Membrane-binding/modification model of signaling protein activation and analysis of its control by cell morphology

Mechanotransduction as a major driver of cell behaviour: mechanisms, and relevance to cell organization and future research

How do cells process environmental cues to make decisions? This simple question is still generating much experimental and theoretical work, at the border of physics, chemistry and biology, with strong implications in medicine. The purpose of mechanobiology is to understand how biochemical and physical cues are turned into signals through mechanotransduction. Here, we review recent evidence showing that (i) mechanotransduction plays a major role in triggering signalling cascades following cell-neighbourhood interaction; (ii) the cell capacity to continually generate forces, and biomolecule properties to undergo conformational changes in response to piconewton forces, provide a molecular basis for understanding mechanotransduction; and (iii) mechanotransduction shapes the guidance cues retrieved by living cells and the information flow they generate. This includes the temporal and spatial properties of intracellular signalling cascades. In conclusion, it is suggested that the described concepts may provide guidelines to define experimentally accessible parameters to describe cell structure and dynamics, as a prerequisite to take advantage of recent progress in high-throughput data gathering, computer simulation and artificial intelligence, in order to build a workable, hopefully predictive, account of cell signalling networks.

A metabolic reaction-diffusion model for PKCα translocation via PIP2 hydrolysis in an endothelial cell

Hydrolysis of the phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2) at the cell membrane induces the release of inositol 1,4,5-trisphosphate (IP3) into the cytoplasm and diffusion of diacylglycerol (DAG) through the membrane, respectively. Release of IP3 subsequently increases Ca2+ levels in the cytoplasm, which results in activation of protein kinase C α (PKCα) by Ca2+ and DAG, and finally the translocation of PKCα from the cytoplasm to the membrane. In this study, we developed a metabolic reaction-diffusion framework to simulate PKCα translocation via PIP2 hydrolysis in an endothelial cell. A three-dimensional cell model, divided into membrane and cytoplasm domains, was reconstructed from confocal microscopy images. The associated metabolic reactions were divided into their corresponding domain; PIP2 hydrolysis at the membrane domain resulted in DAG diffusion at the membrane domain and IP3 release into the cytoplasm domain. In the cytoplasm domain, Ca2+ was released from the endoplasmic reticulum, and IP3, Ca2+, and PKCα diffused through the cytoplasm. PKCα bound Ca2+ at, and diffused through, the cytoplasm, and was finally activated by binding with DAG at the membrane. Using our model, we analyzed IP3 and DAG dynamics, Ca2+ waves, and PKCα translocation in response to a microscopic stimulus. We found a qualitative agreement between our simulation results and our experimental results obtained by live-cell imaging. Interestingly, our results suggest that PKCα translocation is dominated by DAG dynamics. This three-dimensional reaction-diffusion mathematical framework could be used to investigate the link between PKCα activation in a cell and cell function.

Mechanistic models of PLC/PKC signaling implicate phosphatidic acid as a key amplifier of chemotactic gradient sensing

Chemotaxis of fibroblasts and other mesenchymal cells is critical for embryonic development and wound healing. Fibroblast chemotaxis directed by a gradient of platelet-derived growth factor (PDGF) requires signaling through the phospholipase C (PLC)/protein kinase C (PKC) pathway. Diacylglycerol (DAG), the lipid product of PLC that activates conventional PKCs, is focally enriched at the up-gradient leading edge of fibroblasts responding to a shallow gradient of PDGF, signifying polarization. To explain the underlying mechanisms, we formulated reaction-diffusion models including as many as three putative feedback loops based on known biochemistry. These include the previously analyzed mechanism of substrate-buffering by myristoylated alanine-rich C kinase substrate (MARCKS) and two newly considered feedback loops involving the lipid, phosphatidic acid (PA). DAG kinases and phospholipase D, the enzymes that produce PA, are identified as key regulators in the models. Paradoxically, increasing DAG kinase activity can enhance the robustness of DAG/active PKC polarization with respect to chemoattractant concentration while decreasing their whole-cell levels. Finally, in simulations of wound invasion, efficient collective migration is achieved with thresholds for chemotaxis matching those of polarization in the reaction-diffusion models. This multi-scale modeling framework offers testable predictions to guide further study of signal transduction and cell behavior that affect mesenchymal chemotaxis.

Cell movement directed by external gradients of chemical composition is critical for immune responses, wound healing, and development. Although theoretical concepts explaining how shallow external gradients might definitively polarize a cell’s motility have been offered over the past two decades, mathematical models cast in terms of defined molecules and mechanisms are uncommon in this context. Based on both recent and older insights from the literature, we offer mechanistic models that are able to explain experimentally observed polarization of signal transduction elicited by shallow attractant gradients. A novel insight of our models is the implicated role of phosphatidic acid, a membrane lipid produced by at least two enzymatic pathways, in two positive feedback loops that amplify signal transduction locally. In separate simulations, we explored the implications of polarization for efficient cell invasion during wound healing. We expected that the ability to polarize in response to shallow gradients would enhance the speed of wound invasion, but an unexpected finding is that this property can promote intermittent polarization throughout the wound.

A Reaction-Diffusion Model Explains Amplification of the PLC/PKC Pathway in Fibroblast Chemotaxis

During the proliferative phase of cutaneous wound healing, dermal fibroblasts are recruited into the clotted wound by a concentration gradient of platelet-derived growth factor (PDGF), together with other spatial cues. Despite the importance of this chemotactic process, the mechanisms controlling the directed migration of slow-moving mesenchymal cells such as fibroblasts are not well understood. Here, we develop and analyze a reaction-diffusion model of phospholipase C/protein kinase C (PKC) signaling, which was recently identified as a requisite PDGF-gradient-sensing pathway, with the goal of identifying mechanisms that can amplify its sensitivity in the shallow external gradients typical of chemotaxis experiments. We show that phosphorylation of myristoylated alanine-rich C kinase substrate by membrane-localized PKC constitutes a positive feedback that is sufficient for local pathway amplification. The release of phosphorylated myristoylated alanine-rich C kinase substrate and its subsequent diffusion and dephosphorylation in the cytosol also serves to suppress the pathway in down-gradient regions of the cell. By itself, this mechanism only weakly amplifies signaling in a shallow PDGF gradient, but it synergizes with other feedback mechanisms to enhance amplification. This model offers a framework for a mechanistic understanding of phospholipase C/PKC signaling in chemotactic gradient sensing and can guide the design of experiments to assess the roles of putative feedback loops.

Formation of morphogen gradients: local accumulation time

Spatial regulation of cell differentiation in embryos can be provided by morphogen gradients, which are defined as the concentration fields of molecules that control gene expression. For example, a cell can use its surface receptors to measure the local concentration of an extracellular ligand and convert this information into a corresponding change in its transcriptional state. We characterize the time needed to establish a steady-state gradient in problems with diffusion and degradation of locally produced chemical signals. A relaxation function is introduced to describe how the morphogen concentration profile approaches its steady state. This function is used to obtain a local accumulation time that provides a time scale that characterizes relaxation to steady state at an arbitrary position within the patterned field. To illustrate the approach we derive local accumulation times for a number of commonly used models of morphogen gradient formation.

Directional persistence of cell migration coincides with stability of asymmetric intracellular signaling

It has long been appreciated that spatiotemporal dynamics of cell migration are under the control of intracellular signaling pathways, which are mediated by adhesion receptors and other transducers of extracellular cues. Further, there is ample evidence that aspects of cell migration are stochastic: how else could it exhibit directional persistence over timescales much longer than typical signal transduction processes, punctuated by abrupt changes in direction? Yet the mechanisms by which signaling processes affect those behaviors remain unclear. We have developed analytical methods for relating parallel live-cell microscopy measurements of cell migration dynamics to the intracellular signaling processes that govern them. In this analysis of phosphoinositide 3-kinase signaling in randomly migrating fibroblasts, we observe that hot spots of intense signaling coincide with localized cell protrusion and endure with characteristic lifetimes that correspond to those of cell migration persistence. We further show that distant hot spots are dynamically and stochastically coupled. These results are indicative of a mechanism by which changes in a cell's direction of migration are determined by a fragile balance of relatively rapid intracellular signaling processes.

Use of virtual cell in studies of cellular dynamics

The Virtual Cell (VCell) is a unique computational environment for modeling and simulation of cell biology. It has been specifically designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists. The models created with VCell can range from the simple, to evaluate hypotheses or to interpret experimental data, to complex multilayered models used to probe the predicted behavior of spatially resolved, highly nonlinear systems. In this chapter, we discuss modeling capabilities of VCell and demonstrate representative examples of the models published by the VCell users.

Analysis of reaction-diffusion systems with anomalous subdiffusion

Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.

Model for Protein Concentration Gradients in the Cytoplasm

Intracellular protein concentration gradients are generally thought to be unsustainable at steady-state due to diffusion. Here we show how protein concentration gradients can theoretically be sustained indefinitely through a relatively simple mechanism that couples diffusion to a spatially segregated kinase-phosphatase system. Although it is appreciated that such systems can theoretically give rise to phosphostate gradients, it has been assumed that they do not give rise to gradients in the total protein concentration. Here we show that this assumption does not hold if the two forms of protein have different diffusion coefficients. If, for example, the phosphorylated state binds selectively to a second larger protein or protein complex then a steady state gradient in total protein concentration will be created. We illustrate the principle with an analytical solution to the diffusion-reaction problem and by stochastic individual-based simulations using the Smoldyn program. We argue that protein gradients created in this way need to be considered in experiments using fluorescent probes and could in principle encode spatial information in the cytoplasm.

How Cells feel their environment: a focus on early dynamic events

It is now well demonstrated that cell adhesion to a foreign surface strongly influences prominent functions such as survival, proliferation, differentiation, migration or mediator release. Thus, a current challenge of major practical and theoretical interest is to understand how cells process and integrate environmental cues to determine future behaviour. The purpose of this review is to summarize some pieces of information that might serve this task. Three sequential points are discussed. First, selected examples are presented to illustrate the influence of substratum chemistry, topography and mechanical properties on nearly all aspects of cell behaviour observed during the days following adhesion. Second, we review reported evidence that long term cell behaviour is highly dependent on the alterations of cell shape and cytoskeletal organization that are often initiated during the minutes to hours following adhesion. Third, we review recently obtained information on cell membrane roughness and dynamics, as well as kinetics and mechanics of molecular interactions. This knowledge is required to understand the influence of substratum structure on cell signaling during the first minute following contact, before the appearance of detectable structural changes. It is suggested that unraveling the earliest phenomena following cell-to-substratum encounter might provide a tractable way of better understanding subsequent events.