Modelling spatio-temporal interactions within the cell

Biological phenomena at the cellular level can be represented by various types of mathematical formulations. Such representations allow us to carry out numerical simulations that provide mechanistic insights into complex behaviours of biological systems and also generate hypotheses that can be experimentally tested. Currently, we are particularly interested in spatio-temporal representations of dynamic cellular phenomena and how such models can be used to understand biological specificity in functional responses. This review describes the capability and limitations of the approaches used to study spatio-temporal dynamics of cell signalling components.     

Determining Disease Intervention Strategies Using Spatially Resolved Simulations

Predicting efficacy and optimal drug delivery strategies for small molecule and biological therapeutics is challenging due to the complex interactions between diverse cell types in different tissues that determine disease outcome. Here we present a new methodology to simulate inflammatory disease manifestation and test potential intervention strategies in silico using agent-based computational models. Simulations created using this methodology have explicit spatial and temporal representations, and capture the heterogeneous and stochastic cellular behaviours that lead to emergence of pathology or disease resolution. To demonstrate this methodology we have simulated the prototypic murine T cell-mediated autoimmune disease experimental autoimmune encephalomyelitis, a mouse model of multiple sclerosis. In the simulation immune cell dynamics, neuronal damage and tissue specific pathology emerge, closely resembling behaviour found in the murine model. Using the calibrated simulation we have analysed how changes in the timing and efficacy of T cell receptor signalling inhibition leads to either disease exacerbation or resolution. The technology described is a powerful new method to understand cellular behaviours in complex inflammatory disease, permits rational design of drug interventional strategies and has provided new insights into the role of TCR signalling in autoimmune disease progression.     

Nitric oxide and metastatic cell behaviour

Nitric oxide (NO) is a pleiotropic signalling molecule that subserves a wide variety of basic cellular functions and also manifests itself pathophysiologically. As regards cancer and its progression, however, the reported role of NO appears surprisingly inconsistent. In this review, we focus on metastasis, the process of cancer cell spread and secondary tumour formation. In a 'reductionist' approach, we consider the metastatic cascade to be made up of a series of basic cellular behaviours (such as proliferation, apoptosis, adhesion, secretion migration, invasion and angiogenesis). We evaluate how NO controls such behaviours, in comparison with normal cells. The available information suggests strongly that NO signalling would be expected to regulate these behaviours both positively and negatively and this probably leads to the observed apparent variability in the NO status of cancer cells and tissues. Thus, the role of NO in cancer is more complex than previously thought. A number of suggestions are made, including consideration of novel mechanisms, such as ion channels, in order to achieve a more consistent and integrated understanding of NO signalling in cancer and to realise its clinical potential.     

Modulation of VEGF signalling output by the Notch pathway

The formation of blood vessels within the vascular system entails a variety of cellular processes, including proliferation, migration and differentiation. In many cases, these diverse processes need to be finely coordinated among neighbouring endothelial cells in order to establish a functional vascular network. For instance, during angiogenic sprouting specialized endothelial tip cells follow guidance cues and migrate extensively into avascular tissues while trailing stalk cells must stay connected to the patent blood vessel. The vascular endothelial growth factor (VEGF) and Notch signalling pathways have emerged as the major players in governing these different cellular behaviours. In particular, recent work indicates an important role for Notch signalling in determining how an endothelial cell responds to VEGF. In this review, we provide an overview of these biochemically distinct pathways and discuss how they may interact during endothelial cell differentiation and angiogenesis.     

Pulsatile contractions and pattern formation in excitable actomyosin cortex

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulates stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.     

Signalling specificity in GPCR-dependent Ca2+ signalling

Cells use signalling networks to translate with high fidelity extracellular signals into specific cellular functions. Signalling networks are often composed of multiple signalling pathways that act in concert to regulate a particular cellular function. In the centre of the networks are the receptors that receive and transduce the signals. A versatile family of receptors that detect a remarkable variety of signals are the G protein-coupled receptors (GPCRs). Virtually all cells express several GPCRs that use the same biochemical machinery to transduce their signals. Considering the specificity and fidelity of signal transduction, a central question in cell signalling is how signalling specificity is achieved, in particular among GPCRs that use the same biochemical machinery. Ca(2+) signalling is particularly suitable to address such questions, since [Ca(2+)](i) can be recorded with excellent spatial and temporal resolutions in living cells and tissues and now in living animals. Ca(2+) is a unique second messenger in that both biochemical and biophysical components form the Ca(2+) signalling complex to regulate its concentration. Both components act in concert to generate repetitive [Ca(2+)](i) oscillations that can be either localized or in the form of global, propagating Ca(2+) waves. Most of the key proteins that form Ca(2+) signalling complexes are known and their activities are reasonably well understood on the biochemical and biophysical levels. We review here the information gained from studying Ca(2+) signalling by GPCRs to gain further understanding of the mechanisms used to generate cellular signalling specificity.     

Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.     

Exploiting the dynamic properties of covalent modification cycle for the design of synthetic analog biomolecular circuitry

Background

Cycles of covalent modification are ubiquitous motifs in cellular signalling. Although such signalling cycles are implemented via a highly concise set of chemical reactions, they have been shown to be capable of producing multiple distinct input-output mapping behaviours – ultrasensitive, hyperbolic, signal-transducing and threshold-hyperbolic.

Results

In this paper, we show how the set of chemical reactions underlying covalent modification cycles can be exploited for the design of synthetic analog biomolecular circuitry. We show that biomolecular circuits based on the dynamics of covalent modification cycles allow (a) the computation of nonlinear operators using far fewer chemical reactions than purely abstract designs based on chemical reaction network theory, and (b) the design of nonlinear feedback controllers with strong performance and robustness properties.

Conclusions

Our designs provide a more efficient route for translation of complex circuits and systems from chemical reactions to DNA strand displacement-based chemistry, thus facilitating their experimental implementation in future Synthetic Biology applications.

     

Upward mobility and alternative lifestyles: a report from the 10th biennial meeting on Bacterial Locomotion and Signal Transduction

This past January, in Cuernavaca Mexico, a conglomerate of scientists met to discuss the contemporary view of Bacterial Locomotion and Signal Transduction (BLAST). The BLAST meetings represent a field that has its roots in chemotaxis and the flagellum-based motility but now encompass all types of cellular movement and signalling. The topics varied from the interactions between molecules to the interactions between species. We heard about 3D reconstructions of transmembrane chemoreceptors within cells, new biophysical methods for understanding cellular engines, intricate phosphorelays, elaborate gene networks, new messenger molecules and emerging behaviours within complex populations of cells. At BLAST X we gained an appreciation for the lifestyle choices bacteria make, how they get to where they are going and the molecular mechanisms that underlie their decisions. Herein we review the highlights of the meeting.     

Integration of calcium and Ras signalling

Calcium is a universal intracellular signal that is responsible for controlling a plethora of cellular processes. Understanding how such a simple ion can regulate so many diverse cellular processes is a key goal of calcium- and cell-biologists. One molecule that is sensitive to changes in intracellular calcium levels is Ras. This small GTPase operates as a binary molecular switch, and regulates cell proliferation and differentiation. Here, we focus on examining the link between calcium and Ras signalling and, in particular, we speculate as to how the complexity of calcium signalling could regulate Ras activity.     

Mitophagy, mitochondrial dynamics and the general stress response in yeast

Autophagy is a fundamental cellular process promoting survival under various environmental stress conditions. Selective types of autophagy have gained much interest recently as they are involved in specific quality control mechanisms removing, for example, aggregated proteins or dysfunctional mitochondria. This is considered to counteract the development of a number of neurodegenerative disorders and aging. Here we review the role of mitophagy and mitochondrial dynamics in ensuring quality control of mitochondria. In particular, we provide possible explanations why mitophagy in yeast, in contrast with the situation in mammals, was found to be independent of mitochondrial fission. We further discuss recent findings linking these processes to nutrient sensing pathways and the general stress response in yeast. In particular, we propose a model for how the stress response protein Whi2 and the Ras/PKA (protein kinase A) signalling pathway are possibly linked and thereby regulate mitophagy.     

Jack of all trades,master of each: the diversity of fibroblast growth factor signalling in eye development

A central question in development biology is how a limited set of signalling pathways can instruct unlimited diversity of multicellular organisms. In this review, we use three ocular tissues as models of increasing complexity to present the astounding versatility of fibroblast growth factor (FGF) signalling. In the lacrimal gland, we highlight the specificity of FGF signalling in a one-dimensional model of budding morphogenesis. In the lens, we showcase the dynamics of FGF signalling in altering functional outcomes in a two-dimensional space. In the retina, we present the prolific utilization of FGF signalling from three-dimensional development to homeostasis. These examples not only shed light on the cellular basis for the perfection and complexity of ocular development, but also serve as paradigms for the diversity of FGF signalling.     

In silico identification of potential calcium dynamics and sarcomere targets for recovering left ventricular function in rat heart failure with preserved ejection fraction

Heart failure with preserved ejection fraction (HFpEF) is a complex disease associated with multiple co-morbidities, where impaired cardiac mechanics are often the end effect. At the cellular level, cardiac mechanics can be pharmacologically manipulated by altering calcium signalling and the sarcomere. However, the link between cellular level modulations and whole organ pump function is incompletely understood. Our goal is to develop and use a multi-scale computational cardiac mechanics model of the obese ZSF1 HFpEF rat to identify important biomechanical mechanisms that underpin impaired cardiac function and to predict how whole-heart mechanical function can be recovered through altering cellular calcium dynamics and/or cellular contraction. The rat heart was modelled using a 3D biventricular biomechanics model. Biomechanics were described by 16 parameters, corresponding to intracellular calcium transient, sarcomere dynamics, cardiac tissue and hemodynamics properties. The model simulated left ventricular (LV) pressure-volume loops that were described by 14 scalar features. We trained a Gaussian process emulator to map the 16 input parameters to each of the 14 outputs. A global sensitivity analysis was performed, and identified calcium dynamics and thin and thick filament kinetics as key determinants of the organ scale pump function. We employed Bayesian history matching to build a model of the ZSF1 rat heart. Next, we recovered the LV function, described by ejection fraction, peak pressure, maximum rate of pressure rise and isovolumetric relaxation time constant. We found that by manipulating calcium, thin and thick filament properties we can recover 34%, 28% and 24% of the LV function in the ZSF1 rat heart, respectively, and 39% if we manipulate all of them together. We demonstrated how a combination of biophysically based models and their derived emulators can be used to identify potential pharmacological targets. We predicted that cardiac function can be best recovered in ZSF1 rats by desensitising the myofilament and reducing the affinity to intracellular calcium concentration and overall prolonging the sarcomere staying in the active force generating state.     

Spatial organization of intracellular Ca2+ signals

The ability of Ca(2+), the simplest of all intracellular messengers, selectively to regulate so many cellular behaviours is due largely to the complex spatiotemporal organization of intracellular Ca(2+) signals. Most signalling pathways, including those that culminate in Ca(2+) signals, comprise sequences of protein-protein interactions linked by diffusible messengers. Using specific examples to illustrate key principles, we consider the roles of both components in defining the spatial organization of Ca(2+) signals. We discuss evidence that regulation of most Ca(2+) channels by Ca(2+) contributes to controlling the duration of Ca(2+) signals, to signal integration and, via Ca(2+)-induced Ca(2+) release, to defining the spatial spread of Ca(2+) signals. We distinguish two types of protein-protein interaction: scaffolds that allow rapid local transfer of diffusible messengers between signalling proteins, and interactions that directly transfer information between signalling proteins. Store-operated Ca(2+) entry provides a ubiquitous example of the latter, and it serves also to illustrate how Ca(2+) signals can be organized at different levels of spatial organization - from interactions between proteins to interactions between organelles.     

Imaging cell signalling and movement in development

Imaging is a method of choice to investigate the complex spatio-temporal cellular dynamics and the signalling pathways that control them during development. The ability to tag many proteins in vivo makes it possible to analyse the detailed dynamics of these interactions ranging over several orders of magnitude; from the study of single molecule events on the millisecond and nanometre scale up to the complex three-dimensional behaviour of cells in tissues on the millimetre scale over time periods of hours to days. Great advances are being made in the detailed study of molecular processes using high resolution imaging techniques in transparent samples close to the surface of cells or tissues, where light scattering is minimal. The major challenge is to translate some of these methods to the study of cells and tissues in their native 3D environment. These imaging methods require novel and innovative analysis methods to fully exploit the information available in these data. We will illustrate some of these points in the investigation of the development of the cellular slime mould Dictyostelium discoideum and the study of cell behaviours during gastrulation in the chick embryo.     

The enigma of phosphoinositides and their derivatives: Their role in regulation of subcellular compartment morphology

The general segregation of a molecular class, lipids, from the pathways of cellular communication, via endo-membranes, has resulted in the over-simplification and misconceptions in deciphering cell signalling mechanisms. Mechanisms in signal transduction and protein activation require targeting of proteins to membranous compartments with a specific localised morphology and dynamics that are dependent on their lipid composition. Many posttranslational events define cellular behaviours and without the active role of membranous compartments these events lead to various dysregulations of the signalling pathways. We summarise the key findings, using tools such as the rapalogue dimerisation, in the structural roles and signalling of the inter-related phosphoinositide lipids and their derivative, diacylglycerol, in the regulation of nuclear envelope biogenesis and other subcellular compartments such as the nucleoplasmic reticulum.     

Cell-signalling dynamics in time and space

The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dynamics of downstream signalling networks. Temporal dynamics are coupled to spatial gradients of signalling activities, which guide pivotal intracellular processes and tightly regulate signal propagation across a cell. Computational models provide insights into the complex relationships between the stimuli and the cellular responses, and reveal the mechanisms that are responsible for signal amplification, noise reduction and generation of discontinuous bistable dynamics or oscillations.