Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks

From transcriptomics to digital twins of organ function

Cell level functions underlie tissue and organ physiology. Gene expression patterns offer extensive views of the pathways and processes within and between cells. Single cell transcriptomics provides detailed information on gene expression within cells, cell types, subtypes and their relative proportions in organs. Functional pathways can be scalably connected to physiological functions at the cell and organ levels. Integrating experimentally obtained gene expression patterns with prior knowledge of pathway interactions enables identification of networks underlying whole cell functions such as growth, contractility, and secretion. These pathways can be computationally modeled using differential equations to simulate cell and organ physiological dynamics regulated by gene expression changes. Such computational systems can be thought of as parts of digital twins of organs. Digital twins, at the core, need computational models that represent in detail and simulate how dynamics of pathways and networks give rise to whole cell level physiological functions. Integration of transcriptomic responses and numerical simulations could simulate and predict whole cell functional outputs from transcriptomic data. We developed a computational pipeline that integrates gene expression timelines and systems of coupled differential equations to generate cell-type selective dynamical models. We tested our integrative algorithm on the eicosanoid biosynthesis network in macrophages. Converting transcriptomic changes to a dynamical model allowed us to predict dynamics of prostaglandin and thromboxane synthesis and secretion by macrophages that matched published lipidomics data obtained in the same experiments. Integration of cell-level system biology simulations with genomic and clinical data using a knowledge graph framework will allow us to create explicit predictive models that mechanistically link genomic determinants to organ function. Such integration requires a multi-domain ontological framework to connect genomic determinants to gene expression and cell pathways and functions to organ level phenotypes in healthy and diseased states. These integrated scalable models of tissues and organs as accurate digital twins predict health and disease states for precision medicine.

Heterogeneous off-target impact of ion-channel deletion on intrinsic properties of hippocampal model neurons that self-regulate calcium

How do neurons that implement cell-autonomous self-regulation of calcium react to knockout of individual ion-channel conductances? To address this question, we used a heterogeneous population of 78 conductance-based models of hippocampal pyramidal neurons that maintained cell-autonomous calcium homeostasis while receiving theta-frequency inputs. At calcium steady-state, we individually deleted each of the 11 active ion-channel conductances from each model. We measured the acute impact of deleting each conductance (one at a time) by comparing intrinsic electrophysiological properties before and immediately after channel deletion. The acute impact of deleting individual conductances on physiological properties (including calcium homeostasis) was heterogeneous, depending on the property, the specific model, and the deleted channel. The underlying many-to-many mapping between ion channels and properties pointed to ion-channel degeneracy. Next, we allowed the other conductances (barring the deleted conductance) to evolve towards achieving calcium homeostasis during theta-frequency activity. When calcium homeostasis was perturbed by ion-channel deletion, post-knockout plasticity in other conductances ensured resilience of calcium homeostasis to ion-channel deletion. These results demonstrate degeneracy in calcium homeostasis, as calcium homeostasis in knockout models was implemented in the absence of a channel that was earlier involved in the homeostatic process. Importantly, in reacquiring homeostasis, ion-channel conductances and physiological properties underwent heterogenous plasticity (dependent on the model, the property, and the deleted channel), even introducing changes in properties that were not directly connected to the deleted channel. Together, post-knockout plasticity geared towards maintaining homeostasis introduced heterogenous off-target effects on several channels and properties, suggesting that extreme caution be exercised in interpreting experimental outcomes involving channel knockouts.

Cellular harmonics for the morphology-invariant analysis of molecular organization at the cell surface

The spatiotemporal organization of membrane-associated molecules is central to the regulation of cellular signals. Powerful new microscopy techniques enable the three-dimensional visualization of localization and activation of these molecules; however, the quantitative interpretation and comparison of molecular organization on the three-dimensional cell surface remains challenging because cells themselves vary greatly in morphology. Here we introduce u-signal3D, a framework to assess the spatial scales of molecular organization at the cell surface in a cell-morphology-invariant manner. We validated the framework by analyzing synthetic signaling patterns painted onto observed cell morphologies, as well as measured distributions of cytoskeletal and signaling molecules. To demonstrate the framework's versatility, we further compared the spatial organization of cell surface signals both within, and between, cell populations, and powered an upstream machine-learning-based analysis of signaling motifs.

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

An Appearance Data-Driven Model Visualizes Cell State and Predicts Mesenchymal Stem Cell Regenerative Capacity

Mesenchymal stem cells (MSCs) are widely used in treating various diseases. However, lack of a reliable evaluation approach to characterize the potency of MSCs has dampened their clinical applications. Here, a function-oriented mathematical model is established to evaluate and predict the regenerative capacity (RC) of MSCs. Processed by exhaustive testing, the model excavates four optimal fitted indices, including nucleus roundness, nucleus/cytoplasm ratio, side-scatter height, and ERK1/2 from the given index combinations. Notably, three of them except ERK1/2 are cell appearance-associated features. The predictive power of the model is validated via screening experiments of these indices by predicting the RC of newly enrolled and chemical inhibitor-treated MSCs. Further RNA-sequencing analysis reveals that cell appearance-based indices may serve as major indicators to visualize the results of integration-weighted signals in and out of cells and reflect MSC stemness. In general, this study proposes an appearance data-driven predictive model for the RC and stemness of MSCs.

Computational framework for single-cell spatiotemporal dynamics of optogenetic membrane recruitment

We describe a modular computational framework for analyzing cell-wide spatiotemporal signaling dynamics in single-cell microscopy experiments that accounts for the experiment-specific geometric and diffractive complexities that arise from heterogeneous cell morphologies and optical instrumentation. Inputs are unique cell geometries and protein concentrations derived from confocal stacks and spatiotemporally varying environmental stimuli. After simulating the system with a model of choice, the output is convolved with the microscope point-spread function for direct comparison with the observable image. We experimentally validate this approach in single cells with BcLOV4, an optogenetic membrane recruitment system for versatile control over cell signaling, using a three-dimensional non-linear finite element model with all parameters experimentally derived. The simulations recapitulate observed subcellular and cell-to-cell variability in BcLOV4 signaling, allowing for inter-experimental differences of cellular and instrumentation origins to be elucidated and resolved for improved interpretive robustness. This single-cell approach will enhance optogenetics and spatiotemporally resolved signaling studies.

Green fluorescent cAMP indicator of high speed and specificity suitable for neuronal live-cell imaging

Cyclic adenosine monophosphate (cAMP) is a canonical intracellular messenger playing diverse roles in cell functions. In neurons, cAMP promotes axonal growth during early development, and mediates sensory transduction and synaptic plasticity after maturation. The molecular cascades of cAMP are well documented, but its spatiotemporal profiles associated with neuronal functions remain hidden. Hence, we developed a genetically encoded cAMP indicator based on a bacterial cAMP-binding protein. This indicator "gCarvi" monitors [cAMP]_i at 0.2 to 20 µM with a subsecond time resolution and a high specificity over cyclic guanosine monophosphate (cGMP). gCarvi can be converted to a ratiometric probe for [cAMP]_i quantification and its expression can be specifically targeted to various subcellular compartments. Monomeric gCarvi also enables simultaneous multisignal monitoring in combination with other indicators. As a proof of concept, simultaneous cAMP/Ca²⁺ imaging in hippocampal neurons revealed a tight linkage of cAMP to Ca²⁺ signals. In cerebellar presynaptic boutons, forskolin induced nonuniform cAMP elevations among boutons, which positively correlated with subsequent increases in the size of the recycling pool of synaptic vesicles assayed using FM dye. Thus, the cAMP domain in presynaptic boutons is an important determinant of the synaptic strength.

Computational investigation of the dynamic control of cAMP signaling by PDE4 isoform types

Cyclic adenosine monophosphate (cAMP) is a generic signaling molecule that, through precise control of its signaling dynamics, exerts distinct cellular effects. Consequently, aberrant cAMP signaling can have detrimental effects. Phosphodiesterase 4 (PDE4) enzymes profoundly control cAMP signaling and comprise different isoform types of which the enzymatic activity is modulated by differential feedback mechanisms. Because these feedback dynamics are non-linear and occur coincidentally, their effects are difficult to examine experimentally, but can be well simulated computationally. Through understanding the role of PDE4 isoform types in regulating cAMP signaling, PDE4-targeted therapeutic strategies can be better specified. Here, we established a computational model to study how feedback mechanisms on different PDE4 isoform types lead to dynamic, isoform-specific control of cAMP signaling. Ordinary differential equations describing cAMP dynamics were implemented in the VirtualCell (VCell) environment. Simulations indicated that long PDE4 isoforms exert the most profound control on oscillatory cAMP signaling, as opposed to the PDE4-mediated control of single cAMP input pulses. Moreover, elevating cAMP levels or decreasing PDE4 levels revealed different effects on downstream signaling. Together these results underline that cAMP signaling is distinctly regulated by different PDE4 isoform types and that this isoform-specificity should be considered in both computational and experimental follow-up studies to better define PDE4 enzymes as therapeutic targets in diseases in which cAMP signaling is aberrant.

A multiscale model of the regulation of aquaporin 2 recycling

The response of cells to their environment is driven by a variety of proteins and messenger molecules. In eukaryotes, their distribution and location in the cell are regulated by the vesicular transport system. The transport of aquaporin 2 between membrane and storage region is a crucial part of the water reabsorption in renal principal cells, and its malfunction can lead to Diabetes insipidus. To understand the regulation of this system, we aggregated pathways and mechanisms from literature and derived three models in a hypothesis-driven approach. Furthermore, we combined the models to a single system to gain insight into key regulatory mechanisms of Aquaporin 2 recycling. To achieve this, we developed a multiscale computational framework for the modeling and simulation of cellular systems. The analysis of the system rationalizes that the compartmentalization of cAMP in renal principal cells is a result of the protein kinase A signalosome and can only occur if specific cellular components are observed in conjunction. Endocytotic and exocytotic processes are inherently connected and can be regulated by the same protein kinase A signal.

Navigating Multi-Scale Cancer Systems Biology Towards Model-Driven Clinical Oncology and Its Applications in Personalized Therapeutics

Rapid advancements in high-throughput omics technologies and experimental protocols have led to the generation of vast amounts of scale-specific biomolecular data on cancer that now populates several online databases and resources. Cancer systems biology models built using this data have the potential to provide specific insights into complex multifactorial aberrations underpinning tumor initiation, development, and metastasis. Furthermore, the annotation of these single- and multi-scale models with patient data can additionally assist in designing personalized therapeutic interventions as well as aid in clinical decision-making. Here, we have systematically reviewed the emergence and evolution of (i) repositories with scale-specific and multi-scale biomolecular cancer data, (ii) systems biology models developed using this data, (iii) associated simulation software for the development of personalized cancer therapeutics, and (iv) translational attempts to pipeline multi-scale panomics data for data-driven in silico clinical oncology. The review concludes that the absence of a generic, zero-code, panomics-based multi-scale modeling pipeline and associated software framework, impedes the development and seamless deployment of personalized in silico multi-scale models in clinical settings.

Stochasticity and positive feedback enable enzyme kinetics at the membrane to sense reaction size

Cellular membranes span a wide range of spatial dimensions, from the plasma membrane with a scale of microns to vesicles on the nanometer scale. The work presented here identifies a molecular mechanism, based on common features of cellular signaling enzymes, that causes the average enzymatic catalytic rate to exhibit reaction size dependency. This effect stems from stochastic variation, but the final results can be essentially deterministic. In competitive enzymatic reaction cycles, the final product can depend on the size of the reaction system. The simplicity of the mechanism suggests that size-dependent reaction rates may be widespread among signaling enzymes and thus enable reaction size to be an important factor in signal regulation at the membrane.

Here, we present detailed kinetic analyses of a panel of soluble lipid kinases and phosphatases, as well as Ras activating proteins, acting on their respective membrane surface substrates. The results reveal that the mean catalytic rate of such interfacial enzymes can exhibit a strong dependence on the size of the reaction system—in this case membrane area. Experimental measurements and kinetic modeling reveal how stochastic effects stemming from low molecular copy numbers of the enzymes alter reaction kinetics based on mechanistic characteristics of the enzyme, such as positive feedback. For the competitive enzymatic cycles studied here, the final product—consisting of a specific lipid composition or Ras activity state—depends on the size of the reaction system. Furthermore, we demonstrate how these reaction size dependencies can be controlled by engineering feedback mechanisms into the enzymes.

Interfacing Live Cells with Surfaces: A Concurrent Control Technique for Quantifying Surface Ligand Activity

Surface ligand activity is a key design parameter for successfully interfacing surfaces with cells─whether in the context of in vitro investigations for understanding cellular signaling pathways or more applied applications in drug delivery and medical implants. Unlike other crucial surface parameters, such as stiffness and roughness, surface ligand activity is typically based on a set of assumptions rather than directly measured, giving rise to interpretations of cell adhesion that can vary with the assumptions made. To fill this void, we have developed a concurrent control technique for directly characterizing in vitro ligand surface activity. Pairs of gold-coated glass chips were biofunctionalized with RGD ligand in a parallel workflow: one chip for in vitro applications and the other for surface plasmon resonance (SPR)-based RGD activity characterization. Recombinant α_Vβ₃ integrins were injected over the SPR chip surface as mimics of the cellular-membrane-bound receptors and the resulting binding kinetics parameterized to quantify surface ligand activity. These activity measurements were correlated with cell morphological features, measured by interfacing MDA-MB-231 cells with the in vitro chip surfaces on the live cell microscope. We demonstrate how the interpretation of a cell phenotype based on direct activity measurements can vary markedly from interpretations based on assumed activity. The SPR concurrent control approach has multiple advantages due to the fact that SPR is a standardized technique and has the sensitivity to measure ligand activity across the most relevant range of extracellular surface densities, while the in vitro chip design can be used with all commonly used light microscopy modalities (e.g., phase contrast, DIC, and fluorescence) so that a wide range of phenotypic and molecular markers can be correlated to the ligand surface activity.

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.

Glycocalyx Curving the Membrane: Forces Emerging from the Cell Exterior

Morphological transitions are typically attributed to the actions of proteins and lipids. Largely overlooked in membrane shape regulation is the glycocalyx, a pericellular membrane coat that resides on all cells in the human body. Comprised of complex sugar polymers known as glycans as well as glycosylated lipids and proteins, the glycocalyx is ideally positioned to impart forces on the plasma membrane. Large, unstructured polysaccharides and glycoproteins in the glycocalyx can generate crowding pressures strong enough to induce membrane curvature. Stress may also originate from glycan chains that convey curvature preference on asymmetrically distributed lipids, which are exploited by binding factors and infectious agents to induce morphological changes. Through such forces, the glycocalyx can have profound effects on the biogenesis of functional cell surface structures as well as the secretion of extracellular vesicles. In this review, we discuss recent evidence and examples of these mechanisms in normal health and disease.

Mechanisms of cAMP compartmentation in cardiac myocytes: experimental and computational approaches to understanding

The small diffusible second messenger 3',5'-cyclic adenosine monophosphate (cAMP) is found in virtually every cell in our bodies, where it mediates responses to a variety of different G protein coupled receptors (GPCRs). In the heart, cAMP plays a critical role in regulating many different aspects of cardiac myocyte function, including gene transcription, cell metabolism, and excitation-contraction coupling. Yet, not all GPCRs that stimulate cAMP production elicit the same responses. Subcellular compartmentation of cAMP is essential to explain how different receptors can utilize the same diffusible second messenger to elicit unique functional responses. However, the mechanisms contributing to this behaviour and its significance in producing physiological and pathological responses are incompletely understood. Mathematical modelling has played an essential role in gaining insight into these questions. This review discusses what we currently know about cAMP compartmentation in cardiac myocytes and questions that are yet to be answered.

Signaling Microdomains in the Spotlight: Visualizing Compartmentalized Signaling Using Genetically Encoded Fluorescent Biosensors

How cells muster a network of interlinking signaling pathways to faithfully convert diverse external cues to specific functional outcomes remains a central question in biology. Through their ability to convert dynamic biochemical activities to rapid and precise optical readouts, genetically encoded fluorescent biosensors have become instrumental in unraveling the molecular logic controlling the specificity of intracellular signaling. In this review, we discuss how the use of genetically encoded fluorescent biosensors to visualize dynamic signaling events within their native cellular context is elucidating the different strategies employed by cells to organize signaling activities into discrete compartments, or signaling microdomains, to ensure functional specificity.

Astrocyte arborization enhances Ca2+ but not cAMP signaling plasticity

The plasticity of astrocytes is fundamental for their principal function, maintaining homeostasis of the central nervous system throughout life, and is associated with diverse exposomal challenges. Here, we used cultured astrocytes to investigate at subcellular level basic cell processes under controlled environmental conditions. We compared astroglial functional and signaling plasticity in standard serum‐containing growth medium, a condition mimicking pathologic conditions, and in medium without serum, favoring the acquisition of arborized morphology. Using opto−/electrophysiologic techniques, we examined cell viability, expression of astroglial markers, vesicle dynamics, and cytosolic Ca²⁺ and cAMP signaling. The results revealed altered vesicle dynamics in arborized astrocytes that was associated with increased resting [Ca²⁺]_i and increased subcellular heterogeneity in [Ca²⁺]_i, whereas [cAMP]_i subcellular dynamics remained stable in both cultures, indicating that cAMP signaling is less prone to plastic remodeling than Ca²⁺ signaling, possibly also in in vivo contexts.

Temporal pattern and synergy influence activity of ERK signaling pathways during L-LTP induction

Long-lasting long-term potentiation (L-LTP) is a cellular mechanism of learning and memory storage. Studies have demonstrated a requirement for extracellular signal-regulated kinase (ERK) activation in L-LTP produced by a diversity of temporal stimulation patterns. Multiple signaling pathways converge to activate ERK, with different pathways being required for different stimulation patterns. To answer whether and how different temporal patterns select different signaling pathways for ERK activation, we developed a computational model of five signaling pathways (including two novel pathways) leading to ERK activation during L-LTP induction. We show that calcium and cAMP work synergistically to activate ERK and that stimuli given with large intertrial intervals activate more ERK than shorter intervals. Furthermore, these pathways contribute to different dynamics of ERK activation. These results suggest that signaling pathways with different temporal sensitivities facilitate ERK activation to diversity of temporal patterns.

Cellular context shapes cyclic nucleotide signaling in neurons through multiple levels of integration

Intracellular signaling with cyclic nucleotides are ubiquitous signaling pathways, yet the dynamics of these signals profoundly differ in different cell types. Biosensor imaging experiments, by providing direct measurements in intact cellular environment, reveal which receptors are activated by neuromodulators and how the coincidence of different neuromodulators is integrated at various levels in the signaling cascade. Phosphodiesterases appear as one important determinant of cross-talk between different signaling pathways. Finally, analysis of signal dynamics reveal that striatal medium-sized spiny neuron obey a different logic than other brain regions such as cortex, probably in relation with the function of this brain region which efficiently detects transient dopamine.

Systems modeling predicts that mitochondria ER contact sites regulate the postsynaptic energy landscape

Spatiotemporal compartmentation of calcium dynamics is critical for neuronal function, particularly in postsynaptic spines. This exquisite level of Ca²⁺ compartmentalization is achieved through the storage and release of Ca²⁺ from various intracellular organelles particularly the endoplasmic reticulum (ER) and the mitochondria. Mitochondria and ER are established storage organelles controlling Ca²⁺ dynamics in neurons. Mitochondria also generate a majority of energy used within postsynaptic spines to support the downstream events associated with neuronal stimulus. Recently, high resolution microscopy has unveiled direct contact sites between the ER and the mitochondria (MERCs), which directly channel Ca²⁺ release from the ER into the mitochondrial membrane. In this study, we develop a computational 3D reaction-diffusion model to investigate the role of MERCs in regulating Ca²⁺ and ATP dynamics. This spatiotemporal model accounts for Ca²⁺ oscillations initiated by glutamate stimulus of metabotropic and ionotropic glutamate receptors and Ca²⁺ changes in four different compartments: cytosol, ER, mitochondria, and the MERC microdomain. Our simulations predict that the organization of these organelles and inter-organellar contact sites play a key role in modulating Ca²⁺ and ATP dynamics.

We further show that the crosstalk between geometry (mitochondria and MERC) and metabolic parameters (cytosolic ATP hydrolysis, ATP generation) influences the neuronal energy state. Our findings shed light on the importance of organelle interactions in predicting Ca²⁺ dynamics in synaptic signaling. Overall, our model predicts that a combination of MERC linkage and mitochondria size is necessary for optimal ATP production in the cytosol.

A spatial model of YAP/TAZ signaling reveals how stiffness, dimensionality, and shape contribute to emergent outcomes

YAP/TAZ is a master regulator of mechanotransduction whose functions rely on translocation from the cytoplasm to the nucleus in response to diverse physical cues. Substrate stiffness, substrate dimensionality, and cell shape are all input signals for YAP/TAZ, and through this pathway, regulate critical cellular functions and tissue homeostasis. Yet, the relative contributions of each biophysical signal and the mechanisms by which they synergistically regulate YAP/TAZ in realistic tissue microenvironments that provide multiplexed input signals remain unclear. For example, in simple two-dimensional culture, YAP/TAZ nuclear localization correlates strongly with substrate stiffness, while in three-dimensional (3D) environments, YAP/TAZ translocation can increase with stiffness, decrease with stiffness, or remain unchanged. Here, we develop a spatial model of YAP/TAZ translocation to enable quantitative analysis of the relationships between substrate stiffness, substrate dimensionality, and cell shape. Our model couples cytosolic stiffness to nuclear mechanics to replicate existing experimental trends, and extends beyond current data to predict that increasing substrate activation area through changes in culture dimensionality, while conserving cell volume, forces distinct shape changes that result in nonlinear effect on YAP/TAZ nuclear localization. Moreover, differences in substrate activation area versus total membrane area can account for counterintuitive trends in YAP/TAZ nuclear localization in 3D culture. Based on this multiscale investigation of the different system features of YAP/TAZ nuclear translocation, we predict that how a cell reads its environment is a complex information transfer function of multiple mechanical and biochemical factors. These predictions reveal a few design principles of cellular and tissue engineering for YAP/TAZ mechanotransduction.

Vertebrate cells differentially interpret ciliary and extraciliary cAMP

Hedgehog pathway components and select G protein-coupled receptors (GPCRs) localize to the primary cilium, an organelle specialized for signal transduction. We investigated whether cells distinguish between ciliary and extraciliary GPCR signaling. To test whether ciliary and extraciliary cyclic AMP (cAMP) convey different information, we engineered optogenetic and chemogenetic tools to control the subcellular site of cAMP generation. Generating equal amounts of ciliary and cytoplasmic cAMP in zebrafish and mammalian cells revealed that ciliary cAMP, but not cytoplasmic cAMP, inhibited Hedgehog signaling. Modeling suggested that the distinct geometries of the cilium and cell body differentially activate local effectors. The search for effectors identified a ciliary pool of protein kinase A (PKA). Blocking the function of ciliary PKA, but not extraciliary PKA, activated Hedgehog signal transduction and reversed the effects of ciliary cAMP. Therefore, cells distinguish ciliary and extraciliary cAMP using functionally and spatially distinct pools of PKA, and different subcellular pools of cAMP convey different information.

Controlling T cells spreading, mechanics and activation by micropatterning

We designed a strategy, based on a careful examination of the activation capabilities of proteins and antibodies used as substrates for adhering T cells, coupled to protein microstamping to control at the same time the position, shape, spreading, mechanics and activation state of T cells. Once adhered on patterns, we examined the capacities of T cells to be activated with soluble anti CD3, in comparison to T cells adhered to a continuously decorated substrate with the same density of ligands. We show that, in our hand, adhering onto an anti CD45 antibody decorated surface was not affecting T cell calcium fluxes, even adhered on variable size micro-patterns. Aside, we analyzed the T cell mechanics, when spread on pattern or not, using Atomic Force Microscopy indentation. By expressing MEGF10 as a non immune adhesion receptor in T cells we measured the very same spreading area on PLL substrates and Young modulus than non modified cells, immobilized on anti CD45 antibodies, while retaining similar activation capabilities using soluble anti CD3 antibodies or through model APC contacts. We propose that our system is a way to test activation or anergy of T cells with defined adhesion and mechanical characteristics, and may allow to dissect fine details of these mechanisms since it allows to observe homogenized populations in standardized T cell activation assays.

G protein-coupled receptor-G protein interactions: a single-molecule perspective

G protein-coupled receptors (GPCRs) regulate many cellular and physiological processes, responding to a diverse range of extracellular stimuli including hormones, neurotransmitters, odorants, and light. Decades of biochemical and pharmacological studies have provided fundamental insights into the mechanisms of GPCR signaling. Thanks to recent advances in structural biology, we now possess an atomistic understanding of receptor activation and G protein coupling. However, how GPCRs and G proteins interact in living cells to confer signaling efficiency and specificity remains insufficiently understood. The development of advanced optical methods, including single-molecule microscopy, has provided the means to study receptors and G proteins in living cells with unprecedented spatio-temporal resolution. The results of these studies reveal an unexpected level of complexity, whereby GPCRs undergo transient interactions among themselves as well as with G proteins and structural elements of the plasma membrane to form short-lived signaling nanodomains that likely confer both rapidity and specificity to GPCR signaling. These findings may provide new strategies to pharmaceutically modulate GPCR function, which might eventually pave the way to innovative drugs for common diseases such as diabetes or heart failure.

Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus

For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules’ diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.

The inside of cells is a complex spatial environment, filled with organelles, filaments and proteins. It is an open question how cell signaling pathways function robustly in the presence of such spatial heterogeneity. In this work we study how organelle barriers influence the most basic of chemical signals; the diffusive propagation of an activated protein from the cell membrane to nucleus. Three-dimensional B cell organelle and membrane geometries reconstructed from soft X-ray tomographic images are used in building mathematical models of the signal propagation process. Our models demonstrate that organelle barriers significantly increase the time required for a diffusing protein to traverse from the cell membrane to nucleus when compared to a cell with an empty cytosolic space. We also show that signal inactivation, a fundamental component of all signaling pathways, can provide robustness in the signal arrival time in two ways. Increasing rates of signal inactivation reduce variability in the arrival time, while also dramatically reducing the degree to which organelle barriers increase the arrival time (in comparison to a cell with an empty cytosol).

Cell shape regulates subcellular organelle location to control early Ca2+ signal dynamics in vascular smooth muscle cells

The shape of the cell is connected to its function; however, we do not fully understand underlying mechanisms by which global shape regulates a cell's functional capabilities. Using theory, experiments and simulation, we investigated how physiologically relevant cell shape changes affect subcellular organization, and consequently intracellular signaling, to control information flow needed for phenotypic function. Vascular smooth muscle cells going from a proliferative and motile circular shape to a contractile fusiform shape show changes in the location of the sarcoplasmic reticulum, inter-organelle distances, and differential distribution of receptors in the plasma membrane. These factors together lead to the modulation of signals transduced by the M3 muscarinic receptor/Gq/PLCβ pathway at the plasma membrane, amplifying Ca2+ dynamics in the cytoplasm, and the nucleus resulting in phenotypic changes, as determined by increased activity of myosin light chain kinase in the cytoplasm and enhanced nuclear localization of the transcription factor NFAT. Taken together, our observations show a systems level phenomenon whereby global cell shape affects subcellular organization to modulate signaling that enables phenotypic changes.

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.

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the finite element method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.

Role of cyclic nucleotides and their downstream signaling cascades in memory function: Being at the right time at the right spot

A plethora of studies indicate the important role of cAMP and cGMP cascades in neuronal plasticity and memory function. As a result, altered cyclic nucleotide signaling has been implicated in the pathophysiology of mnemonic dysfunction encountered in several diseases. In the present review we provide a wide overview of studies regarding the involvement of cyclic nucleotides, as well as their upstream and downstream molecules, in physiological and pathological mnemonic processes. Next, we discuss the regulation of the intracellular concentration of cyclic nucleotides via phosphodiesterases, the enzymes that degrade cAMP and/or cGMP, and via A-kinase-anchoring proteins that refine signal compartmentalization of cAMP signaling. We also provide an overview of the available data pointing to the existence of specific time windows in cyclic nucleotide signaling during neuroplasticity and memory formation and the significance to target these specific time phases for improving memory formation. Finally, we highlight the importance of emerging imaging tools like Förster resonance energy transfer imaging and optogenetics in detecting, measuring and manipulating the action of cyclic nucleotide signaling cascades.

The road to ERK activation: Do neurons take alternate routes?

The ERK cascade is a central signaling pathway that regulates a wide variety of cellular processes including proliferation, differentiation, learning and memory, development, and synaptic plasticity. A wide range of inputs travel from the membrane through different signaling pathway routes to reach activation of one set of output kinases, ERK1&2. The classical ERK activation pathway beings with growth factor activation of receptor tyrosine kinases. Numerous G-protein coupled receptors and ionotropic receptors also lead to ERK through increases in the second messengers calcium and cAMP. Though both types of pathways are present in diverse cell types, a key difference is that most stimuli to neurons, e.g. synaptic inputs, are transient, on the order of milliseconds to seconds, whereas many stimuli acting on non-neural tissue, e.g. growth factors, are longer duration. The ability to consolidate these inputs to regulate the activation of ERK in response to diverse signals raises the question of which factors influence the difference in ERK activation pathways. This review presents both experimental studies and computational models aimed at understanding the control of ERK activation and whether there are fundamental differences between neurons and other cells. Our main conclusion is that differences between cell types are quite subtle, often related to differences in expression pattern and quantity of some molecules such as Raf isoforms. In addition, the spatial location of ERK is critical, with regulation by scaffolding proteins producing differences due to colocalization of upstream molecules that may differ between neurons and other cells.

Robust emergence of sharply tuned place-cell responses in hippocampal neurons with structural and biophysical heterogeneities

Hippocampal pyramidal neurons sustain propagation of fast electrical signals and are electrotonically non-compact structures exhibiting cell-to-cell variability in their complex dendritic arborization. In this study, we demonstrate that sharp place-field tuning and several somatodendritic functional maps concomitantly emerge despite the presence of geometrical heterogeneities in these neurons. We establish this employing an unbiased stochastic search strategy involving thousands of models that spanned several morphologies and distinct profiles of dispersed synaptic localization and channel expression. Mechanistically, employing virtual knockout models (VKMs), we explored the impact of bidirectional modulation in dendritic spike prevalence on place-field tuning sharpness. Consistent with the prior literature, we found that across all morphologies, virtual knockout of either dendritic fast sodium channels or N-methyl-D-aspartate receptors led to a reduction in dendritic spike prevalence, whereas A-type potassium channel knockouts resulted in a non-specific increase in dendritic spike prevalence. However, place-field tuning sharpness was critically impaired in all three sets of VKMs, demonstrating that sharpness in feature tuning is maintained by an intricate balance between mechanisms that promote and those that prevent dendritic spike initiation. From the functional standpoint of the emergence of sharp feature tuning and intrinsic functional maps, within this framework, geometric variability was compensated by a combination of synaptic democracy, the ability of randomly dispersed synapses to yield sharp tuning through dendritic spike initiation, and ion-channel degeneracy. Our results suggest electrotonically non-compact neurons to be endowed with several degrees of freedom, encompassing channel expression, synaptic localization and morphological microstructure, in achieving sharp feature encoding and excitability homeostasis.

A Three-Dimensional Culture Model of Reversibly Quiescent Myogenic Cells

Satellite cells (SC) are the stem cells of skeletal muscles. They are quiescent in adult animals but resume proliferation to allow muscle hypertrophy or regeneration after injury. The mechanisms balancing quiescence, self-renewal, and differentiation of SC are difficult to analyze in vivo owing to their complexity and in vitro because the staminal character of SC is lost when they are removed from the niche and is not adequately reproduced in the culture models currently available. To overcome these difficulties, we set up a culture model of the myogenic C2C12 cell line in suspension. When C2C12 cells are cultured in suspension, they enter a state of quiescence and form three-dimensional aggregates (myospheres) that produce the extracellular matrix and express markers of quiescent SC. In the initial phase of culture, a portion of the cells fuses in syncytia and abandons the myospheres. The remaining cells are mononucleated and quiescent but resume proliferation and differentiation when plated in a monolayer. The notch pathway controls the quiescent state of the cells as shown by the fact that its inhibition leads to the resumption of differentiation. Within this context, notch3 appears to play a central role in the activity of this pathway since the expression of notch1 declines soon after aggregation. In summary, the culture model of C2C12 in suspension may be used to study the cellular interactions of muscle stem cells and the pathways controlling SC quiescence entrance and maintenance.

Computational Modeling Reveals Frequency Modulation of Calcium-cAMP/PKA Pathway in Dendritic Spines

Dendritic spines are the primary excitatory postsynaptic sites that act as subcompartments of signaling. Ca²⁺ is often the first and most rapid signal in spines. Downstream of calcium, the cyclic adenosine monophosphate (cAMP)/protein kinase A (PKA) pathway plays a critical role in the regulation of spine formation, morphological modifications, and ultimately, learning and memory. Although the dynamics of calcium are reasonably well-studied, calcium-induced cAMP/PKA dynamics, particularly with respect to frequency modulation, are not fully explored. In this study, we present a well-mixed model for the dynamics of calcium-induced cAMP/PKA dynamics in dendritic spines. The model is constrained using experimental observations in the literature. Further, we measured the calcium oscillation frequency in dendritic spines of cultured hippocampal CA1 neurons and used these dynamics as model inputs. Our model predicts that the various steps in this pathway act as frequency modulators for calcium, and the high frequency of calcium input is filtered by adenylyl cyclase 1 and phosphodiesterases in this pathway such that cAMP/PKA only responds to lower frequencies. This prediction has important implications for noise filtering and long-timescale signal transduction in dendritic spines. A companion manuscript presents a three-dimensional spatial model for the same pathway.

Geometric Control of Frequency Modulation of cAMP Oscillations due to Calcium in Dendritic Spines

The spatiotemporal regulation of cyclic adenosine monophosphate (cAMP) and its dynamic interactions with other second messengers such as calcium are critical features of signaling specificity required for neuronal development and connectivity. cAMP is known to contribute to long-term potentiation and memory formation by controlling the formation and regulation of dendritic spines. Despite the recent advances in biosensing techniques for monitoring spatiotemporal cAMP dynamics, the underlying molecular mechanisms that attribute to the subcellular modulation of cAMP remain unknown. In this work, we model the spatiotemporal dynamics of calcium-induced cAMP signaling pathway in dendritic spines. Using a three-dimensional reaction-diffusion model, we investigate the effect of different spatial characteristics of cAMP dynamics that may be responsible for subcellular regulation of cAMP concentrations. Our model predicts that the volume/surface ratio of the spine, regulated through the spine head size, spine neck size, and the presence of physical barriers (spine apparatus), is an important regulator of cAMP dynamics. Furthermore, localization of the enzymes responsible for the synthesis and degradation of cAMP in different compartments also modulates the oscillatory patterns of cAMP through exponential relationships. Our findings shed light on the significance of complex geometric and localization relationships for cAMP dynamics in dendritic spines.

Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Emerging themes and unifying concepts underlying cell behavior regulation by the pericellular space

Cells reside in a complex three-dimensional (3D) microenvironment where physical, chemical, and architectural features of the pericellular space regulate important cellular functions like migration, differentiation, and morphogenesis. A major goal of tissue engineering is to identify which properties of the pericellular space orchestrate these emergent cell behaviors and how. In this review, we highlight recent studies at the interface of biomaterials and single cell biophysics that are lending deeper insight towards this goal. Advanced methods have enabled the decoupling of architectural and mechanical features of the microenvironment, revealing multiple mechanisms of adhesion and mechanosensing modulation by biomaterials. Such studies are revealing important roles for pericellular space degradability, hydration, and adhesion competition in cell shape, volume, and differentiation regulation. STATEMENT OF SIGNIFICANCE: Cell fate and function are closely regulated by the local extracellular microenvironment. Advanced methods at the interface of single cell biophysics and biomaterials have shed new light on regulators of cell-pericellular space interactions by decoupling more features of the complex pericellular milieu than ever before. These findings lend deeper mechanistic insight into how biomaterials can be designed to fine-tune outcomes like differentiation, migration, and collective morphogenesis.

Characterizing building blocks of resource constrained biological networks

Background

Identification of motifs–recurrent and statistically significant patterns–in biological networks is the key to understand the design principles, and to infer governing mechanisms of biological systems. This, however, is a computationally challenging task. This task is further complicated as biological interactions depend on limited resources, i.e., a reaction takes place if the reactant molecule concentrations are above a certain threshold level. This biochemical property implies that network edges can participate in a limited number of motifs simultaneously. Existing motif counting methods ignore this problem. This simplification often leads to inaccurate motif counts (over- or under-estimates), and thus, wrong biological interpretations.

Results

In this paper, we develop a novel motif counting algorithm, Partially Overlapping MOtif Counting (POMOC), that considers capacity levels for all interactions in counting motifs.

Conclusions

Our experiments on real and synthetic networks demonstrate that motif count using the POMOC method significantly differs from the existing motif counting approaches, and our method extends to large-scale biological networks in practical time. Our results also show that our method makes it possible to characterize the impact of different stress factors on cell’s organization of network. In this regard, analysis of a S. cerevisiae transcriptional regulatory network using our method shows that oxidative stress is more disruptive to organization and abundance of motifs in this network than mutations of individual genes. Our analysis also suggests that by focusing on the edges that lead to variation in motif counts, our method can be used to find important genes, and to reveal subtle topological and functional differences of the biological networks under different cell states.

Stochasticity of Biological Soft Matter: Emerging Concepts in Intrinsically Disordered Proteins and Biological Phase Separation

At the turn of this century, cardinal changes took place in the perceptions of the structure and function of proteins, as well as in the organizational principles of membrane-less organelles. As a result, the model of the organization of living matter is changing to one described by highly dynamic biological soft matter positioned at the edge of chaos. Intrinsically disordered proteins (IDPs) and membrane-less organelles are key examples of this new outlook and may represent a critical foundation of life, defining its complexity and the evolution of living things.

Stores, Channels, Glue, and Trees: Active Glial and Active Dendritic Physiology

Glial cells and neuronal dendrites were historically assumed to be passive structures that play only supportive physiological roles, with no active contribution to information processing in the central nervous system. Research spanning the past few decades has clearly established this assumption to be far from physiological realities. Whereas the discovery of active channel conductances and their localized plasticity was the turning point for dendritic structures, the demonstration that glial cells release transmitter molecules and communicate across the neuroglia syncytium through calcium wave propagation constituted path-breaking discoveries for glial cell physiology. An additional commonality between these two structures is the ability of calcium stores within their endoplasmic reticulum (ER) to support active propagation of calcium waves, which play crucial roles in the spatiotemporal integration of information within and across cells. Although there have been several demonstrations of regulatory roles of glial cells and dendritic structures in achieving common physiological goals such as information propagation and adaptability through plasticity, studies assessing physiological interactions between these two active structures have been few and far. This lacuna is especially striking given the strong connectivity that is known to exist between these two structures through several complex and tightly intercoupled mechanisms that also recruit their respective ER structures. In this review, we present brief overviews of the parallel literatures on active dendrites and active glial physiology and make a strong case for future studies to directly assess the strong interactions between these two structures in regulating physiology and pathophysiology of the brain.

From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity

Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.

Genetically Encoded Fluorescent Biosensors Illuminate the Spatiotemporal Regulation of Signaling Networks

Cellular signaling networks are the foundation which determines the fate and function of cells as they respond to various cues and stimuli. The discovery of fluorescent proteins over 25 years ago enabled the development of a diverse array of genetically encodable fluorescent biosensors that are capable of measuring the spatiotemporal dynamics of signal transduction pathways in live cells. In an effort to encapsulate the breadth over which fluorescent biosensors have expanded, we endeavored to assemble a comprehensive list of published engineered biosensors, and we discuss many of the molecular designs utilized in their development. Then, we review how the high temporal and spatial resolution afforded by fluorescent biosensors has aided our understanding of the spatiotemporal regulation of signaling networks at the cellular and subcellular level. Finally, we highlight some emerging areas of research in both biosensor design and applications that are on the forefront of biosensor development.

Steps in Mechanotransduction Pathways that Control Cell Morphology

It is increasingly clear that mechanotransduction pathways play important roles in regulating fundamental cellular functions. Of the basic mechanical functions, the determination of cellular morphology is critical. Cells typically use many mechanosensitive steps and different cell states to achieve a polarized shape through repeated testing of the microenvironment. Indeed, morphology is determined by the microenvironment through periodic activation of motility, mechanotesting, and mechanoresponse functions by hormones, internal clocks, and receptor tyrosine kinases. Patterned substrates and controlled environments with defined rigidities limit the range of cell behavior and influence cell state decisions and are thus very useful for studying these steps. The recently defined rigidity sensing process provides a good example of how cells repeatedly test their microenvironment and is also linked to cancer. In general, aberrant extracellular matrix mechanosensing is associated with numerous conditions, including cardiovascular disease, aging, and fibrosis, that correlate with changes in tissue morphology and matrix composition. Hence, detailed descriptions of the steps involved in sensing and responding to the microenvironment are needed to better understand both the mechanisms of tissue homeostasis and the pathomechanisms of human disease.

Active dendrites regulate the spatiotemporal spread of signaling microdomains

Microdomains that emerge from spatially constricted spread of biochemical signaling components play a central role in several neuronal computations. Although dendrites, endowed with several voltage-gated ion channels, form a prominent structural substrate for microdomain physiology, it is not known if these channels regulate the spatiotemporal spread of signaling microdomains. Here, we employed a multiscale, morphologically realistic, conductance-based model of the hippocampal pyramidal neuron that accounted for experimental details of electrical and calcium-dependent biochemical signaling. We activated synaptic N-Methyl-d-Aspartate receptors through theta-burst stimulation (TBS) or pairing (TBP) and assessed microdomain propagation along a signaling pathway that included calmodulin, calcium/calmodulin-dependent protein kinase II (CaMKII) and protein phosphatase 1. We found that the spatiotemporal spread of the TBS-evoked microdomain in phosphorylated CaMKII (pCaMKII) was amplified in comparison to that of the corresponding calcium microdomain. Next, we assessed the role of two dendritically expressed inactivating channels, one restorative (A-type potassium) and another regenerative (T-type calcium), by systematically varying their conductances. Whereas A-type potassium channels suppressed the spread of pCaMKII microdomains by altering the voltage response to TBS, T-type calcium channels enhanced this spread by modulating TBS-induced calcium influx without changing the voltage. Finally, we explored cross-dependencies of these channels with other model components, and demonstrated the heavy mutual interdependence of several biophysical and biochemical properties in regulating microdomains and their spread. Our conclusions unveil a pivotal role for dendritic voltage-gated ion channels in actively amplifying or suppressing biochemical signals and their spatiotemporal spread, with critical implications for clustered synaptic plasticity, robust information transfer and efficient neural coding.

The spatiotemporal spread of biochemical signals in neurons and other cells regulate signaling specificity, tuning of signal propagation, along with specificity and clustering of adaptive plasticity. Theoretical and experimental studies have demonstrated a critical role for cellular morphology and the topology of signaling networks in regulating this spread. In this study, we add a significantly complex dimension to this narrative by demonstrating that voltage-gated ion channels on the plasma membrane could actively amplify or suppress the strength and spread of downstream signaling components. Given the expression of different ion channels with wide-ranging heterogeneity in gating kinetics, localization and density, our results point to an increase in complexity of and degeneracy in signaling spread, and unveil a powerful mechanism for regulating biochemical-signaling pathways across different cell types.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

Spectral imaging of FRET-based sensors reveals sustained cAMP gradients in three spatial dimensions

Cyclic AMP is a ubiquitous second messenger that orchestrates a variety of cellular functions over different timescales. The mechanisms underlying specificity within this signaling pathway are still not well understood. Several lines of evidence suggest the existence of spatial cAMP gradients within cells, and that compartmentalization underlies specificity within the cAMP signaling pathway. However, to date, no studies have visualized cAMP gradients in three spatial dimensions (3D: x, y, z).This is in part due to the limitations of FRET-based cAMP sensors, specifically the low signal-to-noise ratio intrinsic to all intracellular FRET probes. Here, we overcome this limitation, at least in part, by implementing spectral imaging approaches to estimate FRET efficiency when multiple fluorescent labels are used and when signals are measured from weakly expressed fluorescent proteins in the presence of background autofluorescence and stray light. Analysis of spectral image stacks in two spatial dimensions (2D) from single confocal slices indicates little or no cAMP gradients formed within pulmonary microvascular endothelial cells (PMVECs) under baseline conditions or following 10 min treatment with the adenylyl cyclase activator forskolin. However, analysis of spectral image stacks in 3D demonstrates marked cAMP gradients from the apical to basolateral face of PMVECs. Results demonstrate that spectral imaging approaches can be used to assess cAMP gradients-and in general gradients in fluorescence and FRET-within intact cells. Results also demonstrate that 2D imaging studies of localized fluorescence signals and, in particular, cAMP signals, whether using epifluorescence or confocal microscopy, may lead to erroneous conclusions about the existence and/or magnitude of gradients in either FRET or the underlying cAMP signals. Thus, with the exception of cellular structures that can be considered in one spatial dimension, such as neuronal processes, 3D measurements are required to assess mechanisms underlying compartmentalization and specificity within intracellular signaling pathways.

The role of traction in membrane curvature generation

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Many studies in cell biology employ global shape descriptors to probe mechanisms of cell morphogenesis. Here, we implement a framework in this paper to profile cellular morphodynamics very locally. We employ the Hilbert-Huang transform (HHT) to extract along the entire cell edge spectra of instantaneous edge motion frequency and magnitude and use them to classify overall cell behavior as well as subcellular edge sectors of distinct dynamics. We find in fibroblast-like COS7 cells that the marked heterogeneity in mobility of an unstimulated population is fully captured by differences in the magnitude spectra, while the frequency spectra are conserved between cells. Using optogenetics to acutely inhibit morphogenetic signaling pathways we find that these molecular shifts are reflected by changes in the frequency spectra but not in the magnitude spectra. After clustering cell edge sectors with distinct morphodynamics we observe in cells expressing a Rac1 activity biosensor that the sectors with different frequency spectra associate with different signaling intensity and dynamics. Together, these observations let us conclude that the frequency spectrum encodes the wiring of the molecular circuitry that regulates edge movements, whereas the magnitude captures the activation level of the circuitry.