Quantitative modeling in cell biology: what is it good for?

Why More Biologists Must Embrace Quantitative Modeling

Biology as a field has transformed since the time of its foundation from an organized enterprise cataloging the diversity of the natural world to a quantitatively rigorous science seeking to answer complex questions about the functions of organisms and their interactions with each other and their environments. As the mathematical rigor of biological analyses has improved, quantitative models have been developed to describe multi-mechanistic systems and to test complex hypotheses. However, applications of quantitative models have been uneven across fields, and many biologists lack the foundational training necessary to apply them in their research or to interpret their results to inform biological problem-solving efforts. This gap in scientific training has created a false dichotomy of "biologists" and "modelers" that only exacerbates the barriers to working biologists seeking additional training in quantitative modeling. Here, we make the argument that all biologists are modelers and are capable of using sophisticated quantitative modeling in their work. We highlight four benefits of conducting biological research within the framework of quantitative models, identify the potential producers and consumers of information produced by such models, and make recommendations for strategies to overcome barriers to their widespread implementation. Improved understanding of quantitative modeling could guide the producers of biological information to better apply biological measurements through analyses that evaluate mechanisms, and allow consumers of biological information to better judge the quality and applications of the information they receive. As our explanations of biological phenomena increase in complexity, so too must we embrace modeling as a foundational skill.

Ten "Cheat Codes" for Measuring Oxidative Stress in Humans

Formidable and often seemingly insurmountable conceptual, technical, and methodological challenges hamper the measurement of oxidative stress in humans. For instance, fraught and flawed methods, such as the thiobarbituric acid reactive substances assay kits for lipid peroxidation, rate-limit progress. To advance translational redox research, we present ten comprehensive "cheat codes" for measuring oxidative stress in humans. The cheat codes include analytical approaches to assess reactive oxygen species, antioxidants, oxidative damage, and redox regulation. They provide essential conceptual, technical, and methodological information inclusive of curated "do" and "don't" guidelines. Given the biochemical complexity of oxidative stress, we present a research question-grounded decision tree guide for selecting the most appropriate cheat code(s) to implement in a prospective human experiment. Worked examples demonstrate the benefits of the decision tree-based cheat code selection tool. The ten cheat codes define an invaluable resource for measuring oxidative stress in humans.

A data-driven approach for timescale decomposition of biochemical reaction networks

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for the timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor-driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications. IMPORTANCE Complex interactions within interconnected biochemical reaction networks enable cellular responses to a wide range of unpredictable environmental perturbations. Understanding how biological functions arise from these intricate interactions has been a long-standing problem in biology. Here, we introduce a computational approach to dissect complex biological systems' dynamics in evolving environments. This approach characterizes the timescale hierarchies of complex reaction networks, offering a system-level understanding at physiologically relevant timescales. Analyzing various hypothetical and biological pathways, we show how stoichiometric properties shape the way energy is dissipated throughout reaction networks. Notably, we establish that glycolysis operates as a cofactor-driven pathway, where the slowest dynamics are governed by a balance between high-energy phosphate bonds and redox trafficking. This approach enhances our understanding of network dynamics and facilitates the development of reduced-order kinetic models with biologically interpretable components.

Quantitative Modelling in Stem Cell Biology and Beyond: How to Make Best Use of It

Purpose of Review

This article gives a broad overview of quantitative modelling approaches in biology and provides guidance on how to employ them to boost stem cell research, by helping to answer biological questions and to predict the outcome of biological processes.

Recent Findings

The twenty-first century has seen a steady increase in the proportion of cell biology publications employing mathematical modelling to aid experimental research. However, quantitative modelling is often used as a rather decorative element to confirm experimental findings, an approach which often yields only marginal added value, and is in many cases scientifically questionable.

Summary

Quantitative modelling can boost biological research in manifold ways, but one has to take some careful considerations before embarking on a modelling campaign, in order to maximise its added value, to avoid pitfalls that may lead to wrong results, and to be aware of its fundamental limitations, imposed by the risks of over-fitting and "universality".

A data-driven approach for timescale decomposition of biochemical reaction networks

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications.

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.

Stability selection enables robust learning of differential equations from limited noisy data

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.

Validation Through Collaboration: Encouraging Team Efforts to Ensure Internal and External Validity of Computational Models of Biochemical Pathways

Computational modelling of biochemical reaction pathways is an increasingly important part of neuroscience research. In order to be useful, computational models need to be valid in two senses: First, they need to be consistent with experimental data and able to make testable predictions (external validity). Second, they need to be internally consistent and independently reproducible (internal validity). Here, we discuss both types of validity and provide a brief overview of tools and technologies used to ensure they are met. We also suggest the introduction of new collaborative technologies to ensure model validity: an incentivised experimental database for external validity and reproducibility audits for internal validity. Both rely on FAIR principles and on collaborative science practices.

A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Ten steps to investigate a cellular system with mathematical modeling

Cellular and intracellular processes are inherently complex due to the large number of components and interactions, which are often nonlinear and occur at different spatiotemporal scales. Because of this complexity, mathematical modeling is increasingly used to simulate such systems and perform experiments in silico, many orders of magnitude faster than real experiments and often at a higher spatiotemporal resolution. In this article, we will focus on the generic modeling process and illustrate it with an example model of membrane lipid turnover.

High-Throughput Methods in the Discovery and Study of Biomaterials and Materiobiology

The complex interaction of cells with biomaterials (i.e., materiobiology) plays an increasingly pivotal role in the development of novel implants, biomedical devices, and tissue engineering scaffolds to treat diseases, aid in the restoration of bodily functions, construct healthy tissues, or regenerate diseased ones. However, the conventional approaches are incapable of screening the huge amount of potential material parameter combinations to identify the optimal cell responses and involve a combination of serendipity and many series of trial-and-error experiments. For advanced tissue engineering and regenerative medicine, highly efficient and complex bioanalysis platforms are expected to explore the complex interaction of cells with biomaterials using combinatorial approaches that offer desired complex microenvironments during healing, development, and homeostasis. In this review, we first introduce materiobiology and its high-throughput screening (HTS). Then we present an in-depth of the recent progress of 2D/3D HTS platforms (i.e., gradient and microarray) in the principle, preparation, screening for materiobiology, and combination with other advanced technologies. The Compendium for Biomaterial Transcriptomics and high content imaging, computational simulations, and their translation toward commercial and clinical uses are highlighted. In the final section, current challenges and future perspectives are discussed. High-throughput experimentation within the field of materiobiology enables the elucidation of the relationships between biomaterial properties and biological behavior and thereby serves as a potential tool for accelerating the development of high-performance biomaterials.

Mitotic spindle: lessons from theoretical modeling

Cell biology is immensely complex. To understand how cells work, we try to find patterns and suggest hypotheses to identify underlying mechanisms. However, it is not always easy to create a coherent picture from a huge amount of experimental data on biological systems, where the main players have multiple interactions or act in redundant pathways. In such situations, when a hypothesis does not lead to a conclusion in a direct way, theoretical modeling is a powerful tool because it allows us to formulate hypotheses in a quantitative manner and understand their consequences. A successful model should not only reproduce the basic features of the system but also provide exciting predictions, motivating new experiments. Much is learned when a model based on generally accepted knowledge cannot explain experiments of interest, as this indicates that the original hypothesis needs to be revised. In this Perspective, we discuss these points using our experiences in combining experiments with theory in the field of mitotic spindle mechanics.

Tools for time-course simulation in systems biology: a brief overview

Dynamic modeling of biological systems is essential for understanding all properties of a given organism as it allows us to look not only at the static picture of an organism but also at its behavior under various conditions. With the increasing amount of experimental data, the number of tools that enable dynamic analysis also grows. However, various tools are based on different approaches, use different types of data and offer different functions for analyses; so it can be difficult to choose the most suitable tool for a selected type of model. Here, we bring a brief overview containing descriptions of 50 tools for the reconstruction of biological models, their time-course simulation and dynamic analysis. We examined each tool using test data and divided them based on the qualitative and quantitative nature of the mathematical apparatus they use.

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

Mechanobiology of the Mitotic Spindle

The mitotic spindle is a microtubule-based assembly that separates the chromosomes during cell division. As the spindle is basically a mechanical micro machine, the understanding of its functioning is constantly motivating the development of experimental approaches based on mechanical perturbations, which are complementary to and work together with the classical genetics and biochemistry methods. Recent data emerging from these approaches in combination with theoretical modeling led to novel ideas and significant revisions of the basic concepts in the field. In this Perspective, we discuss the advances in the understanding of spindle mechanics, focusing on microtubule forces that control chromosome movements.

The analysis of living systems can generate both knowledge and illusions

Life relies on phenomena that range from changes in molecules that occur within nanoseconds to changes in populations that occur over millions of years. Researchers have developed a vast range of experimental techniques to analyze living systems, but a given technique usually only works over a limited range of length or time scales. Therefore, gaining a full understanding of a living system usually requires the integration of information obtained at multiple different scales by two or more techniques. This approach has undoubtedly led to a much better understanding of living systems but, equally, the staggering complexity of these systems, the sophistication and limitations of the techniques available in modern biology, and the need to use two or more techniques, can lead to persistent illusions of knowledge. Here, in an effort to make better use of the experimental techniques we have at our disposal, I propose a broad classification of techniques into six complementary approaches: perturbation, visualization, substitution, characterization, reconstitution, and simulation. Such a taxonomy might also help increase the reproducibility of inferences and improve peer review.

Combining in silico and in vitro models to inform cell seeding strategies in tissue engineering

The seeding density of therapeutic cells in engineered tissue impacts both cell survival and vascularization. Excessively high seeded cell densities can result in increased death and thus waste of valuable cells, whereas lower seeded cell densities may not provide sufficient support for the tissue in vivo, reducing efficacy. Additionally, the production of growth factors by therapeutic cells in low oxygen environments offers a way of generating growth factor gradients, which are important for vascularization, but hypoxia can also induce unwanted levels of cell death. This is a complex problem that lends itself to a combination of computational modelling and experimentation. Here, we present a spatio-temporal mathematical model parametrized using in vitro data capable of simulating the interactions between a therapeutic cell population, oxygen concentrations and vascular endothelial growth factor (VEGF) concentrations in engineered tissues. Simulations of collagen nerve repair constructs suggest that specific seeded cell densities and non-uniform spatial distributions of seeded cells could enhance cell survival and the generation of VEGF gradients. These predictions can now be tested using targeted experiments.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

Before a cell divides, it must make a copy of its genetic material and then promptly split in two. This process, called mitosis, is coordinated by many different molecular machines. The DNA is copied, then the duplicated chromosomes line up at the middle of the cell. Next, an apparatus called the mitotic spindle latches onto the chromosomes before pulling them apart. The mitotic spindle is a bundle of long, thin filaments called microtubules. It attaches to chromosomes at the kinetochore, the point where two copied chromosomes are cinched together in their middle.

Proper cell division is vital for the healthy growth of all organisms, big and small, and yet some parts of the process remain poorly understood despite extensive study. Specifically, there is more to learn about how the mitotic spindle self-assembles, and how microtubules and kinetochores work together to correctly orient and segregate chromosomes into two sister cells. These nanoscale processes are happening a hundred times a minute, so computer simulations are a good way to test what we know.

Edelmaier et al. developed a computer model to simulate cell division in fission yeast, a species of yeast often used to study fundamental processes in the cell. The model simulates how the mitotic spindle assembles, how its microtubules attach to the kinetochore and the force required to pull two sister chromosomes apart. Building the simulation involved modelling interactions between the mitotic spindle and kinetochore, their movement and forces applied. To test its accuracy, model simulations were compared to recordings of the mitotic spindle – including its length, structure and position – imaged from dividing yeast cells.

Running the simulation, Edelmaier et al. found that several key effects are essential for the proper movement of chromosomes in mitosis. This includes holding chromosomes in the correct orientation as the mitotic spindle assembles and controlling the relative position of microtubules as they attach to the kinetochore. Misaligned attachments must also be readily deconstructed and corrected to prevent any errors. The simulations also showed that kinetochores must begin to exert more force (to separate the chromosomes) once the mitotic spindle is attached correctly.

Altogether, these findings improve the current understanding of how the mitotic spindle and its counterparts control cell division. Errors in chromosome segregation are associated with birth defects and cancer in humans, and this new simulation could potentially now be used to help make predictions about how to correct mistakes in the process.

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling

MOTIVATION

Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell).

RESULTS

PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen.

AVAILABILITY AND IMPLEMENTATION

PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Cellular Automata Modeling of Stem-Cell-Driven Development of Tissue in the Nervous System

Mathematical and computational modeling enables biologists to integrate data from observations and experiments into a theoretical framework. In this review, we describe how developmental processes associated with stem-cell-driven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the single-cell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.

"Essentially, all models are wrong, but some are useful"-a cross-disciplinary agenda for building useful models in cell biology and biophysics

Intuition alone often fails to decipher the mechanisms underlying the experimental data in Cell Biology and Biophysics, and mathematical modeling has become a critical tool in these fields. However, mathematical modeling is not as widespread as it could be, because experimentalists and modelers often have difficulties communicating with each other, and are not always on the same page about what a model can or should achieve. Here, we present a framework to develop models that increase the understanding of the mechanisms underlying one's favorite biological system. Development of the most insightful models starts with identifying a good biological question in light of what is known and unknown in the field, and determining the proper level of details that are sufficient to address this question. The model should aim not only to explain already available data, but also to make predictions that can be experimentally tested. We hope that both experimentalists and modelers who are driven by mechanistic questions will find these guidelines useful to develop models with maximum impact in their field.

Memory functions reveal structural properties of gene regulatory networks

Gene regulatory networks (GRNs) control cellular function and decision making during tissue development and homeostasis. Mathematical tools based on dynamical systems theory are often used to model these networks, but the size and complexity of these models mean that their behaviour is not always intuitive and the underlying mechanisms can be difficult to decipher. For this reason, methods that simplify and aid exploration of complex networks are necessary. To this end we develop a broadly applicable form of the Zwanzig-Mori projection. By first converting a thermodynamic state ensemble model of gene regulation into mass action reactions we derive a general method that produces a set of time evolution equations for a subset of components of a network. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. These memory functions provide probes of near-steady state dynamics, revealing information not easily accessible otherwise. We illustrate the method on a simple cross-repressive transcriptional motif to show that memory functions not only simplify the analysis of the subnetwork but also have a natural interpretation. We then apply the approach to a GRN from the vertebrate neural tube, a well characterised developmental transcriptional network composed of four interacting transcription factors. The memory functions reveal the function of specific links within the neural tube network and identify features of the regulatory structure that specifically increase the robustness of the network to initial conditions. Taken together, the study provides evidence that Zwanzig-Mori projections offer powerful and effective tools for simplifying and exploring the behaviour of GRNs.

Gene regulatory networks are essential for cell fate specification and function. But the recursive links that comprise these networks often make determining their properties and behaviour complicated. Computational models of these networks can also be difficult to decipher. To reduce the complexity of such models we employ a Zwanzig-Mori projection approach. This allows a system of ordinary differential equations, representing a network, to be reduced to an arbitrary subnetwork consisting of part of the initial network, with the rest of the network (bulk) captured by memory functions. These memory functions account for the bulk by describing signals that return to the subnetwork after some time, having passed through the bulk. We show how this approach can be used to simplify analysis and to probe the behaviour of a gene regulatory network. Applying the method to a transcriptional network in the vertebrate neural tube reveals previously unappreciated properties of the network. By taking advantage of the structure of the memory functions we identify interactions within the network that are unnecessary for sustaining correct patterning. Upon further investigation we find that these interactions are important for conferring robustness to variation in initial conditions. Taken together we demonstrate the validity and applicability of the Zwanzig-Mori projection approach to gene regulatory networks.

A framework to find the logic backbone of a biological network

Background

Cellular behaviors are governed by interaction networks among biomolecules, for example gene regulatory and signal transduction networks. An often used dynamic modeling framework for these networks, Boolean modeling, can obtain their attractors (which correspond to cell types and behaviors) and their trajectories from an initial state (e.g. a resting state) to the attractors, for example in response to an external signal. The existing methods however do not elucidate the causal relationships between distant nodes in the network.

Results

In this work, we propose a simple logic framework, based on categorizing causal relationships as sufficient or necessary, as a complement to Boolean networks. We identify and explore the properties of complex subnetworks that are distillable into a single logic relationship. We also identify cyclic subnetworks that ensure the stabilization of the state of participating nodes regardless of the rest of the network. We identify the logic backbone of biomolecular networks, consisting of external signals, self-sustaining cyclic subnetworks (stable motifs), and output nodes. Furthermore, we use the logic framework to identify crucial nodes whose override can drive the system from one steady state to another. We apply these techniques to two biological networks: the epithelial-to-mesenchymal transition network corresponding to a developmental process exploited in tumor invasion, and the network of abscisic acid induced stomatal closure in plants. We find interesting subnetworks with logical implications in these networks. Using these subgraphs and motifs, we efficiently reduce both networks to succinct backbone structures.

Conclusions

The logic representation identifies the causal relationships between distant nodes and subnetworks. This knowledge can form the basis of network control or used in the reverse engineering of networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0482-5) contains supplementary material, which is available to authorized users.

Agents and networks to model the dynamic interactions of intracellular transport

Cell biology is increasingly evolving to become a more formal and quantitative science. The field of intracellular transport is no exception. However, it is extremely challenging to formulate mathematical and computational models for processes that involve dynamic structures that continuously change their shape, position and composition, leading to information transfer and functional outcomes. The two major strategies employed to represent intracellular trafficking are based on "ordinary differential equations" and "agent-" based modeling. Both approaches have advantages and drawbacks. Combinations of both modeling strategies have promising characteristics to generate meaningful simulations for intracellular transport and allow the formulation of new hypotheses and provide new insights. In the near future, cell biologists will encounter and hopefully overcome the challenge of translating descriptive cartoon representations of biological systems into mathematical network models.

Applications of Microfluidics in Quantitative Biology

Quantitative biology is dedicated to taking advantage of quantitative reasoning and advanced engineering technologies to make biology more predictable. Microfluidics, as an emerging technique, provides new approaches to precisely control fluidic conditions on small scales and collect data in high-throughput and quantitative manners. In this review, the authors present the relevant applications of microfluidics to quantitative biology based on two major categories (channel-based microfluidics and droplet-based microfluidics), and their typical features. We also envision some other microfluidic techniques that may not be employed in quantitative biology right now, but have great potential in the near future.

Measuring the Viscosity of the Escherichia coli Plasma Membrane Using Molecular Rotors

The viscosity is a highly important parameter within the cell membrane, affecting the diffusion of small molecules and, hence, controlling the rates of intracellular reactions. There is significant interest in the direct, quantitative assessment of membrane viscosity. Here we report the use of fluorescence lifetime imaging microscopy of the molecular rotor BODIPY C10 in the membranes of live Escherichia coli bacteria to permit direct quantification of the viscosity. Using this approach, we investigated the viscosity in live E. coli cells, spheroplasts, and liposomes made from E. coli membrane extracts. For live cells and spheroplasts, the viscosity was measured at both room temperature (23°C) and the E. coli growth temperature (37°C), while the membrane extract liposomes were studied over a range of measurement temperatures (5–40°C). At 37°C, we recorded a membrane viscosity in live E. coli cells of 950 cP, which is considerably higher than that previously observed in other live cell membranes (e.g., eukaryotic cells, membranes of Bacillus vegetative cells). Interestingly, this indicates that E. coli cells exhibit a high degree of lipid ordering within their liquid-phase plasma membranes.

Significance of Inactivated Genes in Leukemia: Pathogenesis and Prognosis

Epigenetic and genetic alterations are two mechanisms participating in leukemia, which can inactivate genes involved in leukemia pathogenesis or progression. The purpose of this review was to introduce various inactivated genes and evaluate their possible role in leukemia pathogenesis and prognosis. By searching the mesh words "Gene, Silencing AND Leukemia" in PubMed website, relevant English articles dealt with human subjects as of 2000 were included in this study. Gene inactivation in leukemia is largely mediated by promoter's hypermethylation of gene involving in cellular functions such as cell cycle, apoptosis, and gene transcription. Inactivated genes, such as ASPP1, TP53, IKZF1 and P15, may correlate with poor prognosis in acute lymphoid leukemia (ALL), chronic lymphoid leukemia (CLL), chronic myelogenous leukemia (CML) and acute myeloid leukemia (AML), respectively. Gene inactivation may play a considerable role in leukemia pathogenesis and prognosis, which can be considered as complementary diagnostic tests to differentiate different leukemia types, determine leukemia prognosis, and also detect response to therapy. In general, this review showed some genes inactivated only in leukemia (with differences between B-ALL, T-ALL, CLL, AML and CML). These differences could be of interest as an additional tool to better categorize leukemia types. Furthermore; based on inactivated genes, a diverse classification of Leukemias could represent a powerful method to address a targeted therapy of the patients, in order to minimize side effects of conventional therapies and to enhance new drug strategies.

Agent-based modeling: case study in cleavage furrow models

The number of studies in cell biology in which quantitative models accompany experiments has been growing steadily. Roughly, mathematical and computational techniques of these models can be classified as "differential equation based" (DE) or "agent based" (AB). Recently AB models have started to outnumber DE models, but understanding of AB philosophy and methodology is much less widespread than familiarity with DE techniques. Here we use the history of modeling a fundamental biological problem-positioning of the cleavage furrow in dividing cells-to explain how and why DE and AB models are used. We discuss differences, advantages, and shortcomings of these two approaches.

SSBD: a database of quantitative data of spatiotemporal dynamics of biological phenomena

Motivation: Rapid advances in live-cell imaging analysis and mathematical modeling have produced a large amount of quantitative data on spatiotemporal dynamics of biological objects ranging from molecules to organisms. There is now a crucial need to bring these large amounts of quantitative biological dynamics data together centrally in a coherent and systematic manner. This will facilitate the reuse of this data for further analysis.

Results: We have developed the Systems Science of Biological Dynamics database (SSBD) to store and share quantitative biological dynamics data. SSBD currently provides 311 sets of quantitative data for single molecules, nuclei and whole organisms in a wide variety of model organisms from Escherichia coli to Mus musculus. The data are provided in Biological Dynamics Markup Language format and also through a REST API. In addition, SSBD provides 188 sets of time-lapse microscopy images from which the quantitative data were obtained and software tools for data visualization and analysis.

Availability and Implementation: SSBD is accessible at http://ssbd.qbic.riken.jp.

Contact:sonami@riken.jp

Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics

Kinetochores are multi-protein complexes that mediate the physical coupling of sister chromatids to spindle microtubule bundles (called kinetochore (K)-fibres) from respective poles. These kinetochore-attached K-fibres generate pushing and pulling forces, which combine with polar ejection forces (PEF) and elastic inter-sister chromatin to govern chromosome movements. Classic experiments in meiotic cells using calibrated micro-needles measured an approximate stall force for a chromosome, but methods that allow the systematic determination of forces acting on a kinetochore in living cells are lacking. Here we report the development of mathematical models that can be fitted (reverse engineered) to high-resolution kinetochore tracking data, thereby estimating the model parameters and allowing us to indirectly compute the (relative) force components (K-fibre, spring force and PEF) acting on individual sister kinetochores in vivo. We applied our methodology to thousands of human kinetochore pair trajectories and report distinct signatures in temporal force profiles during directional switches. We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature. There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude. This data driven reverse engineering approach is sufficiently flexible to allow fitting of more complex mechanistic models; mathematical models of kinetochore dynamics can therefore be thoroughly tested on experimental data for the first time. Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

To achieve proper cell division, newly duplicated chromosomes must be segregated into daughter cells with high fidelity. This occurs in mitosis where during the crucial metaphase stage chromosomes are aligned on an imaginary plate, called the metaphase plate. Chromosomes are attached to a structural scaffold—the mitotic spindle, which is composed of dynamic fibres called microtubules—by protein machines called kinetochores. Observation of kinetochores during metaphase reveals they undergo a series of forward and backward movements. The mechanical system generating this oscillatory motion is not well understood. By tracking kinetochores in live cell 3D confocal microscopy and reverse engineering their trajectories we decompose the forces acting on kinetochores into the three main force generating components. Kinetochore dynamics are dominated by K-fibre forces, although changes in the minor spring force over time suggests an important role in controlling directional switching. In addition, we show that the strength of forces can vary both spatially within cells throughout the plate and between cells.

Robust and efficient parameter estimation in dynamic models of biological systems

Background

Dynamic modelling provides a systematic framework to understand function in biological systems. Parameter estimation in nonlinear dynamic models remains a very challenging inverse problem due to its nonconvexity and ill-conditioning. Associated issues like overfitting and local solutions are usually not properly addressed in the systems biology literature despite their importance.

Here we present a method for robust and efficient parameter estimation which uses two main strategies to surmount the aforementioned difficulties: (i) efficient global optimization to deal with nonconvexity, and (ii) proper regularization methods to handle ill-conditioning. In the case of regularization, we present a detailed critical comparison of methods and guidelines for properly tuning them. Further, we show how regularized estimations ensure the best trade-offs between bias and variance, reducing overfitting, and allowing the incorporation of prior knowledge in a systematic way.

Results

We illustrate the performance of the presented method with seven case studies of different nature and increasing complexity, considering several scenarios of data availability, measurement noise and prior knowledge. We show how our method ensures improved estimations with faster and more stable convergence. We also show how the calibrated models are more generalizable. Finally, we give a set of simple guidelines to apply this strategy to a wide variety of calibration problems.

Conclusions

Here we provide a parameter estimation strategy which combines efficient global optimization with a regularization scheme. This method is able to calibrate dynamic models in an efficient and robust way, effectively fighting overfitting and allowing the incorporation of prior information.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0219-2) contains supplementary material, which is available to authorized users.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.

Biological Dynamics Markup Language (BDML): an open format for representing quantitative biological dynamics data

Motivation: Recent progress in live-cell imaging and modeling techniques has resulted in generation of a large amount of quantitative data (from experimental measurements and computer simulations) on spatiotemporal dynamics of biological objects such as molecules, cells and organisms. Although many research groups have independently dedicated their efforts to developing software tools for visualizing and analyzing these data, these tools are often not compatible with each other because of different data formats.

Results: We developed an open unified format, Biological Dynamics Markup Language (BDML; current version: 0.2), which provides a basic framework for representing quantitative biological dynamics data for objects ranging from molecules to cells to organisms. BDML is based on Extensible Markup Language (XML). Its advantages are machine and human readability and extensibility. BDML will improve the efficiency of development and evaluation of software tools for data visualization and analysis.

Availability and implementation: A specification and a schema file for BDML are freely available online at http://ssbd.qbic.riken.jp/bdml/.

Contact:sonami@riken.jp

Supplementary Information:Supplementary data are available at Bioinformatics online.

The neural crest: a versatile organ system

The neural crest is the name given to the strip of cells at the junction between neural and epidermal ectoderm in neurula-stage vertebrate embryos, which is later brought to the dorsal neural tube as the neural folds elevate. The neural crest is a heterogeneous and multipotent progenitor cell population whose cells undergo EMT then extensively and accurately migrate throughout the embryo. Neural crest cells contribute to nearly every organ system in the body, with derivatives of neuronal, glial, neuroendocrine, pigment, and also mesodermal lineages. This breadth of developmental capacity has led to the neural crest being termed the fourth germ layer. The neural crest has occupied a prominent place in developmental biology, due to its exaggerated migratory morphogenesis and its remarkably wide developmental potential. As such, neural crest cells have become an attractive model for developmental biologists for studying these processes. Problems in neural crest development cause a number of human syndromes and birth defects known collectively as neurocristopathies; these include Treacher Collins syndrome, Hirschsprung disease, and 22q11.2 deletion syndromes. Tumors in the neural crest lineage are also of clinical importance, including the aggressive melanoma and neuroblastoma types. These clinical aspects have drawn attention to the selection or creation of neural crest progenitor cells, particularly of human origin, for studying pathologies of the neural crest at the cellular level, and also for possible cell therapeutics. The versatility of the neural crest lends itself to interlinked research, spanning basic developmental biology, birth defect research, oncology, and stem/progenitor cell biology and therapy.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here.

Single-molecule studies of actin assembly and disassembly factors

The actin cytoskeleton is very dynamic and highly regulated by multiple associated proteins in vivo. Understanding how this system of proteins functions in the processes of actin network assembly and disassembly requires methods to dissect the mechanisms of activity of individual factors and of multiple factors acting in concert. The advent of single-filament and single-molecule fluorescence imaging methods has provided a powerful new approach to discovering actin-regulatory activities and obtaining direct, quantitative insights into the pathways of molecular interactions that regulate actin network architecture and dynamics. Here we describe techniques for acquisition and analysis of single-molecule data, applied to the novel challenges of studying the filament assembly and disassembly activities of actin-associated proteins in vitro. We discuss the advantages of single-molecule analysis in directly visualizing the order of molecular events, measuring the kinetic rates of filament binding and dissociation, and studying the coordination among multiple factors. The methods described here complement traditional biochemical approaches in elucidating actin-regulatory mechanisms in reconstituted filamentous networks.

Automated platform for sensor-based monitoring and controlled assays of living cells and tissues

Cellular assays have become a fundamental technique in scientific research, pharmaceutical drug screening or toxicity testing. Therefore, the requirements of technical developments for automated assays raised in the same rate. A novel measuring platform was developed, which combines automated assay processing with label-free high-content measuring and real-time monitoring of multiple metabolic and morphologic parameters of living cells or tissues. Core of the system is a test plate with 24 cell culture wells, each equipped with opto-chemical sensor-spots for the determination of cellular oxygen consumption and extracellular acidification, next to electrode-structures for electrical impedance sensing. An automated microscope provides the optical sensor read-out and allows continuous cell imaging. Media and drugs are supplied by a pipetting robot system. Therefore, assay can run over several days without personnel interaction. To demonstrate the performance of the platform in physiologic assays, we continuously recorded the kinetics of metabolic and morphologic parameters of MCF-7 breast cancer cells under the influence of the cytotoxin chloroacetaldehyde. The data point out the time resolved effect kinetics over the complete treatment period. Thereby, the measuring platform overcomes problems of endpoint tests, which cannot monitor the kinetics of different parameters of the same cell population over longer time periods.

An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks

Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches that can directly relate the network structure to its dynamics. Of special interest is identifying the stable patterns of activity, i.e., the attractors of the system. This is a problem for large networks, because the state space of the system increases exponentially with network size. In this work, we present a novel network reduction approach that is based on finding network motifs that stabilize in a fixed state. Notably, we use a topological criterion to identify these motifs. Specifically, we find certain types of strongly connected components in a suitably expanded representation of the network. To test our method, we apply it to a dynamic network model for a type of cytotoxic T cell cancer and to an ensemble of random Boolean networks of size up to 200. Our results show that our method goes beyond reducing the network and in most cases can actually predict the dynamical repertoire of the nodes (fixed states or oscillations) in the attractors of the system.

The simulation approach in synthetic biology

Synthetic biology and systems biology are often highlighted as antagonistic strategies for dealing with the overwhelming complexity of biology (engineering versus understanding; tinkering in the lab versus modelling in the computer). However, a closer view of contemporary engineering methods (inextricably interwoven with mathematical modelling and simulation) and of the situation in biology (inextricably confronted with the intrinsic complexity of biomolecular environments) demonstrates that tinkering in the lab is increasingly supported by rational design methods. In other words: Synthetic biology and systems biology are merged by the use of computational techniques. These computational techniques are needed because the intrinsic complexity of biomolecular environments (stochasticity, non-linearities, system-level organization, evolution, independence, etc.) require advanced concepts of bio bricks and devices. A philosophical investigation of the history and nature of bio parts and devices reveals that these objects are imitating generic objects of engineering (switches, gates, oscillators, sensors, etc.), but the well-known design principles of generic objects are not sufficient for complex environments like cells. Therefore, the rational design methods have to be used to create more advanced generic objects, which are not only generic in their use, but also adaptive in their behavior. Case studies will show how simulation-based rational design methods are used to identify adequate parameters for synthesized designs (stability analyses), to improve lab experiments by 'looking through noise' (estimation of hidden variables and parameters), and to replace laborious and time-consuming post hoc tweaking in the lab by in-silico guidance (in-silico variation of bio brick properties). The overall aim of these developments, as will be argued in the discussion, is to achieve adaptive-generic instrumentality for bio parts and devices and thus increasingly merging systems and synthetic biology.

NMR line shapes and multi-state binding equilibria

Biological function of proteins relies on conformational transitions and binding of specific ligands. Protein-ligand interactions are thermodynamically and kinetically coupled to conformational changes in protein structures as conceptualized by the models of pre-existing equilibria and induced fit. NMR spectroscopy is particularly sensitive to complex ligand-binding modes-NMR line-shape analysis can provide for thermodynamic and kinetic constants of ligand-binding equilibria with the site-specific resolution. However, broad use of line shape analysis is hampered by complexity of NMR line shapes in multi-state systems. To facilitate interpretation of such spectral patterns, I computationally explored systems where isomerization or dimerization of a protein (receptor) molecule is coupled to binding of a ligand. Through an extensive analysis of multiple exchange regimes for a family of three-state models, I identified signature features to guide an NMR experimentalist in recognizing specific interaction mechanisms. Results show that distinct multi-state models may produce very similar spectral patterns. I also discussed aggregation of a receptor as a possible source of spurious three-state line shapes and provided specific suggestions for complementary experiments that can ensure reliable mechanistic insight.

Direct comparison of small RNA and transcription factor signaling

Small RNAs (sRNAs) and proteins acting as transcription factors (TFs) are the principal components of gene networks. These two classes of signaling molecules have distinct mechanisms of action; sRNAs control mRNA translation, whereas TFs control mRNA transcription. Here, we directly compare the properties of sRNA and TF signaling using mathematical models and synthetic gene circuits in Escherichia coli. We show the abilities of sRNAs to act on existing target mRNAs (as opposed to TFs, which alter the production of future target mRNAs) and, without needing to be first translated, have surprisingly little impact on the dynamics. Instead, the dynamics are primarily determined by the clearance rates, steady-state concentrations and response curves of the sRNAs and TFs; these factors determine the time delay before a target gene’s expression can maximally respond to changes in sRNA and TF transcription. The findings are broadly applicable to the analysis of signaling in gene networks, and we demonstrate that they can be used to rationally reprogram the dynamics of synthetic circuits.

Computer simulation and mathematical models of the noncentrosomal plant cortical microtubule cytoskeleton

There is rising interest in modeling the noncentrosomal cortical microtubule cytoskeleton of plant cells, particularly its organization into ordered arrays and the mechanisms that facilitate this organization. In this review, we discuss quantitative models of this highly complex and dynamic structure both at a cellular and molecular level. We report differences in methodologies and assumptions of different models as well as their controversial results. Our review provides insights for future studies to resolve these controversies, in addition to underlining the common results between various models. We also highlight the need to compare the results from simulation and mathematical models with quantitative data from biological experiments in order to test the validity of the models and to further improve them. It is our hope that this review will serve to provide guidelines for how to combine quantitative and experimental techniques to develop higher-level models of the plant cytoskeleton in the future.

Phosphoinositides in chemotaxis

Phosphatidylinositol lipids generated through the action of phosphinositide 3-kinase (PI3K) are key mediators of a wide array of biological responses. In particular, their role in the regulation of cell migration has been extensively studied and extends to amoeboid as well as mesenchymal migration. Through the emergence of fluorescent probes that target PI3K products as well as the use of specific inhibitors and knockout technologies, the spatio-temporal distribution of PI3K products in chemotaxing cells has been shown to represent a key anterior polarity signal that targets downstream effectors to actin polymerization. In addition, through intricate cross-talk networks PI3K products have been shown to regulate signals that control posterior effectors. Yet, in more complex environments or in conditions where chemoattractant gradients are steep, a variety of cell types can still chemotax in the absence of PI3K signals. Indeed, parallel signal transduction pathways have been shown to coordinately regulate cell polarity and directed movement. In this chapter, we will review the current role PI3K products play in the regulation of directed cell migration in various cell types, highlight the importance of mathematical modeling in the study of chemotaxis, and end with a brief overview of other signaling cascades known to also regulate chemotaxis.