAA) are environmental and food contaminants that are potentially carcinogenic for humans. 2-Amino-3,8-dimethylimidazo[4,5-f]quinoxaline (MeIQx) is one of the most abundant HAA formed in cooked meat. MeIQx is metabolized by cytochrome P450 1A2 in the human liver into detoxificated and bioactivated products. Once bioactivated, MeIQx metabolites can lead to DNA adduct formation responsible for further genome instability.

METHODS

Using a computational approach, we developed a numerical model for MeIQx metabolism in the liver that predicts the MeIQx biotransformation into detoxification or bioactivation pathways according to the concentration of MeIQx.

RESULTS

Our results demonstrate that (1) the detoxification pathway predominates, (2) the ratio between detoxification and bioactivation pathways is not linear and shows a maximum at 10 µM of MeIQx in hepatocyte cell models, and (3) CYP1A2 is a key enzyme in the system that regulates the balance between bioactivation and detoxification. Our analysis suggests that such a ratio could be considered as an indicator of MeIQx genotoxicity at a low concentration of MeIQx.

CONCLUSIONS

Our model permits the investigation of the balance between bioactivation (i.e., DNA adduct formation pathway through the prediction of potential genotoxic compounds) and detoxification of MeIQx in order to predict the behaviour of this environmental contaminant in the human liver. It highlights the importance of complex regulations of enzyme competitions that should be taken into account in any further multi-organ models.

Performance of objective functions and optimisation procedures for parameter estimation in system biology models

Mathematical modelling of signalling pathways aids experimental investigation in system and synthetic biology. Ever increasing data availability prompts the development of large dynamic models with numerous parameters. In this paper, we investigate how the number of unknown parameters affects the convergence of three frequently used optimisation algorithms and four objective functions. We compare objective functions that use data-driven normalisation of the simulations with those that use scaling factors. The data-driven normalisation of the simulation approach implies that simulations are normalised in the same way as the data, making both directly comparable. The scaling factor approach, which is commonly used for parameter estimation in dynamic systems, introduces scaling factors that multiply the simulations to convert them to the scale of the data. Here we show that the scaling factor approach increases, compared to data-driven normalisation of the simulations, the degree of practical non-identifiability, defined as the number of directions in the parameter space, along which parameters are not identifiable. Further, the results indicate that data-driven normalisation of the simulations greatly improve the speed of convergence of all tested algorithms when the overall number of unknown parameters is relatively large (74 parameters in our test problems). Data-driven normalisation of the simulations also markedly improve the performance of the non-gradient-based algorithm tested even when the number of unknown parameters is relatively small (10 parameters in our test problems). As the models and the unknown parameters increase in size, the data-driven normalisation of the simulation approach can be the preferred option, because it does not aggravate non-identifiability and allows for obtaining parameter estimates in a reasonable amount of time.

A systematic comparison of critical choices for faithful parameter-estimation identifies a combination of a hybrid optimisation algorithm (GLSDC) with data-driven normalisation of simulations (DNS) as the generally best option. Experimental data are often provided in relative, arbitrary units. To match simulations to data, two approaches are common: i) using scaling-factors that have to be estimated (SF); or ii) normalising the simulations in the same way as the data (DNS). Using three test-models of increasing complexity, we explored how this choice affects parameter identifiability and estimation performance. We show that in contrast to SF, DNS does not aggravate non-identifiability and a global-hybrid method combined with DNS outperformed local-multi-start methods. The advantage of DNS in terms of estimation speed was particularly pronounced for the most complex test-problem.

Systems modelling ageing: from single senescent cells to simple multi-cellular models

Systems modelling has been successfully used to investigate several key molecular mechanisms of ageing. Modelling frameworks to allow integration of models and methods to enhance confidence in models are now well established. In this article, we discuss these issues and work through the process of building an integrated model for cellular senescence as a single cell and in a simple tissue context.

Search for a Minimal Set of Parameters by Assessing the Total Optimization Potential for a Dynamic Model of a Biochemical Network

Selecting an efficient small set of adjustable parameters to improve metabolic features of an organism is important for a reduction of implementation costs and risks of unpredicted side effects. In practice, to avoid the analysis of a huge combinatorial space for the possible sets of adjustable parameters, experience-, and intuition-based subsets of parameters are often chosen, possibly leaving some interesting counter-intuitive combinations of parameters unrevealed. The combinatorial scan of possible adjustable parameter combinations at the model optimization level is possible; however, the number of analyzed combinations is still limited. The total optimization potential (TOP) approach is proposed to assess the full potential for increasing the value of the objective function by optimizing all possible adjustable parameters. This seemingly unpractical combination of adjustable parameters allows assessing the maximum attainable value of the objective function and stopping the combinatorial space scanning when the desired fraction of TOP is reached and any further increase in the number of adjustable parameters cannot bring any reasonable improvement. The relation between the number of adjustable parameters and the reachable fraction of TOP is a valuable guideline in choosing a rational solution for industrial implementation. The TOP approach is demonstrated on the basis of two case studies.

Identification of Nascent Memory CD8 T Cells and Modeling of Their Ontogeny

Primary immune responses generate short-term effectors and long-term protective memory cells. The delineation of the genealogy linking naive, effector, and memory cells has been complicated by the lack of phenotypes discriminating effector from memory differentiation stages. Using transcriptomics and phenotypic analyses, we identify Bcl2 and Mki67 as a marker combination that enables the tracking of nascent memory cells within the effector phase. We then use a formal approach based on mathematical models describing the dynamics of population size evolution to test potential progeny links and demonstrate that most cells follow a linear naive→early effector→late effector→memory pathway. Moreover, our mathematical model allows long-term prediction of memory cell numbers from a few early experimental measurements. Our work thus provides a phenotypic means to identify effector and memory cells, as well as a mathematical framework to investigate their genealogy and to predict the outcome of immunization regimens in terms of memory cell numbers generated.

Modeling of Receptor Tyrosine Kinase Signaling: Computational and Experimental Protocols

The advent of systems biology has convincingly demonstrated that the integration of experiments and dynamic modelling is a powerful approach to understand the cellular network biology. Here we present experimental and computational protocols that are necessary for applying this integrative approach to the quantitative studies of receptor tyrosine kinase (RTK) signaling networks. Signaling by RTKs controls multiple cellular processes, including the regulation of cell survival, motility, proliferation, differentiation, glucose metabolism, and apoptosis. We describe methods of model building and training on experimentally obtained quantitative datasets, as well as experimental methods of obtaining quantitative dose-response and temporal dependencies of protein phosphorylation and activities. The presented methods make possible (1) both the fine-grained modeling of complex signaling dynamics and identification of salient, course-grained network structures (such as feedback loops) that bring about intricate dynamics, and (2) experimental validation of dynamic models.

A systems study reveals concurrent activation of AMPK and mTOR by amino acids

Amino acids (aa) are not only building blocks for proteins, but also signalling molecules, with the mammalian target of rapamycin complex 1 (mTORC1) acting as a key mediator. However, little is known about whether aa, independently of mTORC1, activate other kinases of the mTOR signalling network. To delineate aa-stimulated mTOR network dynamics, we here combine a computational–experimental approach with text mining-enhanced quantitative proteomics. We report that AMP-activated protein kinase (AMPK), phosphatidylinositide 3-kinase (PI3K) and mTOR complex 2 (mTORC2) are acutely activated by aa-readdition in an mTORC1-independent manner. AMPK activation by aa is mediated by Ca²⁺/calmodulin-dependent protein kinase kinase β (CaMKKβ). In response, AMPK impinges on the autophagy regulators Unc-51-like kinase-1 (ULK1) and c-Jun. AMPK is widely recognized as an mTORC1 antagonist that is activated by starvation. We find that aa acutely activate AMPK concurrently with mTOR. We show that AMPK under aa sufficiency acts to sustain autophagy. This may be required to maintain protein homoeostasis and deliver metabolite intermediates for biosynthetic processes.

mTORC1 is known to mediate the signalling activity of amino acids. Here, the authors combine modelling with experiments and find that amino acids acutely stimulate mTORC2, IRS/PI3K and AMPK, independently of mTORC1. AMPK activation through CaMKKβ sustains autophagy under non-starvation conditions.

Modeling the LPS-induced effects on transcription factor activation and gene expression in murine macrophages

Macrophages within the liver are of particular importance for a functional defense against bacterial infection. They exhibit a complex response to lipopolysaccharide and secrete a variety of pro-inflammatory cytokines and chemokines that both coordinate the immune response and regulate activity of the macrophages, themselves. In this context, the dynamic of pathway activation and gene expression is important for a better understanding of the role of activated macrophages in healthy and diseased states. Therefore, we present a representative model of LPS-induced macrophage activation that covers the principle regulatory motifs. Based on that, we propose a simplified model with a reduced number of states and parameters that allows estimation of transcription factor activity from gene expression data and can be easily extended to describe the full spectrum of gene regulation in LPS-activated macrophages.

Model-Based Characterization of Inflammatory Gene Expression Patterns of Activated Macrophages

Macrophages are cells with remarkable plasticity. They integrate signals from their microenvironment leading to context-dependent polarization into classically (M1) or alternatively (M2) activated macrophages, representing two extremes of a broad spectrum of divergent phenotypes. Thereby, macrophages deliver protective and pro-regenerative signals towards injured tissue but, depending on the eliciting damage, may also be responsible for the generation and aggravation of tissue injury. Although incompletely understood, there is emerging evidence that macrophage polarization is critical for these antagonistic roles. To identify activation-specific expression patterns of chemokines and cytokines that may confer these distinct effects a systems biology approach was applied. A comprehensive literature-based Boolean model was developed to describe the M1 (LPS-activated) and M2 (IL-4/13-activated) polarization types. The model was validated using high-throughput transcript expression data from murine bone marrow derived macrophages. By dynamic modeling of gene expression, the chronology of pathway activation and autocrine signaling was estimated. Our results provide a deepened understanding of the physiological balance leading to M1/M2 activation, indicating the relevance of co-regulatory signals at the level of Akt1 or Akt2 that may be important for directing macrophage polarization.

Macrophages are essential cells of the immune system and indispensable for a defense against bacterial infection. They reside as resting, immune modulatory cells in several tissues of the human body where they continuously sense inputs from their local environment. They react to stimuli such as toxins, injury or bacterial products in a process termed macrophage activation or polarization. For example, the bacterial component lipopolysaccharide induces so-called classical activation of macrophages into the M1 phenotype that secretes a number of inflammatory cytokines and chemokines leading to killing of bacteria and resolution of inflammation. Another prominent phenotype of macrophages is the M2 polarization state that is associated with wound healing and tissue regeneration. Unbalanced activation of macrophages is implicated in a number of diseases. An improved knowledge and extensive characterization of these macrophages as well as the factors determining their phenotypes will improve the understanding of the role of macrophages in disease progression.

Modeling and gene knockdown to assess the contribution of nonsense-mediated decay, premature termination, and selenocysteine insertion to the selenoprotein hierarchy

The expression of selenoproteins, a specific group of proteins that incorporates selenocysteine, is hierarchically regulated by the availability of Se, with some, but not all selenoprotein mRNA transcripts decreasing in abundance with decreasing Se. Selenocysteine insertion into the peptide chain occurs during translation following recoding of an internal UGA stop codon. There is increasing evidence that this UGA recoding competes with premature translation termination, which is followed by nonsense-mediated decay (NMD) of the transcript. In this study, we tested the hypothesis that the susceptibility of different selenoprotein mRNAs to premature termination during translation and differential sensitivity of selenoprotein transcripts to NMD are major factors in the selenoprotein hierarchy. Selenoprotein transcript abundance was measured in Caco-2 cells using real-time PCR under different Se conditions and the data obtained fitted to mathematical models of selenoprotein translation. A calibrated model that included a combination of differential sensitivity of selenoprotein transcripts to NMD and different frequency of non-NMD related premature translation termination was able to fit all the measurements. The model predictions were tested using SiRNA to knock down expression of the crucial NMD factor UPF1 (up-frameshift protein 1) and selenoprotein mRNA expression. The calibrated model was able to predict the effect of UPF1 knockdown on gene expression for all tested selenoproteins, except SPS2 (selenophosphate synthetase), which itself is essential for selenoprotein synthesis. These results indicate an important role for NMD in the hierarchical regulation of selenoprotein mRNAs, with the exception of SPS2 whose expression is likely regulated by a different mechanism.

Model calibration and uncertainty analysis in signaling networks

For a long time the biggest challenges in modeling cellular signal transduction networks has been the inference of crucial pathway components and the qualitative description of their interactions. As a result of the emergence of powerful high-throughput experiments, it is now possible to measure data of high temporal and spatial resolution and to analyze signaling dynamics quantitatively. In addition, this increase of high-quality data is the basis for a better understanding of model limitations and their influence on the predictive power of models. We review established approaches in signal transduction network modeling with a focus on ordinary differential equation models as well as related developments in model calibration. As central aspects of the calibration process we discuss possibilities of model adaptation based on data-driven parameter optimization and the concomitant objective of reducing model uncertainties.

T160‐phosphorylated CDK2 defines threshold for HGF dependent proliferation in primary hepatocytes

Liver regeneration is a tightly controlled process mainly achieved by proliferation of usually quiescent hepatocytes. The specific molecular mechanisms ensuring cell division only in response to proliferative signals such as hepatocyte growth factor (HGF) are not fully understood. Here, we combined quantitative time-resolved analysis of primary mouse hepatocyte proliferation at the single cell and at the population level with mathematical modeling. We showed that numerous G1/S transition components are activated upon hepatocyte isolation whereas DNA replication only occurs upon additional HGF stimulation. In response to HGF, Cyclin:CDK complex formation was increased, p21 rather than p27 was regulated, and Rb expression was enhanced. Quantification of protein levels at the restriction point showed an excess of CDK2 over CDK4 and limiting amounts of the transcription factor E2F-1. Analysis with our mathematical model revealed that T160 phosphorylation of CDK2 correlated best with growth factor-dependent proliferation, which we validated experimentally on both the population and the single cell level. In conclusion, we identified CDK2 phosphorylation as a gate-keeping mechanism to maintain hepatocyte quiescence in the absence of HGF.

Autocrine TGF-β/ZEB/microRNA-200 signal transduction drives epithelial-mesenchymal transition: Kinetic models predict minimal drug dose to inhibit metastasis

The epithelial-mesenchymal transition (EMT) is the crucial step that cancer cells must pass before they can undergo metastasis. The transition requires the activity of complex functional networks that downregulate properties of the epithelial phenotype and upregulate characteristics of the mesenchymal phenotype. The networks frequently include reciprocal repressions between transcription factors (TFs) driving the EMT and microRNAs (miRs) inducing the reverse process, termed mesenchymal-epithelial transition (MET). In this work we develop four kinetic models that are based on experimental data and hypotheses describing how autocrine transforming growth factor-β (TGF-β) signal transduction induces and maintains an EMT by upregulating the TFs ZEB1 and ZEB2 which repress the expression of the miR-200b/c family members. After successful model calibration we validate our models by predicting requirements for the maintenance of the mesenchymal steady state which agree with experimental data. Finally, we apply our validated kinetic models for the design of experiments in cancer therapy. We demonstrate how steady state properties of the kinetic models, combined with data from tumor-derived cell lines of individual patients, can predict the minimal amount of an inhibitor to induce a MET.

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.

PeTTSy: a computational tool for perturbation analysis of complex systems biology models

Background

Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary.

Results

Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems.

To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters.

Conclusions

PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-0972-2) contains supplementary material, which is available to authorized users.