Integrated mechanistic and data-driven modelling for multivariate analysis of signalling pathways

Combined mechanistic modeling and machine-learning approaches in systems biology - A systematic literature review

BACKGROUND AND OBJECTIVE

Mechanistic-based Model simulations (MM) are an effective approach commonly employed, for research and learning purposes, to better investigate and understand the inherent behavior of biological systems. Recent advancements in modern technologies and the large availability of omics data allowed the application of Machine Learning (ML) techniques to different research fields, including systems biology. However, the availability of information regarding the analyzed biological context, sufficient experimental data, as well as the degree of computational complexity, represent some of the issues that both MMs and ML techniques could present individually. For this reason, recently, several studies suggest overcoming or significantly reducing these drawbacks by combining the above-mentioned two methods. In the wake of the growing interest in this hybrid analysis approach, with the present review, we want to systematically investigate the studies available in the scientific literature in which both MMs and ML have been combined to explain biological processes at genomics, proteomics, and metabolomics levels, or the behavior of entire cellular populations.

METHODS

Elsevier Scopus®, Clarivate Web of Science™ and National Library of Medicine PubMed® databases were enquired using the queries reported in Table 1, resulting in 350 scientific articles.

RESULTS

Only 14 of the 350 documents returned by the comprehensive search conducted on the three major online databases met our search criteria, i.e. present a hybrid approach consisting of the synergistic combination of MMs and ML to treat a particular aspect of systems biology.

CONCLUSIONS

Despite the recent interest in this methodology, from a careful analysis of the selected papers, it emerged how examples of integration between MMs and ML are already present in systems biology, highlighting the great potential of this hybrid approach to both at micro and macro biological scales.

Machine learning methods for predicting the key metabolic parameters of Halomonas elongata DSM 2581 T

Ectoine is generally produced by the fermentation process of Halomonas elongata DSM 2581 ^T, which is one of the primary industrial ectoine production techniques. To effectively monitor and control the fermentation process, the important parameters require accurate real-time measurement. However, for ectoine fermentation, three critical parameters (cell optical density, glucose, and product concentration) cannot be measured conveniently in real-time due to time variation, strong coupling, and other constraints. As a result, our work effectively created a series of hybrid models to predict the values of these three parameters incorporating both fermentation kinetics and machine learning approaches. Compared with the traditional machine learning models, our models solve the problem of insufficient data which is common in fermentation. In addition, a simple kinetic modeling is only applicable to specific physical conditions, so different physical conditions require refitting the function, which is tedious to operate. However, our models also overcome this limitation. In this work, we compared different hybrid models based on 5 feature engineering methods, 11 machine-learning approaches, and 2 kinetic models. The best models for predicting three key parameters, respectively, are as follows: CORR-Ensemble (R²: 0.983 ± 0.0, RMSE: 0.086 ± 0.0, MAE: 0.07 ± 0.0), SBE-Ensemble (R²: 0.972 ± 0.0, RMSE: 0.127 ± 0.0, MAE: 0.078 ± 0.0), and SBE-Ensemble (R²:0.98 ± 0.0, RMSE: 0.023 ± 0.001, MAE: 0.018 ± 0.001). To verify the universality and stability of constructed models, we have done an experimental verification, and its results showed that our proposed models have excellent performance. KEY POINTS: • Using the kinetic models for producing simulated data • Through different feature engineering methods for dimension reduction • Creating a series of hybrid models to predict the values of three parameters in the fermentation process of Halomonas elongata DSM 2581 ^T.

Towards systems immunology of critical illness at scale: from single cell 'omics to digital twins

Single-cell 'omics methodology has yielded unprecedented insights based largely on data-centric informatics for reducing, and thus interpreting, massive datasets. In parallel, parsimonious mathematical modeling based on abstractions of pathobiology has also yielded major insights into inflammation and immunity, with these models being extended to describe multi-organ disease pathophysiology as the basis of 'digital twins' and in silico clinical trials. The integration of these distinct methods at scale can drive both basic and translational advances, especially in the context of critical illness, including diseases such as COVID-19. Here, I explore achievements and argue the challenges that are inherent to the integration of data-driven and mechanistic modeling approaches, highlighting the potential of modeling-based strategies for rational immune system reprogramming.

Understanding virtual patients efficiently and rigorously by combining machine learning with dynamical modelling

Individual biological organisms are characterized by daunting heterogeneity, which precludes describing or understanding populations of ‘patients’ with a single mathematical model. Recently, the field of quantitative systems pharmacology (QSP) has adopted the notion of virtual patients (VPs) to cope with this challenge. A typical population of VPs represents the behavior of a heterogeneous patient population with a distribution of parameter values over a mathematical model of fixed structure. Though this notion of VPs is a powerful tool to describe patients’ heterogeneity, the analysis and understanding of these VPs present new challenges to systems pharmacologists. Here, using a model of the hypothalamic–pituitary–adrenal axis, we show that an integrated pipeline that combines machine learning (ML) and bifurcation analysis can be used to effectively and efficiently analyse the behaviors observed in populations of VPs. Compared with local sensitivity analyses, ML allows us to capture and analyse the contributions of simultaneous changes of multiple model parameters. Following up with bifurcation analysis, we are able to provide rigorous mechanistic insight regarding the influences of ML-identified parameters on the dynamical system’s behaviors. In this work, we illustrate the utility of this pipeline and suggest that its wider adoption will facilitate the use of VPs in the practice of systems pharmacology.

Data-driven analysis of a mechanistic model of CAR T cell signaling predicts effects of cell-to-cell heterogeneity

Due to the variability of protein expression, cells of the same population can exhibit different responses to stimuli. It is important to understand this heterogeneity at the individual level, as population averages mask these underlying differences. Using computational modeling, we can interrogate a system much more precisely than by using experiments alone, in order to learn how the expression of each protein affects a biological system. Here, we examine a mechanistic model of CAR T cell signaling, which connects receptor-antigen binding to MAPK activation, to determine intracellular modulations that can increase cellular response. CAR T cell cancer therapy involves removing a patient's T cells, modifying them to express engineered receptors that can bind to tumor-associated antigens to promote tumor cell killing, and then injecting the cells back into the patient. This population of cells, like all cell populations, would have heterogeneous protein expression, which could affect the efficacy of treatment. Thus, it is important to examine the effects of cell-to-cell heterogeneity. We first generated a dataset of simulated cell responses via Monte Carlo simulations of the mechanistic model, where the initial protein concentrations were randomly sampled. We analyzed the dataset using partial least-squares modeling to determine the relationships between protein expression and ERK phosphorylation, the output of the mechanistic model. Using this data-driven analysis, we found that only the expressions of proteins relating directly to the receptor and the MAPK cascade, the beginning and end of the network, respectively, are relevant to the cells' response. We also found, surprisingly, that increasing the amount of receptor present can actually inhibit the cell's ability to respond due to increasing the strength of negative feedback from phosphatases. Overall, we have combined data-driven and mechanistic modeling to generate detailed insight into CAR T cell signaling.

Systems Biology of Cancer Metastasis

Cancer metastasis is no longer viewed as a linear cascade of events but rather as a series of concurrent, partially overlapping processes, as successfully metastasizing cells assume new phenotypes while jettisoning older behaviors. The lack of a systemic understanding of this complex phenomenon has limited progress in developing treatments for metastatic disease. Because metastasis has traditionally been investigated in distinct physiological compartments, the integration of these complex and interlinked aspects remains a challenge for both systems-level experimental and computational modeling of metastasis. Here, we present some of the current perspectives on the complexity of cancer metastasis, the multiscale nature of its progression, and a systems-level view of the processes underlying the invasive spread of cancer cells. We also highlight the gaps in our current understanding of cancer metastasis as well as insights emerging from interdisciplinary systems biology approaches to understand this complex phenomenon.

Systems Biomedicine of Rabies Delineates the Affected Signaling Pathways

The prototypical neurotropic virus, rabies, is a member of the Rhabdoviridae family that causes lethal encephalomyelitis. Although there have been a plethora of studies investigating the etiological mechanism of the rabies virus and many precautionary methods have been implemented to avert the disease outbreak over the last century, the disease has surprisingly no definite remedy at its late stages. The psychological symptoms and the underlying etiology, as well as the rare survival rate from rabies encephalitis, has still remained a mystery. We, therefore, undertook a systems biomedicine approach to identify the network of gene products implicated in rabies. This was done by meta-analyzing whole-transcriptome microarray datasets of the CNS infected by strain CVS-11, and integrating them with interactome data using computational and statistical methods. We first determined the differentially expressed genes (DEGs) in each study and horizontally integrated the results at the mRNA and microRNA levels separately. A total of 61 seed genes involved in signal propagation system were obtained by means of unifying mRNA and microRNA detected integrated DEGs. We then reconstructed a refined protein–protein interaction network (PPIN) of infected cells to elucidate the rabies-implicated signal transduction network (RISN). To validate our findings, we confirmed differential expression of randomly selected genes in the network using Real-time PCR. In conclusion, the identification of seed genes and their network neighborhood within the refined PPIN can be useful for demonstrating signaling pathways including interferon circumvent, toward proliferation and survival, and neuropathological clue, explaining the intricate underlying molecular neuropathology of rabies infection and thus rendered a molecular framework for predicting potential drug targets.

Descriptive vs. mechanistic network models in plant development in the post-genomic era

Network modeling is now a widespread practice in systems biology, as well as in integrative genomics, and it constitutes a rich and diverse scientific research field. A conceptually clear understanding of the reasoning behind the main existing modeling approaches, and their associated technical terminologies, is required to avoid confusions and accelerate the transition towards an undeniable necessary more quantitative, multidisciplinary approach to biology. Herein, we focus on two main network-based modeling approaches that are commonly used depending on the information available and the intended goals: inference-based methods and system dynamics approaches. As far as data-based network inference methods are concerned, they enable the discovery of potential functional influences among molecular components. On the other hand, experimentally grounded network dynamical models have been shown to be perfectly suited for the mechanistic study of developmental processes. How do these two perspectives relate to each other? In this chapter, we describe and compare both approaches and then apply them to a given specific developmental module. Along with the step-by-step practical implementation of each approach, we also focus on discussing their respective goals, utility, assumptions, and associated limitations. We use the gene regulatory network (GRN) involved in Arabidopsis thaliana Root Stem Cell Niche patterning as our illustrative example. We show that descriptive models based on functional genomics data can provide important background information consistent with experimentally supported functional relationships integrated in mechanistic GRN models. The rationale of analysis and modeling can be applied to any other well-characterized functional developmental module in multicellular organisms, like plants and animals.

From data patterns to mechanistic models in acute critical illness

The complexity of the physiologic and inflammatory response in acute critical illness has stymied the accurate diagnosis and development of therapies. The Society for Complex Acute Illness was formed a decade ago with the goal of leveraging multiple complex systems approaches to address this unmet need. Two main paths of development have characterized the society's approach: (i) data pattern analysis, either defining the diagnostic/prognostic utility of complexity metrics of physiologic signals or multivariate analyses of molecular and genetic data and (ii) mechanistic mathematical and computational modeling, all being performed with an explicit translational goal. Here, we summarize the progress to date on each of these approaches, along with pitfalls inherent in the use of each approach alone. We suggest that the next decade holds the potential to merge these approaches, connecting patient diagnosis to treatment via mechanism-based dynamical system modeling and feedback control and allowing extrapolation from physiologic signals to biomarkers to novel drug candidates. As a predicate example, we focus on the role of data-driven and mechanistic models in neuroscience and the impact that merging these modeling approaches can have on general anesthesia.

A computational pipeline for identifying kinetic motifs to aid in the design and improvement of synthetic gene circuits

BACKGROUND

An increasing number of genetic components are available in several depositories of such components to facilitate synthetic biology research, but picking out those that will allow a designed circuit to achieve the specified function still requires multiple cycles of testing. Here, we addressed this problem by developing a computational pipeline to mathematically simulate a gene circuit for a comprehensive range and combination of the kinetic parameters of the biological components that constitute the gene circuit.

RESULTS

We showed that, using a well-studied transcriptional repression cascade as an example, the sets of kinetic parameters that could produce the specified system dynamics of the gene circuit formed clusters of recurrent combinations, referred to as kinetic motifs, which appear to be associated with both the specific topology and specified dynamics of the circuit. Furthermore, the use of the resulting "handbook" of performance-ranked kinetic motifs in finding suitable circuit components was illustrated in two application scenarios.

CONCLUSIONS

These results show that the computational pipeline developed here can provide a rational-based guide to aid in the design and improvement of synthetic gene circuits.

Insights into proteomic immune cell signaling and communication via data-driven modeling

Over the past decade, studies applying data-driven modeling approaches have demonstrated significant contributions toward the integrative understanding of multivariate cell regulatory system operation. Here we review applications of several of these approaches, including principal component analysis, partial least squares regression, partial least squares discriminant analysis, decision trees, and Bayesian networks, and describe the advances they have offered in systems-level understanding of immune cell signaling and communication. We show how these approaches generate novel insights from high-throughput proteomic data, from classification to association to influence to mechanisms. Looking forward, new experimental technologies involving single-cell measurements of cytokine expression beckon extension of these modeling techniques to inference of immune cell-cell communication networks, with a goal of aiding development of improved vaccine therapeutics.

Understanding dynamics using sensitivity analysis: caveat and solution

Background

Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.

Results

A careful interpretation of parametric perturbations used in the PSA is presented here to explain the issue of using this analysis in inferring dynamics. In short, the PSA coefficients quantify the integrated change in the system behaviour due to persistent parametric perturbations, and thus the dynamical information of when a parameter perturbation matters is lost. To get around this issue, we present a new sensitivity analysis based on impulse perturbations on system parameters, which is named impulse parametric sensitivity analysis (iPSA). The inability of PSA and the efficacy of iPSA in revealing mechanistic information of a dynamical system are illustrated using two examples involving switch activation.

Conclusions

The interpretation of the PSA coefficients of dynamical systems should take into account the persistent nature of parametric perturbations involved in the derivation of this analysis. The application of PSA to identify the controlling mechanism of dynamical behaviour can be misleading. By using impulse perturbations, introduced at different times, the iPSA provides the necessary information to understand how dynamics is achieved, i.e. which parameters are essential and when they become important.

Robust dynamic balance of AP-1 transcription factors in a neuronal gene regulatory network

BACKGROUND

The octapeptide Angiotensin II is a key hormone that acts via its receptor AT1R in the brainstem to modulate the blood pressure control circuits and thus plays a central role in the cardiac and respiratory homeostasis. This modulation occurs via activation of a complex network of signaling proteins and transcription factors, leading to changes in levels of key genes and proteins. AT1R initiated activity in the nucleus tractus solitarius (NTS), which regulates blood pressure, has been the subject of extensive molecular analysis. But the adaptive network interactions in the NTS response to AT1R, plausibly related to the development of hypertension, are not understood.

RESULTS

We developed and analyzed a mathematical model of AT1R-activated signaling kinases and a downstream gene regulatory network, with structural basis in our transcriptomic data analysis and literature. To our knowledge, our report presents the first computational model of this key regulatory network. Our simulations and analysis reveal a dynamic balance among distinct dimers of the AP-1 family of transcription factors. We investigated the robustness of this behavior to simultaneous perturbations in the network parameters using a novel multivariate approach that integrates global sensitivity analysis with decision-tree methods. Our analysis implicates a subset of Fos and Jun dependent mechanisms, with dynamic sensitivities shifting from Fos-regulating kinase (FRK)-mediated processes to those downstream of c-Jun N-terminal kinase (JNK). Decision-tree analysis indicated that while there may be a large combinatorial functional space feasible for neuronal states and parameters, the network behavior is constrained to a small set of AP-1 response profiles. Many of the paths through the combinatorial parameter space lead to a dynamic balance of AP-1 dimer forms, yielding a robust AP-1 response counteracting the biological variability.

CONCLUSIONS

Based on the simulation and analysis results, we demonstrate that a dynamic balance among distinct dimers of the AP-1 family of transcription factors underlies the robust activation of neuronal gene expression in the NTS response to AT1R activation. Such a differential sensitivity to limited set of mechanisms is likely to underlie the stable homeostatic physiological response.

PSExplorer: whole parameter space exploration for molecular signaling pathway dynamics

Motivation: Mathematical models of biological systems often have a large number of parameters whose combinational variations can yield distinct qualitative behaviors. Since it is intractable to examine all possible combinations of parameters for non-trivial biological pathways, it is required to have a systematic strategy to explore the parameter space in a computational way so that dynamic behaviors of a given pathway are estimated.

Results: We present PSExplorer, a computational tool for exploring qualitative behaviors and key parameters of molecular signaling pathways. Utilizing the Latin hypercube sampling and a clustering technique in a recursive paradigm, the software enables users to explore the whole parameter space of the models to search for robust qualitative behaviors. The parameter space is partitioned into sub-regions according to behavioral differences. Sub-regions showing robust behaviors can be identified for further analyses. The partitioning result presents a tree structure from which individual and combinational effects of parameters on model behaviors can be assessed and key factors of the models are readily identified.

Availability: The software, tutorial manual and test models are available for download at the following address: http://gto.kaist.ac.kr/∼psexplorer

Contact:tqtung@kaist.ac.kr; tqtung@gmail.com

A hybrid continuum-discrete modelling approach to predict and control angiogenesis: analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology

Angiogenesis is crucial during many physiological processes and is influenced by various biochemical and biomechanical factors. Models have proved useful in understanding the mechanisms of angiogenesis and also the characteristics of the capillaries formed as part of the process. We have developed a three-dimensional hybrid, agent-field model where individual cells are modelled as sprout-forming agents in a matrix field. Cell independence, cell-cell communication and stochastic cell response are integral parts of the model. The model simulations incorporate probabilities of an individual cell to transition into one of four stages--quiescence, proliferation, migration and apoptosis. We demonstrate that several features, such as continuous sprouts, cell clustering and branching, that are observed in microfluidic experiments conducted under controlled conditions using few angiogenic factors can be reproduced by this model. We also identify the transition probabilities that result in specific sprout characteristics such as long continuous sprouts and specific branching patterns. Thus, this model can be used to cluster sprout morphology as a function of various influencing factors.

Toxicity testing in the 21st century: a vision and a strategy

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

Toxicity testing in the 21st century: a vision and a strategy

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

Dynamical analysis of cellular networks based on the Green's function matrix

The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.

Mechanistic systems biology of inflammatory gene expression in airway smooth muscle as tool for asthma drug development

There is compelling evidence that airway smooth muscle cells may function as inflammatory cells in the airway system by producing multiple inflammatory cytokines in response to a large array of external stimuli such as acetylcholine, bradykinin, inflammatory cytokines, and toll-like receptor activators. However, how multiple extracellular stimuli interact in the regulation of inflammatory gene expression in an airway smooth muscle cell remains poorly understood. This review addresses the mechanistic systems biology of inflammatory gene expression in airway smooth muscle by discussing: a) redundancy underlying multiple stimulus-product relations in receptor-mediated inflammatory gene expression, and their regulation by convergent activation of Erk1/2 mitogen-activated protein kinase (MAPK), b) Erk1/2 MAPK-dependent induction of phosphatase expression as a negative feedback mechanism in the robust maintenance of inflammatory gene expression, and c) cyclooxygenase 2-dependent regulation of the differential temporal dynamics of early and late inflammatory gene expression. It is becoming recognized that a single-target approach is unlikely to be effective for the treatment of inflammatory airway diseases because airway inflammation is a result of complex interactions among multiple inflammatory mediators and cells types in the airway system. Understanding the mechanistic systems biology of inflammatory gene expression in airway smooth muscle and other cell types in the airway system may lead to the development of multi-target drug regimens for the treatment of inflammatory airway diseases such as asthma.

Construction and analysis of a modular model of caspase activation in apoptosis

Background

A key physiological mechanism employed by multicellular organisms is apoptosis, or programmed cell death. Apoptosis is triggered by the activation of caspases in response to both extracellular (extrinsic) and intracellular (intrinsic) signals. The extrinsic and intrinsic pathways are characterized by the formation of the death-inducing signaling complex (DISC) and the apoptosome, respectively; both the DISC and the apoptosome are oligomers with complex formation dynamics. Additionally, the extrinsic and intrinsic pathways are coupled through the mitochondrial apoptosis-induced channel via the Bcl-2 family of proteins.

Results

A model of caspase activation is constructed and analyzed. The apoptosis signaling network is simplified through modularization methodologies and equilibrium abstractions for three functional modules. The mathematical model is composed of a system of ordinary differential equations which is numerically solved. Multiple linear regression analysis investigates the role of each module and reduced models are constructed to identify key contributions of the extrinsic and intrinsic pathways in triggering apoptosis for different cell lines.

Conclusion

Through linear regression techniques, we identified the feedbacks, dissociation of complexes, and negative regulators as the key components in apoptosis. The analysis and reduced models for our model formulation reveal that the chosen cell lines predominately exhibit strong extrinsic caspase, typical of type I cell, behavior. Furthermore, under the simplified model framework, the selected cells lines exhibit different modes by which caspase activation may occur. Finally the proposed modularized model of apoptosis may generalize behavior for additional cells and tissues, specifically identifying and predicting components responsible for the transition from type I to type II cell behavior.

Identifying fragilities in biochemical networks: robust performance analysis of Fas signaling-induced apoptosis

Proper control of apoptotic signaling is critical to immune response and development in multicellular organisms. Two tools from control engineering are applied to a mathematical model of Fas ligand signaling-induced apoptosis. Structured singular value analysis determines the volume in parameter space within which the system parameters may exist and still maintain efficacious signaling, but is limited to linear behaviors. Sensitivity analysis can be applied to nonlinear systems but is difficult to relate to performance criteria. Thus, structured singular value analysis is used to quantify performance during apoptosis rejection, ensuring that the system remains sensitive but not overly so to apoptotic stimuli. Sensitivity analysis is applied when the system has switched to the death-inducing, apoptotic steady state to determine parameters significant to maintaining the bistability. The analyses reveal that the magnitude of the death signal is fragile to perturbations in degradation parameters (failures in the ubiquitin/proteasome mechanism) while the timing of signal expression can be tuned by manipulating local parameters. Simultaneous parameter uncertainty highlights apoptotic fragility to disturbances in the ubiquitin/proteasome system. Sensitivity analysis reveals that the robust signaling characteristics of the apoptotic network is due to network architecture, and the apoptotic signaling threshold is best manipulated by interactions upstream of the apoptosome.

Nanovehicular intracellular delivery systems

This article provides an overview of principles and barriers relevant to intracellular drug and gene transport, accumulation and retention (collectively called as drug delivery) by means of nanovehicles (NV). The aim is to deliver a cargo to a particular intracellular site, if possible, to exert a local action. Some of the principles discussed in this article apply to noncolloidal drugs that are not permeable to the plasma membrane or to the blood-brain barrier. NV are defined as a wide range of nanosized particles leading to colloidal objects which are capable of entering cells and tissues and delivering a cargo intracelullarly. Different localization and targeting means are discussed. Limited discussion on pharmacokinetics and pharmacodynamics is also presented. NVs are contrasted to micro-delivery and current nanotechnologies which are already in commercial use. Newer developments in NV technologies are outlined and future applications are stressed. We also briefly review the existing modeling tools and approaches to quantitatively describe the behavior of targeted NV within the vascular and tumor compartments, an area of particular importance. While we list "elementary" phenomena related to different level of complexity of delivery to cancer, we also stress importance of multi-scale modeling and bottom-up systems biology approach.

Kinetic model for lamellipodal actin-integrin 'clutch' dynamics

In migrating cells, with especial prominence in lamellipodial protrusions at the cell front, highly dynamic connections are formed between the actin cytoskeleton and the extracellular matrix through linkages of integrin adhesion receptors to actin filaments via complexes of cytosolic "connector" proteins. Myosin-mediated contractile forces strongly influence the dynamic behavior of these adhesion complexes, apparently in two counter-acting ways: negatively as the cell-generated forces enhance complex dissociation, and at the same time positively as force-induced signaling can lead to strengthening of the linkage complexes. The net balance arising from this dynamic interplay is challenging to ascertain a priori, rendering experimental studies difficult to interpret and molecular manipulations of cell and/or environment difficult to predict. We have constructed a kinetics-based model governing the dynamic behavior of this system. We obtained ranges of parameter value sets yielding behavior consistent with that observed experimentally for 3T3 cells and for CHO cells, respectively. Model simulations are able to produce results for the effects of paxillin mutations on the turnover rate of actin/integrin linkages in CHO cells, which are consistent with recent literature reports. Overall, although this current model is quite simple it provides a useful foundation for more detailed models extending upon it.

Executable cell biology

Computational modeling of biological systems is becoming increasingly important in efforts to better understand complex biological behaviors. In this review, we distinguish between two types of biological models--mathematical and computational--which differ in their representations of biological phenomena. We call the approach of constructing computational models of biological systems 'executable biology', as it focuses on the design of executable computer algorithms that mimic biological phenomena. We survey the main modeling efforts in this direction, emphasize the applicability and benefits of executable models in biological research and highlight some of the challenges that executable biology poses for biology and computer science. We claim that for executable biology to reach its full potential as a mainstream biological technique, formal and algorithmic approaches must be integrated into biological research. This will drive biology toward a more precise engineering discipline.

Scale relativity theory and integrative systems biology: 1. Founding principles and scale laws

In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, and discuss how scale laws of increasing complexity can be used to model and understand the behaviour of complex biological systems. In scale relativity theory, the geometry of space is considered to be continuous but non-differentiable, therefore fractal (i.e., explicitly scale-dependent). One writes the equations of motion in such a space as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the non-differentiable and fractal geometry. In this first review paper, the scale laws that describe the new dependence on resolutions of physical quantities are obtained as solutions of differential equations acting in the scale space. This leads to several possible levels of description for these laws, from the simplest scale invariant laws to generalized laws with variable fractal dimensions. Initial applications of these laws to the study of species evolution, embryogenesis and cell confinement are discussed.