Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell

A mathematical model captures the role of adenyl cyclase Cyr1 and guanidine exchange factor Ira2 in creating a growth-to-hyphal bistable switch in Candida albicans

Recent biochemical experiments have indicated that in Candida albicans, a commensal fungal pathogen, the Ras signaling pathway plays a significant role in the yeast-to-hyphal transition; specifically, two enzymes in this pathway, Adenyl Cyclase Cyr1 and GTPase activating protein Ira2, facilitate this transition, in the presence of energy sensor ATP. However, the precise mechanism by which protein interactions between Ira2 and Cyr1 and the energy sensor ATP result in the yeast-to-hyphal transition and create a switch-like process are unknown. We propose a new set of biochemical reaction steps that captures all the essential interactions between Ira2, Cyr1, and ATP in the Ras pathway. With the help of chemical reaction network theory, we demonstrate that this set of biochemical reaction steps results in bistability. Further, bifurcation analysis of the differential equations based on this set of reaction steps supports the existence of a bistable switch, and this switch may act as a checkpoint mechanism for the promotion of growth-to-hyphal transition in C. albicans.

Neuronal RNA granules are ribosome complexes stalled at the pre-translocation state

The polarized cell morphology of neurons dictates many neuronal processes, including the axodendridic transport of specific mRNAs and subsequent translation. mRNAs together with ribosomes and RNA-binding proteins form RNA granules that are targeted to axodendrites for localized translation in neurons. It has been established that localized protein synthesis in neurons is essential for long-term memory formation, synaptic plasticity, and neurodegeneration. We have used proteomics and electron microscopy to characterize neuronal RNA granules (nRNAg) isolated from rat brain tissues or human neuroblastoma. We show that ribosome containing RNA granules are morula-like structures when visualized by electron microscopy. Crosslinking-coupled mass-spectrometry identified potential G3BP2 binding site on the ribosome near the eIF3d-binding site on the 40S ribosomal subunit. We used cryo-EM to resolve the structure of the ribosome-component of nRNAg. The cryo-EM reveals that predominant particles in nRNAg are 80S ribosomes, resembling the pre-translocation state where tRNA's are in the hybrid A/P and P/E site. We also describe a new kind of principal motion of the ribosome, which we call the rocking motion.

Rate and oscillatory switching dynamics of a multilayer visual microcircuit model

The neocortex is organized around layered microcircuits consisting of a variety of excitatory and inhibitory neuronal types which perform rate- and oscillation-based computations. Using modeling, we show that both superficial and deep layers of the primary mouse visual cortex implement two ultrasensitive and bistable switches built on mutual inhibitory connectivity motives between somatostatin, parvalbumin, and vasoactive intestinal polypeptide cells. The switches toggle pyramidal neurons between high and low firing rate states that are synchronized across layers through translaminar connectivity. Moreover, inhibited and disinhibited states are characterized by low- and high-frequency oscillations, respectively, with layer-specific differences in frequency and power which show asymmetric changes during state transitions. These findings are consistent with a number of experimental observations and embed firing rate together with oscillatory changes within a switch interpretation of the microcircuit.

Dynamic Catalysis Guided by Nucleic Acid Networks and DNA Nanostructures

Nucleic acid networks conjugated to native enzymes and supramolecular DNA nanostructures modified with enzymes or DNAzymes act as functional reaction modules for guiding dynamic catalytic transformations. These systems are exemplified with the assembly of constitutional dynamic networks (CDNs) composed of nucleic acid-functionalized enzymes, as constituents, undergoing triggered structural reconfiguration, leading to dynamically switched biocatalytic cascades. By coupling two nucleic acid/enzyme networks, the intercommunicated feedback-driven dynamic biocatalytic operation of the system is demonstrated. In addition, the tailoring of a nucleic acid/enzyme reaction network driving a dissipative, transient, biocatalytic cascade is introduced as a model system for out-of-equilibrium dynamically modulated biocatalytic transformation in nature. Also, supramolecular nucleic acid machines or DNA nanostructures, modified with DNAzyme or enzyme constituents, act as functional reaction modules driving temporal dynamic catalysis. The design of dynamic supramolecular machines is exemplified with the introduction of an interlocked two-ring catenane device that is dynamically reversibly switched between two states operating two different DNAzymes, and with the tailoring of a DNA-tweezers device functionalized with enzyme/DNAzyme constituents that guides the dynamic ON/OFF operation of a biocatalytic cascade by opening and closing the molecular device. In addition, DNA origami nanostructures provide functional scaffolds for the programmed positioning of enzymes or DNAzyme for the switchable operation of catalytic transformations. This is introduced by the tailored functionalization of the edges of origami tiles with nucleic acids guiding the switchable formation of DNAzyme catalysts through the dimerization/separation of the tiles. In addition, the programmed deposition of two-enzyme/cofactor constituents on the origami raft allowed the dynamic photochemical activation of the cofactor-mediated biocatalytic cascade on the spatially biocatalytic assembly on the scaffold. Furthermore, photoinduced "mechanical" switchable and reversible unlocking and closing of nanoholes in the origami frameworks allow the "ON" and "OFF" operation of DNAzyme units in the nanoholes, confined environments. The future challenges and potential applications of dynamic nucleic acid/enzyme and DNAzyme conjugates are discussed in the conclusion paragraph.

A Temperature-Dependent Model for Tritrophic Interactions Involving Tea Plants, Tea Green Leafhoppers and Natural Enemies

The tea green leaf hopper, Empoasca onukii Matsuda, is a severe pest of tea plants. Volatile emissions from tea shoots infested by the tea green leafhopper may directly repel insect feeding or attract natural enemies. Many studies have been conducted on various aspects of the tritrophic relationship involving tea plants, tea green leafhoppers and natural enemies. However, mathematic models which could explain the dynamic mechanisms of this tritrophic interaction are still lacking. In the current work, we constructed a realistic and stochastic model with temperature-dependent features to characterize the tritrophic interactions in the tea agroecosystem. Model outputs showed that two leafhopper outbreaks occur in a year, with their features being consistent with field observations. Simulations showed that daily average effective accumulated temperature (EAT) might be an important metric for outbreak prediction. We also showed that application of slow-releasing semiochemicals, as either repellents or attractants, may be highly efficacious for pest biocontrol and can significantly increase tea yields. Furthermore, the start date of applying semiochemicals can be optimized to effectively increase tea yields. The current model qualitatively characterizes key features of the tritrophic interactions and provides critical insight into pest control in tea ecosystems.

Cascaded dissipative DNAzyme-driven layered networks guide transient replication of coded-strands as gene models

Dynamic, transient, out-of-equilibrium networks guide cellular genetic, metabolic or signaling processes. Designing synthetic networks emulating natural processes imposes important challenges including the ordered connectivity of transient reaction modules, engineering of the appropriate balance between production and depletion of reaction constituents, and coupling of the reaction modules with emerging chemical functions dictated by the networks. Here we introduce the assembly of three coupled reaction modules executing a cascaded dynamic process leading to the transient formation and depletion of three different Mg²⁺-ion-dependent DNAzymes. The transient operation of the DNAzyme in one layer triggers the dynamic activation of the DNAzyme in the subsequent layer, leading to a three-layer transient catalytic cascade. The kinetics of the transient cascade is computationally simulated. The cascaded network is coupled to a polymerization/nicking DNA machinery guiding transient synthesis of three coded strands acting as “gene models”, and to the rolling circle polymerization machinery leading to the transient synthesis of fluorescent Zn(II)-PPIX/G-quadruplex chains or hemin/G-quadruplex catalytic wires.

A reaction network executing a cascaded transient formation and depletion of three different catalytic strands is introduced. The system is coupled to the secondary temporal synthesis of different coded strands as gene models.

A Model for the Proliferation–Quiescence Transition in Human Cells

The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher multi-cellular organisms such as mammals. Deregulation of proliferation-quiescence transition is related to many diseases, such as cancer. Recent studies have revealed that this proliferation–quiescence process is regulated tightly by the Rb−E2F bistable switch mechanism. Based on experimental observations, in this study, we formulate a mathematical model to examine the effect of the growth factor concentration on the proliferation–quiescence transition in human cells. Working with a non-dimensionalised model, we prove the positivity, boundedness and uniqueness of solutions. To understand model solution behaviour close to bifurcation points, we carry out bifurcation analysis, which is further illustrated by the use of numerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcation and numerical analysis of the model predicted a transition between bistable and stable states, which are dependent on the growth factor concentration parameter (GF). The derived predictions confirm experimental observations.

NETISCE: a network-based tool for cell fate reprogramming

The search for effective therapeutic targets in fields like regenerative medicine and cancer research has generated interest in cell fate reprogramming. This cellular reprogramming paradigm can drive cells to a desired target state from any initial state. However, methods for identifying reprogramming targets remain limited for biological systems that lack large sets of experimental data or a dynamical characterization. We present NETISCE, a novel computational tool for identifying cell fate reprogramming targets in static networks. In combination with machine learning algorithms, NETISCE estimates the attractor landscape and predicts reprogramming targets using signal flow analysis and feedback vertex set control, respectively. Through validations in studies of cell fate reprogramming from developmental, stem cell, and cancer biology, we show that NETISCE can predict previously identified cell fate reprogramming targets and identify potentially novel combinations of targets. NETISCE extends cell fate reprogramming studies to larger-scale biological networks without the need for full model parameterization and can be implemented by experimental and computational biologists to identify parts of a biological system relevant to the desired reprogramming task.

Structure-based approach to identifying small sets of driver nodes in biological networks

In network control theory, driving all the nodes in the Feedback Vertex Set (FVS) by node-state override forces the network into one of its attractors (long-term dynamic behaviors). The FVS is often composed of more nodes than can be realistically manipulated in a system; for example, only up to three nodes can be controlled in intracellular networks, while their FVS may contain more than 10 nodes. Thus, we developed an approach to rank subsets of the FVS on Boolean models of intracellular networks using topological, dynamics-independent measures. We investigated the use of seven topological prediction measures sorted into three categories-centrality measures, propagation measures, and cycle-based measures. Using each measure, every subset was ranked and then evaluated against two dynamics-based metrics that measure the ability of interventions to drive the system toward or away from its attractors: To Control and Away Control. After examining an array of biological networks, we found that the FVS subsets that ranked in the top according to the propagation metrics can most effectively control the network. This result was independently corroborated on a second array of different Boolean models of biological networks. Consequently, overriding the entire FVS is not required to drive a biological network to one of its attractors, and this method provides a way to reliably identify effective FVS subsets without the knowledge of the network dynamics.

Mechanisms and mathematical modelling of ROS production by the mitochondrial electron transport chain

Reactive oxygen species (ROS) are recognised both as damaging molecules and intracellular signalling entities. In addition to its role in ATP generation, the mitochondrial electron transport chain (ETC) constitutes a relevant source of mitochondrial ROS, in particular during pathological conditions. Mitochondrial ROS homeostasis depends on species- and site-dependent ROS production, their bioreactivity, diffusion, and scavenging. However, our quantitative understanding of mitochondrial ROS homeostasis has thus far been hampered by technical limitations, including lack of truly site- and/or ROS-specific reporter molecules. In this context, the use of computational models is of great value to complement and interpret empirical data, as well as to predict variables that are difficult to assess experimentally. During the last decades, various mechanistic models of ETC-mediated ROS production have been developed. Although these often-complex models have generated novel insights, their parameterisation, analysis, and integration with other computational models is not straightforward. In contrast, phenomenological (sometimes termed "minimal") models use a relatively small set of equations to describe empirical relationship(s) between ROS-related and other parameters, and generally aim to explore system behaviour and generate hypotheses for experimental validation. In this review, we first discuss ETC-linked ROS homeostasis and introduce various detailed mechanistic models. Next, we present how bioenergetic parameters (e.g. NADH/NAD⁺ ratio, mitochondrial membrane potential) relate to site-specific ROS production within the ETC and how these relationships can be used to design minimal models of ROS homeostasis. Finally, we illustrate how minimal models have been applied to explore pathophysiological aspects of ROS.

Modulating gene regulation function by chemically controlled transcription factor clustering

Recent studies have suggested that transcriptional protein condensates (or clusters) may play key roles in gene regulation and cell fate determination. However, it remains largely unclear how the gene regulation function is quantitatively tuned by transcription factor (TF) clustering and whether TF clustering may confer emergent behaviors as in cell fate control systems. Here, to address this, we construct synthetic TFs whose clustering behavior can be chemically controlled. Through single-parameter tuning of the system (i.e., TF clustering propensity), we provide lines of evidence supporting the direct transcriptional activation and amplification of target genes by TF clustering. Single-gene imaging suggests that such amplification results from the modulation of transcriptional dynamics. Importantly, TF clustering propensity modulates the gene regulation function by significantly tuning the effective TF binding affinity and to a lesser extent the ultrasensitivity, contributing to bimodality and sustained response behavior that are reminiscent of canonical cell fate control systems. Collectively, these results demonstrate that TF clustering can modulate the gene regulation function to enable emergent behaviors, and highlight the potential applications of chemically controlled protein clustering.

Transcription factor (TF) condensates appear to be pervasive, yet their roles remain debated. Here, the authors use a synthetic biology approach to show that TF clusters causally amplify transcription and can confer bimodality and “memory”.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.

Chloroquine and COVID-19—A systems biology model uncovers the drug’s detrimental effect on autophagy and explains its failure

The COVID-19 pandemic caused by SARS-CoV-2 has resulted in an urgent need for identifying potential therapeutic drugs. In the first half of 2020 tropic antimalarial drugs, such as chloroquine (CQ) or hydroxochloroquine (HCQ) were the focus of tremendous public attention. In the initial periods of the pandemic, many scientific results pointed out that CQ/HCQ could be very effective for patients with severe COVID. While CQ and HCQ have successfully been used against several diseases (such as malaria, autoimmune disease and rheumatic illnesses); long term use of these agents are associated with serious adverse effects (i.e. inducing acute kidney injury, among many others) due to their role in blocking autophagy-dependent self-degradation. Recent experimental and clinical trial data also confirmed that there is no sufficient evidence about the efficient usage of CQ/HCQ against COVID-19. By using systems biology techniques, here we show that the cellular effect of CQ/HCQ on autophagy during endoplasmic reticulum (ER) stress or following SARS-CoV-2 infection results in upregulation of ER stress. By presenting a simple mathematical model, we claim that although CQ/HCQ might be able to ameliorate virus infection, the permanent inhibition of autophagy by CQ/HCQ has serious negative effects on the cell. Since CQ/HCQ promotes apoptotic cell death, here we confirm that addition of CQ/HCQ cannot be really effective even in severe cases. Only a transient treatment seemed to be able to avoid apoptotic cell death, but this type of therapy could not limit virus replication in the infected host. The presented theoretical analysis clearly points out the utility and applicability of systems biology modelling to test the cellular effect of a drug targeting key major processes, such as autophagy and apoptosis. Applying these approaches could decrease the cost of pre-clinical studies and facilitate the selection of promising clinical trials in a timely fashion.

Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support mammalian progenitor cells’ capacity to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species—applicable to nearly half of human protein-coding genes—can generate sustained oscillations without explicit feedback. Diverging oscillation periods synergize with noise to robustly restore cell populations’ bimodal expression on timescales of days. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism underlying development, tissue regeneration, and cancer cell heterogeneity.

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations.

History Dependence in a Chemical Reaction Network Enables Dynamic Switching

This work describes an enzymatic autocatalytic network capable of dynamic switching under out-of-equilibrium conditions. The network, wherein a molecular fuel (trypsinogen) and an inhibitor (soybean trypsin inhibitor) compete for a catalyst (trypsin), is kept from reaching equilibria using a continuous flow stirred tank reactor. A so-called 'linear inhibition sweep' is developed (i.e., a molecular analogue of linear sweep voltammetry) to intentionally perturb the competition between autocatalysis and inhibition, and used to demonstrate that a simple molecular system, comprising only three components, is already capable of a variety of essential neuromorphic behaviors (hysteresis, synchronization, resonance, and adaptation). This research provides the first steps in the development of a strategy that uses the principles in systems chemistry to transform chemical reaction networks into platforms capable of neural network computing.

In vitro cell cycle oscillations exhibit a robust and hysteretic response to changes in cytoplasmic density

Cells control the properties of the cytoplasm to ensure proper functioning of biochemical processes. Recent studies showed that cytoplasmic density varies in both physiological and pathological states of cells undergoing growth, division, differentiation, apoptosis, senescence, and metabolic starvation. Little is known about how cellular processes cope with these cytoplasmic variations. Here, we study how a cell cycle oscillator comprising cyclin-dependent kinase (Cdk1) responds to changes in cytoplasmic density by systematically diluting or concentrating cycling Xenopus egg extracts in cell-like microfluidic droplets. We found that the cell cycle maintains robust oscillations over a wide range of deviations from the endogenous density: as low as 0.2× to more than 1.22× relative cytoplasmic density (RCD). A further dilution or concentration from these values arrested the system in a low or high steady state of Cdk1 activity, respectively. Interestingly, diluting an arrested cytoplasm of 1.22× RCD recovers oscillations at lower than 1× RCD. Thus, the cell cycle switches reversibly between oscillatory and stable steady states at distinct thresholds depending on the direction of tuning, forming a hysteresis loop. We propose a mathematical model which recapitulates these observations and predicts that the Cdk1/Wee1/Cdc25 positive feedback loops do not contribute to the observed robustness, supported by experiments. Our system can be applied to study how cytoplasmic density affects other cellular processes.

Thermal Input/Concentration Output Systems Processed by Chemical Reactions of Helicene Oligomers

This article describes thermal input/concentration output systems processed by chemical reactions. Various sophisticated thermal inputs can be converted into concentration outputs through the double-helix formation of helicene oligomers exhibiting thermal hysteresis. The inputs include high or low temperature, cooling or heating state, slow or fast cooling state, heating state, and cooling history. The chemical basis for the properties of the chemical reactions includes the reversibility out of chemical equilibrium, sigmoidal relationship and kinetics, bistability involving metastable states, positive feedback by self-catalytic chemical reactions, competitive chemical reactions, and fine tunability for parallel processing. The interfacing of concentration outputs in other systems is considered, and biological cells are considered to have been utilizing such input/output systems processed by chemical reactions.

Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

Living systems are products of evolution, and their present forms reflect their evolutionary history. Thus, to investigate the particularity of the evolutionary process by computer simulations, an appropriate reference system is needed for comparison with the outcomes of evolutionary simulations. In this study, we considered a model of gene regulatory networks (GRNs). Our idea was to construct a reference ensemble comprising randomly generated GRNs. To produce GRNs with high fitness values, which are rare, we employed a “rare event sampling” method developed in statistical physics. In particular, we focused on the evolution of mutational robustness. Living systems do not lose viability readily, even when some genes are mutated. This trait, called mutational robustness, has developed throughout evolution, along with functionality. Using the abovementioned method, we found that mutational robustness resulting from evolution exceeded that of the reference set. Therefore, mutational robustness is enhanced by evolution. We also found that the emergence of a new phenotype was significantly delayed in evolution. Our results suggest that this delay is a consequence of the fact that mutationally robust GRNs are favored by evolution.

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.

Mathematical Modeling in Circadian Rhythmicity

Circadian clocks are autonomous systems able to oscillate in a self-sustained manner in the absence of external cues, although such Zeitgebers are typically present. At the cellular level, the molecular clockwork consists of a complex network of interlocked feedback loops. This chapter discusses self-sustained circadian oscillators in the context of nonlinear dynamics theory. We suggest basic steps that can help in constructing a mathematical model and introduce how self-sustained generations can be modeled using ordinary differential equations. Moreover, we discuss how coupled oscillators synchronize among themselves or entrain to periodic signals. The development of mathematical models over the last years has helped to understand such complex network systems and to highlight the basic building blocks in which oscillating systems are built upon. We argue that, through theoretical predictions, the use of simple models can guide experimental research and is thus suitable to model biological systems qualitatively.

Mathematical Modelling in Plant Synthetic Biology

Mathematical modelling techniques are integral to current research in plant synthetic biology. Modelling approaches can provide mechanistic understanding of a system, allowing predictions of behaviour and thus providing a tool to help design and analyse biological circuits. In this chapter, we provide an overview of mathematical modelling methods and their significance for plant synthetic biology. Starting with the basics of dynamics, we describe the process of constructing a model over both temporal and spatial scales and highlight crucial approaches, such as stochastic modelling and model-based design. Next, we focus on the model parameters and the techniques required in parameter analysis. We then describe the process of selecting a model based on tests and criteria and proceed to methods that allow closer analysis of the system's behaviour. Finally, we highlight the importance of uncertainty in modelling approaches and how to deal with a lack of knowledge, noisy data, and biological variability; all aspects that play a crucial role in the cooperation between the experimental and modelling components. Overall, this chapter aims to illustrate the importance of mathematical modelling in plant synthetic biology, providing an introduction for those researchers who are working with or working on modelling techniques.

Teaching computational systems biology with an eye on quantitative systems pharmacology at the undergraduate level: Why do it, who would take it, and what should we teach?

Computational systems biology (CSB) is a field that emerged primarily as the product of research activities. As such, it grew in several directions in a distributed and uncoordinated manner making the area appealing and fascinating. The idea of not having to follow a specific path but instead creating one fueled innovation. As the field matured, several interdisciplinary graduate programs emerged attempting to educate future generations of computational systems biologists. These educational initiatives coordinated the dissemination of information across student populations that had already decided to specialize in this field. However, we are now entering an era where CSB, having established itself as a valuable research discipline, is attempting the next major step: Entering undergraduate curricula. As interesting as this endeavor may sound, it has several difficulties, mainly because the field is not uniformly defined. In this manuscript, we argue that this diversity is a significant advantage and that several incarnations of an undergraduate-level CSB biology course could, and should, be developed tailored to programmatic needs. In this manuscript, we share our experiences creating a course as part of a Biomedical Engineering program.

Toward a Logic of the Organism: A Process Philosophical Consideration

Mathematical models applied in contemporary theoretical and systems biology are based on some implicit ontological assumptions about the nature of organisms. This article aims to show that real organisms reveal a logic of internal causality transcending the tacit logic of biological modeling. Systems biology has focused on models consisting of static systems of differential equations operating with fixed control parameters that are measured or fitted to experimental data. However, the structure of real organisms is a highly dynamic process, the internal causality of which can only be captured by continuously changing systems of equations. In addition, in real physiological settings kinetic parameters can vary by orders of magnitude, i.e., organisms vary the value of internal quantities that in models are represented by fixed control parameters. Both the plasticity of organisms and the state dependence of kinetic parameters adds indeterminacy to the picture and asks for a new statistical perspective. This requirement could be met by the arising Biological Statistical Mechanics project, which promises to do more justice to the nature of real organisms than contemporary modeling. This article concludes that Biological Statistical Mechanics allows for a wider range of organismic ontologies than does the tacitly followed ontology of contemporary theoretical and systems biology, which are implicitly and explicitly based on systems theory.

A single-cell resolved cell-cell communication model explains lineage commitment in hematopoiesis

Cells do not make fate decisions independently. Arguably, every cell-fate decision occurs in response to environmental signals. In many cases, cell-cell communication alters the dynamics of the internal gene regulatory network of a cell to initiate cell-fate transitions, yet models rarely take this into account. Here, we have developed a multiscale perspective to study the granulocyte-monocyte versus megakaryocyte-erythrocyte fate decisions. This transition is dictated by the GATA1-PU.1 network: a classical example of a bistable cell-fate system. We show that, for a wide range of cell communication topologies, even subtle changes in signaling can have pronounced effects on cell-fate decisions. We go on to show how cell-cell coupling through signaling can spontaneously break the symmetry of a homogenous cell population. Noise, both intrinsic and extrinsic, shapes the decision landscape profoundly, and affects the transcriptional dynamics underlying this important hematopoietic cell-fate decision-making system.

This article has an associated ‘The people behind the papers’ interview.

Summary: Through theory and computational modeling, cell-cell communication is revealed to be a crucial and under-appreciated determinant of cell-fate decision-making during hematopoiesis.

The finding and researching algorithm for potentially oscillating enzymatic systems

Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations' own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case - oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.

Cyclin/Forkhead-mediated coordination of cyclin waves: an autonomous oscillator rationalizing the quantitative model of Cdk control for budding yeast

Networks of interacting molecules organize topology, amount, and timing of biological functions. Systems biology concepts required to pin down 'network motifs' or 'design principles' for time-dependent processes have been developed for the cell division cycle, through integration of predictive computer modeling with quantitative experimentation. A dynamic coordination of sequential waves of cyclin-dependent kinases (cyclin/Cdk) with the transcription factors network offers insights to investigate how incompatible processes are kept separate in time during the eukaryotic cell cycle. Here this coordination is discussed for the Forkhead transcription factors in light of missing gaps in the current knowledge of cell cycle control in budding yeast. An emergent design principle is proposed where cyclin waves are synchronized by a cyclin/Cdk-mediated feed-forward regulation through the Forkhead as a transcriptional timer. This design is rationalized by the bidirectional interaction between mitotic cyclins and the Forkhead transcriptional timer, resulting in an autonomous oscillator that may be instrumental for a well-timed progression throughout the cell cycle. The regulation centered around the cyclin/Cdk-Forkhead axis can be pivotal to timely coordinate cell cycle dynamics, thereby to actuate the quantitative model of Cdk control.

Incoherent modulation of bi-stable dynamics orchestrates the Mushroom and Isola bifurcations

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington's landscape theory and bifurcation analysis, we demonstrate that Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining a positive feedback motif with various incoherent feed-forward loops. Our study reveals that the intrinsic bi-stable dynamics originating from the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these minimal networks to produce these complex bifurcations. These modeling insights will be useful in identifying the possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

Systematic analysis of noise reduction properties of coupled and isolated feed-forward loops

Cells can maintain their homeostasis in a noisy environment since their signaling pathways can filter out noise somehow. Several network motifs have been proposed for biological noise filtering and, among these, feed-forward loops have received special attention. Specific feed-forward loops show noise reducing capabilities, but we notice that this feature comes together with a reduced signal transducing performance. In posttranslational signaling pathways feed-forward loops do not function in isolation, rather they are coupled with other motifs to serve a more complex function. Feed-forward loops are often coupled to other feed-forward loops, which could affect their noise-reducing capabilities. Here we systematically study all feed-forward loop motifs and all their pairwise coupled systems with activation-inactivation kinetics to identify which networks are capable of good noise reduction, while keeping their signal transducing performance. Our analysis shows that coupled feed-forward loops can provide better noise reduction and, at the same time, can increase the signal transduction of the system. The coupling of two coherent 1 or one coherent 1 and one incoherent 4 feed-forward loops can give the best performance in both of these measures.

Cellular behavior can be affected by noise in molecular interactions. Signaling pathways should process noisy input signals and support cellular decision making by properly transducing the signals, while removing noise from them. Three component networks of feed-forward loops (FFLs) have been proposed to serve as ideal noise reducers, while linear pathways were shown to be good signal transducers. These signaling units do not work in isolation, so there is a possibility that a combination of various feed-forward loops can provide good noise reduction, while maintaining good signal transduction. To test this hypothesis, we have systematically tested the noise reducing and signal transducing capabilities of all possible combinations of feed-forward loops and compared them with the performance of individual FFLs. We built mathematical models of all these systems and compared their capabilities at reducing noise in the input signal while maintaining responses to meaningful changes in the incoming signal. We found that a combination of two copies of a special type of fully positive signaling FFLs is the best noise reducer, while a combination of two incoherent (one positive, one negative signal) FFLs can provide the best signal transduction. The combination of these two FFLs could provide good signal processing where both noise reduction and signal transduction are achieved.

Effective description of bistability and irreversibility in apoptosis

Apoptosis is a mechanism of programmed cell death in which cells engage in a controlled demolition and prepare to be digested without damaging their environment. In normal conditions, apoptosis is repressed until it is irreversibly induced by an appropriate signal. In adult organisms, apoptosis is a natural way to dispose of damaged cells and its disruption or excess is associated with cancer and autoimmune diseases. Apoptosis is regulated by a complex signaling network controlled by caspases, specialized enzymes that digest essential cellular components and promote the degradation of genomic DNA. In this work, we propose an effective description of the signaling network focused on caspase-3 as a readout of cell fate. We integrate intermediate network interactions into a nonlinear feedback function acting on caspase-3 and introduce the effect of pro-apoptotic stimuli and regulatory elements as a saturating activation function. We show that activation dynamics in the theory is similar to previously reported experimental results. We compute bifurcation diagrams and obtain cell fate maps describing how stimulus intensity and feedback strength affect cell survival and death fates. These fates overlap within a bistable region that depends on total caspase concentration, regulatory elements, and feedback nonlinearity. We study a strongly nonlinear regime to obtain analytical expressions for bifurcation curves and fate map boundaries. For a broad range of parameters, strong stimuli can induce an irreversible switch to the death fate. We use the theory to explore dynamical stimulation conditions and determine how cell fate depends on stimulation temporal patterns. This analysis predicts a critical relation between transient stimuli intensity and duration to trigger irreversible apoptosis. We derive an analytical expression for this critical relation, valid for short stimuli. Our description provides distinct predictions and offers a framework to study how this signaling network processes different stimuli to make a cell fate decision.

Emergent Bistable Switches from the Incoherent Feed-Forward Signaling of a Positive Feedback Loop

Bistability is intrinsically connected to various decision making processes in living systems. The operating principles of a bistable switch, generated from a positive feedback loop, are well understood both in natural and synthetic settings. However, the fate of dynamic modularity of a positive feedback loop is unknown when it is connected to another dynamically modular signaling motif. In order to address this, here we investigate feed-forward signaling of a positive feedback loop to determine the fate of a bistable switch under such signaling. Using the potential energy based high-throughput bifurcation analysis method, we uncover that in addition to the conventional bistability the hybrid motifs generate various emergent bistable switches, namely mushroom and isola switches, which are not produced by the individual motifs. Using random parameter sampling, network perturbation, and phase plane analysis, we establish the design principles of such emergent behaviors. Incoherent feed-forward signaling of a positive feedback loop with distinct regulatory thresholds of the two arms of the feed-forward loop are the key requirements for such emergent behaviors. Our calculations show that the specific types of atypical bistable responses depend on the logic gate configuration of the signals. However, the emergent bistable behaviors of the hybrid networks do not depend on the nature of the positive feedback loop.

The complex landscape of haematopoietic lineage commitments is encoded in the coarse-grained endogenous network

Haematopoietic lineage commitments are presented by a canonical roadmap in which haematopoietic stem cells or multipotent progenitors (MPPs) bifurcate into progenitors of more restricted lineages and ultimately mature to terminally differentiated cells. Although transcription factors playing significant roles in cell-fate commitments have been extensively studied, integrating such knowledge into the dynamic models to understand the underlying biological mechanism remains challenging. The hypothesis and modelling approach of the endogenous network has been developed previously and tested in various biological processes and is used in the present study of haematopoietic lineage commitments. The endogenous network is constructed based on the key transcription factors and their interactions that determine haematopoietic cell-fate decisions at each lineage branchpoint. We demonstrate that the process of haematopoietic lineage commitments can be reproduced from the landscape which orchestrates robust states of network dynamics and their transitions. Furthermore, some non-trivial characteristics are unveiled in the dynamical model. Our model also predicted previously under-represented regulatory interactions and heterogeneous MPP states by which distinct differentiation routes are intermediated. Moreover, network perturbations resulting in state transitions indicate the effects of ectopic gene expression on cellular reprogrammes. This study provides a predictive model to integrate experimental data and uncover the possible regulatory mechanism of haematopoietic lineage commitments.

Stochastic pH Oscillations in a Model of the Urea-Urease Reaction Confined to Lipid Vesicles

The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.

Optimal ligand discrimination by asymmetric dimerization and turnover of interferon receptors

In multicellular organisms, antiviral defense mechanisms evoke a reliable collective immune response despite the noisy nature of biochemical communication between tissue cells. A molecular hub of this response, the interferon I receptor (IFNAR), discriminates between ligand types by their affinity regardless of concentration. To understand how ligand type can be decoded robustly by a single receptor, we frame ligand discrimination as an information-theoretic problem and systematically compare the major classes of receptor architectures: allosteric, homodimerizing, and heterodimerizing. We demonstrate that asymmetric heterodimers achieve the best discrimination power over the entire physiological range of local ligand concentrations. This design enables sensing of ligand presence and type, and it buffers against moderate concentration fluctuations. In addition, receptor turnover, which drives the receptor system out of thermodynamic equilibrium, allows alignment of activation points for ligands of different affinities and thereby makes ligand discrimination practically independent of concentration. IFNAR exhibits this optimal architecture, and our findings thus suggest that this specialized receptor can robustly decode digital messages carried by its different ligands.

Data-driven network models for genetic circuits from time-series data with incomplete measurements

Synthetic gene networks are frequently conceptualized and visualized as static graphs. This view of biological programming stands in stark contrast to the transient nature of biomolecular interaction, which is frequently enacted by labile molecules that are often unmeasured. Thus, the network topology and dynamics of synthetic gene networks can be difficult to verify in vivo or in vitro, due to the presence of unmeasured biological states. Here we introduce the dynamical structure function as a new mesoscopic, data-driven class of models to describe gene networks with incomplete measurements of state dynamics. We develop a network reconstruction algorithm and a code base for reconstructing the dynamical structure function from data, to enable discovery and visualization of graphical relationships in a genetic circuit diagram as time-dependent functions rather than static, unknown weights. We prove a theorem, showing that dynamical structure functions can provide a data-driven estimate of the size of crosstalk fluctuations from an idealized model. We illustrate this idea with numerical examples. Finally, we show how data-driven estimation of dynamical structure functions can explain failure modes in two experimentally implemented genetic circuits, a previously reported in vitro genetic circuit and a new E. coli-based transcriptional event detector.

Multi-scale network targeting: A holistic systems-biology approach to cancer treatment

The vulnerabilities of cancer at the cellular and, recently, with the introduction of immunotherapy, at the tissue level, have been exploited with variable success. Evaluating the cancer system vulnerabilities at the organismic level through analysis of network topology and network dynamics can potentially predict novel anti-cancer drug targets directed at the macroscopic cancer networks. Theoretical work analyzing the properties and the vulnerabilities of the multi-scale network of cancer needs to go hand-in-hand with experimental research that uncovers the biological nature of the relevant networks and reveals new targetable vulnerabilities. It is our hope that attacking cancer on different spatial scales, in a concerted integrated approach, may present opportunities for novel ways to prevent treatment resistance.

Are There Biomimetic Lessons from Genetic Regulatory Networks for Developing a Lunar Industrial Ecology?

We examine the prospect for employing a bio-inspired architecture for a lunar industrial ecology based on genetic regulatory networks. The lunar industrial ecology resembles a metabolic system in that it comprises multiple chemical processes interlinked through waste recycling. Initially, we examine lessons from factory organisation which have evolved into a bio-inspired concept, the reconfigurable holonic architecture. We then examine genetic regulatory networks and their application in the biological cell cycle. There are numerous subtleties that would be challenging to implement in a lunar industrial ecology but much of the essence of biological circuitry (as implemented in synthetic biology, for example) is captured by traditional electrical engineering design with emphasis on feedforward and feedback loops to implement robustness.

Towards a physical understanding of developmental patterning

The temporal coordination of events at cellular and tissue scales is essential for the proper development of organisms, and involves cell-intrinsic processes that can be coupled by local cellular signalling and instructed by global signalling, thereby creating spatial patterns of cellular states that change over time. The timing and structure of these patterns determine how an organism develops. Traditional developmental genetic methods have revealed the complex molecular circuits regulating these processes but are limited in their ability to predict and understand the emergent spatio-temporal dynamics. Increasingly, approaches from physics are now being used to help capture the dynamics of the system by providing simplified, generic descriptions. Combined with advances in imaging and computational power, such approaches aim to provide insight into timing and patterning in developing systems.

Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR), a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex-complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a 'prozone' effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.

Resonating neurons stabilize heterogeneous grid-cell networks

A central theme that governs the functional design of biological networks is their ability to sustain stable function despite widespread parametric variability. Here, we investigated the impact of distinct forms of biological heterogeneities on the stability of a two-dimensional continuous attractor network (CAN) implicated in grid-patterned activity generation. We show that increasing degrees of biological heterogeneities progressively disrupted the emergence of grid-patterned activity and resulted in progressively large perturbations in low-frequency neural activity. We postulated that targeted suppression of low-frequency perturbations could ameliorate heterogeneity-induced disruptions of grid-patterned activity. To test this, we introduced intrinsic resonance, a physiological mechanism to suppress low-frequency activity, either by adding an additional high-pass filter (phenomenological) or by incorporating a slow negative feedback loop (mechanistic) into our model neurons. Strikingly, CAN models with resonating neurons were resilient to the incorporation of heterogeneities and exhibited stable grid-patterned firing. We found CAN models with mechanistic resonators to be more effective in targeted suppression of low-frequency activity, with the slow kinetics of the negative feedback loop essential in stabilizing these networks. As low-frequency perturbations (1/f noise) are pervasive across biological systems, our analyses suggest a universal role for mechanisms that suppress low-frequency activity in stabilizing heterogeneous biological networks.

Biophysical and Quantitative Principles of Centrosome Biogenesis and Structure

The centrosome is a main orchestrator of the animal cellular microtubule cytoskeleton. Dissecting its structure and assembly mechanisms has been a goal of cell biologists for over a century. In the last two decades, a good understanding of the molecular constituents of centrosomes has been achieved. Moreover, recent breakthroughs in electron and light microscopy techniques have enabled the inspection of the centrosome and the mapping of its components with unprecedented detail. However, we now need a profound and dynamic understanding of how these constituents interact in space and time. Here, we review the latest findings on the structural and molecular architecture of the centrosome and how its biogenesis is regulated, highlighting how biophysical techniques and principles as well as quantitative modeling are changing our understanding of this enigmatic cellular organelle. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Modeling the Influence of Chronic Sleep Restriction on Cortisol Circadian Rhythms, with Implications for Metabolic Disorders

Chronic sleep deficiency is prevalent in modern society and is associated with increased risk of metabolic and other diseases. While the mechanisms by which chronic sleep deficiency induces pathophysiological changes are yet to be elucidated, the hypothalamic–pituitary–adrenal (HPA) axis may be an important mediator of these effects. Cortisol, the primary hormone of the HPA axis, exhibits robust circadian rhythmicity and is moderately influenced by sleep and wake states and other physiology. Several studies have explored the effects of acute or chronic sleep deficiency (i.e., usually from self-selected chronic sleep restriction, CSR) on the HPA axis. Quantifying long-term changes in the circadian rhythm of cortisol under CSR in controlled conditions is inadequately studied due to practical limitations. We use a semi-mechanistic mathematical model of the HPA axis and the sleep/wake cycle to explore the influence of CSR on cortisol circadian rhythmicity. In qualitative agreement with experimental findings, model simulations predict that CSR results in physiologically relevant disruptions in the phase and amplitude of the cortisol rhythm. The mathematical model presented in this work provides a mechanistic framework to further explore how CSR might lead to HPA axis disruption and subsequent development of chronic metabolic complications.

Collapse of Intra-Tumor Cooperation Induced by Engineered Defector Cells

Anti-cancer therapies promote clonal selection of resistant cells that evade treatment. Effective therapy must be stable against the evolution of resistance. A potential strategy based on concepts from evolutionary game theory is to impair intra-tumor cooperation using genetically modified cells in which genes coding for essential growth factors have been knocked out. Such engineered cells would spread by clonal selection, driving the collapse of intra-tumor cooperation and a consequent reduction in tumor growth. Here, I test this idea in vitro in four cancer types (neuroendocrine pancreatic cancer, mesothelioma, lung adenocarcinoma and multiple myeloma). A reduction, or even complete eradication, of the producer clone and the consequent reduction in cell proliferation, is achieved in some but not all cases by introducing a small fraction of non-producer cells in the population. I show that the collapse of intra-tumor cooperation depends on the cost/benefit ratio of growth factor production. When stable cooperation among producer and non-producer cells occurs, its collapse can be induced by increasing the number of growth factors available to the cells. Considerations on nonlinear dynamics in the framework of evolutionary game theory explain this as the result of perturbation of the equilibrium of a system that resembles a public goods game, in which the production of growth factors is a cooperative phenotype. Inducing collapse of intra-tumor cooperation by engineering cancer cells will require the identification of growth factors that are essential for the tumor and that have a high cost of production for the cell.

Life and death saddles in the heart

Saddle points are responsible for threshold phenomena of many biological systems. In the heart, saddle points determine the normal excitability and conduction, but are also responsible for certain abnormal action potential behaviors associated with lethal arrhythmias. We investigate the dynamical mechanisms for the genesis of lethal extra heartbeats in heterogeneous cardiac tissue under two diseased conditions. For both conditions, the lethal events occur when the system is close to the saddle point, implying the pivotal role of the saddle point in cardiac arrhythmogenesis.

Akt phosphorylates insulin receptor substrate to limit PI3K-mediated PIP3 synthesis

The phosphoinositide 3-kinase (PI3K)-Akt network is tightly controlled by feedback mechanisms that regulate signal flow and ensure signal fidelity. A rapid overshoot in insulin-stimulated recruitment of Akt to the plasma membrane has previously been reported, which is indicative of negative feedback operating on acute timescales. Here, we show that Akt itself engages this negative feedback by phosphorylating insulin receptor substrate (IRS) 1 and 2 on a number of residues. Phosphorylation results in the depletion of plasma membrane-localised IRS1/2, reducing the pool available for interaction with the insulin receptor. Together these events limit plasma membrane-associated PI3K and phosphatidylinositol (3,4,5)-trisphosphate (PIP3) synthesis. We identified two Akt-dependent phosphorylation sites in IRS2 at S306 (S303 in mouse) and S577 (S573 in mouse) that are key drivers of this negative feedback. These findings establish a novel mechanism by which the kinase Akt acutely controls PIP3 abundance, through post-translational modification of the IRS scaffold.