Spatial gradients of cellular phospho-proteins

Order from chaos: cellular asymmetries explained with modelling

Molecules inside cells are subject to physical forces and undergo biochemical interactions, continuously changing their physical properties and dynamics. Despite this, cells achieve highly ordered molecular patterns that are crucial to regulate various cellular functions and to specify cell fate. In the Caenorhabditis elegans one-cell embryo, protein asymmetries are established in the narrow time window of a cell division. What are the mechanisms that allow molecules to establish asymmetries, defying the randomness imposed by Brownian motion? Mathematical and computational models have paved the way to the understanding of protein dynamics up to the 'single-molecule level' when resolution represents an issue for precise experimental measurements. Here we review the models that interpret cortical and cytoplasmic asymmetries in the one-cell C. elegans embryo.

Technologies for whole-cell modeling: Genome-wide reconstruction of a cell in silico

With advances in high-throughput, large-scale in vivo measurement and genome modification techniques at the single-nucleotide level, there is an increasing demand for the development of new technologies for the flexible design and control of cellular systems. Computer-aided design is a powerful tool to design new cells. Whole-cell modeling aims to integrate various cellular subsystems, determine their interactions and cooperative mechanisms, and predict comprehensive cellular behaviors by computational simulations on a genome-wide scale. It has been applied to prokaryotes, yeasts, and higher eukaryotic cells, and utilized in a wide range of applications, including production of valuable substances, drug discovery, and controlled differentiation. Whole-cell modeling, consisting of several thousand elements with diverse scales and properties, requires innovative model construction, simulation, and analysis techniques. Furthermore, whole-cell modeling has been extended to multiple scales, including high-resolution modeling at the single-nucleotide and single-amino acid levels and multicellular modeling of tissues and organs. This review presents an overview of the current state of whole-cell modeling, discusses the novel computational and experimental technologies driving it, and introduces further developments toward multihierarchical modeling on a whole-genome scale.

Progressive Local Accumulation of Self-Assembled Nanoreactors in a Hydrogel Matrix through Repetitive Injections of ATP

Cellular functions are regulated with high spatial control through the local activation of chemical processes in a complex inhomogeneous matrix. The development of synthetic macroscopic systems with a similar capacity allows fundamental studies aimed at understanding the relationship between local molecular events and the emergence of functional properties at the macroscopic level. Here, we show that a kinetically stable inhomogeneous hydrogel matrix is spontaneously formed upon the local injection of ATP. Locally, ATP templates the self-assembly of amphiphiles into large nanoreactors with a much lower diffusion rate compared to unassembled amphiphiles. The local depletion of unassembled amphiphiles near the injection point installs a concentration gradient along which unassembled amphiphiles diffuse from the surroundings to the center. This allows for a progressive local accumulation of self-assembled nanoreactors in the matrix upon repetitive cycles of ATP injection separated by time intervals during which diffusion of unassembled amphiphiles takes place. Contrary to the homogeneous matrix containing the same components, in the inhomogeneous matrix the local upregulation of a chemical reaction occurs. Depending on the way the same amount of injected ATP is administered to the hydrogel matrix different macroscopic distributions of nanoreactors are obtained, which affect the location in the matrix where the chemical reaction is upregulated.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

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.

Proofreading through spatial gradients

Key enzymatic processes use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. The applicability of traditional proofreading schemes, however, is limited because they typically require dedicated structural features in the enzyme, such as a nucleotide hydrolysis site or multiple intermediate conformations. Here, we explore an alternative conceptual mechanism that achieves error correction by having substrate binding and subsequent product formation occur at distinct physical locations. The time taken by the enzyme–substrate complex to diffuse from one location to another is leveraged to discard wrong substrates. This mechanism does not have the typical structural requirements, making it easier to overlook in experiments. We discuss how the length scales of molecular gradients dictate proofreading performance, and quantify the limitations imposed by realistic diffusion and reaction rates. Our work broadens the applicability of kinetic proofreading and sets the stage for studying spatial gradients as a possible route to specificity.

The interplay of spatial organization and biochemistry in building blocks of cellular signalling pathways

Biochemical pathways and networks are central to cellular information processing. While a broad range of studies have dissected multiple aspects of information processing in biochemical pathways, the effect of spatial organization remains much less understood. It is clear that space is central to intracellular organization, plays important roles in cellular information processing and has been exploited in evolution; additionally, it is being increasingly exploited in synthetic biology through the development of artificial compartments, in a variety of ways. In this paper, we dissect different aspects of the interplay between spatial organization and biochemical pathways, by focusing on basic building blocks of these pathways: covalent modification cycles and two-component systems, with enzymes which may be monofunctional or bifunctional. Our analysis of spatial organization is performed by examining a range of 'spatial designs': patterns of localization or non-localization of enzymes/substrates, theoretically and computationally. Using these well-characterized in silico systems, we analyse the following. (i) The effect of different types of spatial organization on the overall kinetics of modification, and the role of distinct modification mechanisms therein. (ii) How different information processing characteristics seen experimentally and studied from the viewpoint of kinetics are perturbed, or generated. (iii) How the activity of enzymes (bifunctional enzymes in particular) may be spatially manipulated, and the relationship between localization and activity. (iv) How transitions in spatial organization (encountered either through evolution or through the lifetime of cells, as seen in multiple model organisms) impacts the kinetic module (and pathway) behaviour, and how transitions in chemistry may be impacted by prior spatial organization. The basic insights which emerge are central to understanding the role of spatial organization in biochemical pathways in both bacteria and eukaryotes, and are of direct relevance to engineering spatial organization of pathways in bottom-up synthetic biology in cellular and cell-free systems.

A Disorder-to-Order Transition Mediates RNA Binding of the Caenorhabditis elegans Protein MEX-5

CCCH-type tandem zinc finger (TZF) domains are found in many RNA-binding proteins (RBPs) that regulate the essential processes of post-transcriptional gene expression and splicing through direct protein-RNA interactions. In Caenorhabditis elegans, RBPs control the translation, stability, or localization of maternal messenger RNAs required for patterning decisions before zygotic gene activation. MEX-5 (Muscle EXcess) is a C. elegans protein that leads a cascade of RBP localization events that is essential for axis polarization and germline differentiation after fertilization. Here, we report that at room temperature, the CCCH-type TZF domain of MEX-5 contains an unstructured zinc finger that folds upon binding of its RNA target. We have characterized the structure and dynamics of the TZF domain of MEX-5 and designed a variant MEX-5 in which both fingers are fully folded in the absence of RNA. Within the thermal range experienced by C. elegans, the population of the unfolded state of the TZF domain of MEX-5 varies. We observe that the TZF domain becomes less disordered at lower temperatures and more disordered at higher temperatures. However, in the temperature range in which C. elegans is fertile, when MEX-5 needs to be functional, only one of the two zinc fingers is folded.

Selective sequestration of signalling proteins in a membraneless organelle reinforces the spatial regulation of asymmetry in Caulobacter crescentus

Selective recruitment and concentration of signalling proteins within membraneless compartments is a ubiquitous mechanism for subcellular organization1-3. The dynamic flow of molecules into and out of these compartments occurs on faster timescales than for membrane-enclosed organelles, presenting a possible mechanism to control spatial patterning within cells. Here, we combine single-molecule tracking and super-resolution microscopy, light-induced subcellular localization, reaction-diffusion modelling and a spatially resolved promoter activation assay to study signal exchange in and out of the 200 nm cytoplasmic pole-organizing protein popZ (PopZ) microdomain at the cell pole of the asymmetrically dividing bacterium Caulobacter crescentus4-8. Two phospho-signalling proteins, the transmembrane histidine kinase CckA and the cytoplasmic phosphotransferase ChpT, provide the only phosphate source for the cell fate-determining transcription factor CtrA9-18. We find that all three proteins exhibit restricted rates of entry into and escape from the microdomain as well as enhanced phospho-signalling within, leading to a submicron gradient of activated CtrA-P19 that is stable and sublinear. Entry into the microdomain is selective for cytosolic proteins and requires a binding pathway to PopZ. Our work demonstrates how nanoscale protein assemblies can modulate signal propagation with fine spatial resolution, and that in Caulobacter, this modulation serves to reinforce asymmetry and differential cell fate of the two daughter cells.

Intracellular morphogens: Specifying patterns at the subcellular scale

The notion that graded distributions of signals underlie the spatial organization of biological systems has long been a central pillar in the fields of cell and developmental biology. During morphogenesis, morphogens spread across tissues to guide development of the embryo. Similarly, a variety of dynamic gradients and pattern-forming networks have been discovered that shape subcellular organization. Here we discuss the principles of intracellular pattern formation by these intracellular morphogens and relate them to conceptually similar processes operating at the tissue scale. We will specifically review mechanisms for generating cellular asymmetry and consider how intracellular patterning networks are controlled and adapt to cellular geometry. Finally, we assess the general concept of intracellular gradients as a mechanism for positional control in light of current data, highlighting how the simple readout of fixed concentration thresholds fails to fully capture the complexity of spatial patterning processes occurring inside cells.

Importance of phosphorylation/dephosphorylation cycles on lipid-dependent modulation of membrane protein topology by posttranslational phosphorylation

Posttranslational modifications of proteins, such as phosphorylation and dephosphorylation, play critical roles in cellular functions through diverse cell signaling pathways. Protein kinases and phosphatases have been described early on as key regulatory elements of the phosphorylated state of proteins. Tight spatial and temporal regulation of protein kinase and phosphatase activities has to be achieved in the cell to ensure accurate signal transduction. We demonstrated previously that phosphorylation of a membrane protein can lead to its topological rearrangement. Additionally, we found that both the rate and extent of topological rearrangement upon phosphorylation are lipid charge- and lipid environment-dependent. Here, using a model membrane protein (the bacterial lactose permease LacY reconstituted in proteoliposomes) and a combination of real-time measurements and steady-state assessments of protein topology, we established a set of experimental conditions to dissect the effects of phosphorylation and dephosphorylation of a membrane protein on its topological orientation. We also demonstrate that the phosphorylation-induced topological switch of a membrane protein can be reversed upon protein dephosphorylation, revealing a new regulatory role for phosphorylation/dephosphorylation cycles. Furthermore, we determined that the rate of topological rearrangement reversal is correlated with phosphatase activity and is influenced by the membrane's lipid composition, presenting new insights into the spatiotemporal control of the protein phosphorylation state. Together, our results highlight the importance of the compartmentalization of phosphorylation/dephosphorylation cycles in controlling membrane protein topology and, therefore, function, which are influenced by the local lipid environment of the membrane protein.

Antimicrobial agent triclosan suppresses mast cell signaling via phospholipase D inhibition

Humans are exposed to the antimicrobial agent triclosan (TCS) through use of TCS-containing products. Exposed tissues contain mast cells, which are involved in numerous biological functions and diseases by secreting various chemical mediators through a process termed degranulation. We previously demonstrated that TCS inhibits both Ca²⁺ influx into antigen-stimulated mast cells and subsequent degranulation. To determine the mechanism linking the TCS cytosolic Ca²⁺ depression to inhibited degranulation, we investigated the effects of TCS on crucial signaling enzymes activated downstream of the Ca²⁺ rise: protein kinase C (PKC; activated by Ca²⁺ and reactive oxygen species [ROS]) and phospholipase D (PLD). We found that TCS strongly inhibits PLD activity within 15 minutes post-antigen, a key mechanism of TCS mast cell inhibition. In addition, experiments using fluorescent constructs and confocal microscopy indicate that TCS delays antigen-induced translocations of PKCβII, PKCδ and PKC substrate myristoylated alanine-rich C-kinase. Surprisingly, TCS does not inhibit PKC activity or overall ability to translocate, and TCS actually increases PKC activity by 45 minutes post-antigen; these results are explained by the timing of both TCS inhibition of cytosolic Ca²⁺ (~15+ minutes post-antigen) and TCS stimulation of ROS (~45 minutes post-antigen). These findings demonstrate that it is incorrect to assume that all Ca²⁺ -dependent processes will be synchronously inhibited when cytosolic Ca²⁺ is inhibited by a toxicant or drug. The results offer molecular predictions of the effects of TCS on other mammalian cell types, which share these crucial signal transduction elements and provide biochemical information that may underlie recent epidemiological findings implicating TCS in human health problems.

Geometric principles of second messenger dynamics in dendritic spines

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Optogenetic dissection of Rac1 and Cdc42 gradient shaping

During cell migration, Rho GTPases spontaneously form spatial gradients that define the front and back of cells. At the front, active Cdc42 forms a steep gradient whereas active Rac1 forms a more extended pattern peaking a few microns away. What are the mechanisms shaping these gradients, and what is the functional role of the shape of these gradients? Here we report, using a combination of optogenetics and micropatterning, that Cdc42 and Rac1 gradients are set by spatial patterns of activators and deactivators and not directly by transport mechanisms. Cdc42 simply follows the distribution of Guanine nucleotide Exchange Factors, whereas Rac1 shaping requires the activity of a GTPase-Activating Protein, β2-chimaerin, which is sharply localized at the tip of the cell through feedbacks from Cdc42 and Rac1. Functionally, the spatial extent of Rho GTPases gradients governs cell migration, a sharp Cdc42 gradient maximizes directionality while an extended Rac1 gradient controls the speed.

A steep gradient of Cdc42 is at the front of migrating cells, whereas the active Rac1 gradient is graded. Here the authors show that Cdc42 gradients follow the distribution of GEFs and govern direction of migration, while Rac1 gradients require the activity of the GAP β2-chimaerin and control cell speed.

Rapid diffusion-state switching underlies stable cytoplasmic gradients in the Caenorhabditis elegans zygote

Protein concentration gradients organize cells and tissues and commonly form through diffusion away from a local source of protein. Interestingly, during the asymmetric division of the Caenorhabditis elegans zygote, the RNA-binding proteins MEX-5 and PIE-1 form opposing concentration gradients in the absence of a local source. In this study, we use near-total internal reflection fluorescence (TIRF) imaging and single-particle tracking to characterize the reaction/diffusion dynamics that maintain the MEX-5 and PIE-1 gradients. Our findings suggest that both proteins interconvert between fast-diffusing and slow-diffusing states on timescales that are much shorter (seconds) than the timescale of gradient formation (minutes). The kinetics of diffusion-state switching are strongly polarized along the anterior/posterior (A/P) axis by the PAR polarity system such that fast-diffusing MEX-5 and PIE-1 particles are approximately symmetrically distributed, whereas slow-diffusing particles are highly enriched in the anterior and posterior cytoplasm, respectively. Using mathematical modeling, we show that local differences in the kinetics of diffusion-state switching can rapidly generate stable concentration gradients over a broad range of spatial and temporal scales.

Protein gradients in single cells induced by their coupling to "morphogen"-like diffusion

One of the many ways cells transmit information within their volume is through steady spatial gradients of different proteins. However, the mechanism through which proteins without any sources or sinks form such single-cell gradients is not yet fully understood. One of the models for such gradient formation, based on differential diffusion, is limited to proteins with large ratios of their diffusion constants or to specific protein-large molecule interactions. We introduce a novel mechanism for gradient formation via the coupling of the proteins within a single cell with a molecule, that we call a "pronogen," whose action is similar to that of morphogens in multi-cell assemblies; the pronogen is produced with a fixed flux at one side of the cell. This coupling results in an effectively non-linear diffusion degradation model for the pronogen dynamics within the cell, which leads to a steady-state gradient of the protein concentration. We use stability analysis to show that these gradients are linearly stable with respect to perturbations.

Spatial modeling of the membrane-cytosolic interface in protein kinase signal transduction

The spatial architecture of signaling pathways and the interaction with cell size and morphology are complex, but little understood. With the advances of single cell imaging and single cell biology, it becomes crucial to understand intracellular processes in time and space. Activation of cell surface receptors often triggers a signaling cascade including the activation of membrane-attached and cytosolic signaling components, which eventually transmit the signal to the cell nucleus. Signaling proteins can form steep gradients in the cytosol, which cause strong cell size dependence. We show that the kinetics at the membrane-cytosolic interface and the ratio of cell membrane area to the enclosed cytosolic volume change the behavior of signaling cascades significantly. We suggest an estimate of average concentration for arbitrary cell shapes depending on the cell volume and cell surface area. The normalized variance, known from image analysis, is suggested as an alternative measure to quantify the deviation from the average concentration. A mathematical analysis of signal transduction in time and space is presented, providing analytical solutions for different spatial arrangements of linear signaling cascades. Quantification of signaling time scales reveals that signal propagation is faster at the membrane than at the nucleus, while this time difference decreases with the number of signaling components in the cytosol. Our investigations are complemented by numerical simulations of non-linear cascades with feedback and asymmetric cell shapes. We conclude that intracellular signal propagation is highly dependent on cell geometry and, thereby, conveys information on cell size and shape to the nucleus.

From dynamic self-assembly to networked chemical systems

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components - on scales from (macro)molecular to macroscopic - can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself - instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities - and, to be sure, new challenges - for DySA research.

Cdk-related kinase 9 regulates RNA polymerase II mediated transcription in Toxoplasma gondii

Cyclin-dependent kinases are an essential part of eukaryotic transcriptional machinery. In Apicomplexan parasites, the role and relevance of the kinases in the multistep process of transcription seeks more attention given the absence of full repertoire of canonical Cdks and cognate cyclin partners. In this study, we functionally characterize T. gondii Cdk-related kinase 9 (TgCrk9) showing maximal homology to eukaryotic Cdk9. An uncanonical cyclin, TgCyclin L, colocalizes with TgCrk9 in the parasite nucleus and co-immunoprecipitate, could activate the kinase in-vitro. We identify two threonines in conserved T-loop domain of TgCrk9 that are important for its activity. The activated TgCrk9 phosphorylates C-terminal domain (CTD) of TgRpb1, the largest subunit of RNA polymerase II highlighting its role in transcription. Selective chemical inhibition of TgCrk9 affected serine 2 phosphorylation in the heptapeptide repeats of TgRpb1-CTD towards 3' end of genes consistent with a possible role in transcription elongation. Interestingly, TgCrk9 kinase activity is regulated by the upstream TgCrk7 based CAK complex. TgCrk9 was found to functionally complement the role of its yeast counterpart Bur1 establishing its role as an important transcriptional kinase. In this study, we provide robust evidence that TgCrk9 is an important part of transcription machinery regulating gene expression in T. gondii.

Polarization of concave domains by traveling wave pinning

Pattern formation is one of the most fundamental yet puzzling phenomena in physics and biology. We propose that traveling front pinning into concave portions of the boundary of 3-dimensional domains can serve as a generic gradient-maintaining mechanism. Such a mechanism of domain polarization arises even for scalar bistable reaction-diffusion equations, and, depending on geometry, a number of stationary fronts may be formed leading to complex spatial patterns. The main advantage of the pinning mechanism, with respect to the Turing bifurcation, is that it allows for maintaining gradients in the specific regions of the domain. By linking the instant domain shape with the spatial pattern, the mechanism can be responsible for cellular polarization and differentiation.

Polo-like Kinase Couples Cytoplasmic Protein Gradients in the C. elegans Zygote

Intracellular protein gradients underlie essential cellular and developmental processes, but the mechanisms by which they are established are incompletely understood. During the asymmetric division of the C. elegans zygote, the RNA-binding protein MEX-5 forms an anterior-rich cytoplasmic gradient that causes the RNA-binding protein POS-1 to form an opposing, posterior-rich gradient. We demonstrate that the polo-like kinase PLK-1 mediates the repulsive coupling between MEX-5 and POS-1 by increasing the mobility of POS-1 in the anterior. PLK-1 is enriched in the anterior cytoplasm and phosphorylates POS-1, which is both necessary and sufficient to increase POS-1 mobility. Regulation of POS-1 mobility depends on both the interaction between PLK-1 and MEX-5 and between MEX-5 and RNA, suggesting that MEX-5 may recruit PLK-1 to RNA in the anterior. The low concentration of MEX-5/PLK-1 in the posterior cytoplasm provides a permissive environment for the retention of POS-1, which depends on POS-1 RNA binding. Our findings describe a novel reaction/diffusion mechanism in which the asymmetric distribution of cytoplasmic PLK-1 couples two RNA-binding protein gradients, thereby partitioning the cytoplasm.

Stochastic Modeling Yields a Mechanistic Framework for Spindle Attachment Error Correction in Budding Yeast Mitosis

Proper segregation of the replicated genome requires that kinetochores form and maintain bioriented, amphitelic attachments to microtubules from opposite spindle poles and eliminate erroneous, syntelic attachments to microtubules from the same spindle pole. Phosphorylation of kinetochore proteins destabilizes low-tension kinetochore-microtubule attachments, yet tension stabilizes bioriented attachments. This conundrum for forming high-tension amphitelic attachments is recognized as the "initiation problem of biorientation (IPBO)." A delay before kinetochore-microtubule detachment solves the IPBO, but it lacks a mechanistic framework. We developed a stochastic mathematical model for kinetochore-microtubule error correction in yeast that reveals: (1) under low chromatin tension, requiring a large number of phosphorylation events at multiple sites to achieve detachment provides the necessary delay; and (2) kinetochore-induced microtubule depolymerization generates tension in amphitelic, but not syntelic, attachments. With these requirements, the model provides a mechanistic framework for the delay before detachment to solve the IPBO and demonstrates the high degree of amphitely observed experimentally for wild-type spindles under optimal conditions.

Relaxation oscillations and hierarchy of feedbacks in MAPK signaling

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

Modeling of Receptor Tyrosine Kinase Signaling: Computational and Experimental Protocols

The advent of systems biology has convincingly demonstrated that the integration of experiments and dynamic modelling is a powerful approach to understand the cellular network biology. Here we present experimental and computational protocols that are necessary for applying this integrative approach to the quantitative studies of receptor tyrosine kinase (RTK) signaling networks. Signaling by RTKs controls multiple cellular processes, including the regulation of cell survival, motility, proliferation, differentiation, glucose metabolism, and apoptosis. We describe methods of model building and training on experimentally obtained quantitative datasets, as well as experimental methods of obtaining quantitative dose-response and temporal dependencies of protein phosphorylation and activities. The presented methods make possible (1) both the fine-grained modeling of complex signaling dynamics and identification of salient, course-grained network structures (such as feedback loops) that bring about intricate dynamics, and (2) experimental validation of dynamic models.

Model of Growth Cone Membrane Polarization via Microtubule Length Regulation

We present a mathematical model of membrane polarization in growth cones. We proceed by coupling an active transport model of cytosolic proteins along a two-dimensional microtubule (MT) network with a modified Dogterom-Leibler model of MT growth. In particular, we consider a Rac1-stathmin-MT pathway in which the growth and catastrophe rates of MTs are regulated by cytosolic stathmin, while the stathmin is regulated by Rac1 at the membrane. We use regular perturbation theory and numerical simulations to determine the steady-state stathmin concentration, the mean MT length distribution, and the resulting distribution of membrane-bound proteins. We thus show how a nonuniform Rac1 distribution on the membrane generates a polarized distribution of membrane proteins. The mean MT length distribution and hence the degree of membrane polarization are sensitive to the precise form of the Rac1 distribution and parameters such as the catastrophe-promoting constant and tubulin association rate. This is a consequence of the fact that the lateral diffusion of stathmin tends to weaken the effects of Rac1 on the distribution of mean MT lengths.

Regulatory principles in metabolism–then and now

The importance of metabolic pathways for life and the nature of participating reactions have challenged physiologists and biochemists for over a hundred years. Eric Arthur Newsholme contributed many original hypotheses and concepts to the field of metabolic regulation, demonstrating that metabolic pathways have a fundamental thermodynamic structure and that near identical regulatory mechanisms exist in multiple species across the animal kingdom. His work at Oxford University from the 1970s to 1990s was groundbreaking and led to better understanding of development and demise across the lifespan as well as the basis of metabolic disruption responsible for the development of obesity, diabetes and many other conditions. In the present review we describe some of the original work of Eric Newsholme, its relevance to metabolic homoeostasis and disease and application to present state-of-the-art studies, which generate substantial amounts of data that are extremely difficult to interpret without a fundamental understanding of regulatory principles. Eric's work is a classical example of how one can unravel very complex problems by considering regulation from a cell, tissue and whole body perspective, thus bringing together metabolic biochemistry, physiology and pathophysiology, opening new avenues that now drive discovery decades thereafter.

Feedback mechanism for microtubule length regulation by stathmin gradients

We formulate and analyze a theoretical model for the regulation of microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin, which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell edge, which closes a positive feedback loop. We investigate both tubulin sequestering and catastrophe promotion as mechanisms for MT growth inhibition by stathmin. For a homogeneous stathmin concentration in the absence of Rac1, we find a switchlike regulation of the MT mean length by stathmin. For constitutively active Rac1 at the cell edge, stathmin is deactivated locally, which establishes a spatial gradient of active stathmin. In this gradient, we find a stationary bimodal MT-length distribution for both mechanisms of MT growth inhibition by stathmin. One subpopulation of the bimodal length distribution can be identified with fast-growing and long pioneering MTs in the region near the cell edge, which have been observed experimentally. The feedback loop is closed through Rac1 activation by MTs. For tubulin sequestering by stathmin, this establishes a bistable switch with two stable states: one stable state corresponds to upregulated MT mean length and bimodal MT length distributions, i.e., pioneering MTs; the other stable state corresponds to an interrupted feedback with short MTs. Stochastic effects as well as external perturbations can trigger switching events. For catastrophe-promoting stathmin, we do not find bistability.

The dynamics of spatio-temporal Rho GTPase signaling: formation of signaling patterns

Rho GTPases are crucial signaling molecules that regulate a plethora of biological functions. Traditional biochemical, cell biological, and genetic approaches have founded the basis of Rho GTPase biology. The development of biosensors then allowed measuring Rho GTPase activity with unprecedented spatio-temporal resolution. This revealed that Rho GTPase activity fluctuates on time and length scales of tens of seconds and micrometers, respectively. In this review, we describe Rho GTPase activity patterns observed in different cell systems. We then discuss the growing body of evidence that upstream regulators such as guanine nucleotide exchange factors and GTPase-activating proteins shape these patterns by precisely controlling the spatio-temporal flux of Rho GTPase activity. Finally, we comment on additional mechanisms that might feed into the regulation of these signaling patterns and on novel technologies required to dissect this spatio-temporal complexity.

Spatial Control of Biochemical Modification Cascades and Pathways

Information transmission in cells occurs through complex networks of proteins and genes and is relayed through cascades of biochemical modifications, which are typically studied through ordinary differential equations. However, it is becoming increasingly clear that spatial factors can strongly influence chemical information transmission in cells. In this article, we systematically disentangle the effects of space in signaling cascades. This is done by examining the effects of localization/compartmentalization and diffusion of enzymes and substrates in multiple variants of chemical modification cascades. This includes situations where the modified form of species at one stage 1) acts as an enzyme for the next stage; 2) acts as a substrate for the next stage; and 3) is involved in phosphotransfer. Our analysis reveals the multiple effects of space in signal transduction cascades. Although in some cases space plays a modulatory effect (itself of interest), in other cases, spatial regulation and control can profoundly affect the nature of information processing as a result of the subtle interplay between the patterns of localization of species, diffusion, and the nature of the modification cascades. Our results provide a platform for disentangling the role of space and spatial control in multiple cellular contexts and a basis for engineering spatial control in signaling cascades through localization/compartmentalization.

Spatio-temporal dynamics of a cell signal pathway with negative feedbacks: the MAPK/ERK pathway

We studied the spatio-temporal dynamics of a cell signal cascade with negative feedback that quantitatively emulates the regulative process that occurs in the Mitogen Activated Protein Kinase/Extracellular Regulated Kinase (MAPK/ERK) pathway. The model consists of a set of six coupled reaction-diffusion equations that describes the dynamics of the six-module pathway. In the basic module the active form of the protein transmits the signal to the next pathway’s module. As suggested by experiments, the model considers that the fifth module's kinase down-regulates the first and third modules. The feedback parameter is defined as, μ(r)( j)= k(kin)5/k(kin)(j), (j = 1, 3). We analysed the pathway's dynamics for μ(r)( j) = 0.10, 1.0, and 10 in the kinetic regimes: i) saturation of both kinases and phosphatases, ii) saturation of the phosphatases and iii) saturation of the kinases. For a regulated pathway the Total Activated Protein Profiles (TAPPs) as a function of time develop a maximum during the transient stage in the three kinetic regimes. These maxima become higher and their positions shift to longer times downstream. This scenario also applies to the TAPP's regulatory kinase that sums up its inhibitory action to that of the phosphatases leading to a maximum. Nevertheless, when μ(r)(j)= 1.0 , the TAPPs develop two maxima, with the second maximum being almost imperceptible. These results are in qualitative agreement with experimental data obtained from NIH 3T3 mouse fibroblasts. In addition, analyses of the stationary states as a function of position indicate that in the kinetic regime i) which is of physiological interest, signal transduction occurs with a relatively large propagation length for the three values of the regulative parameter. However, for μ(r)(j)= 0.10 , the sixth module concentration profile is transmitted with approximately 45% of its full value. The results obtained for μ(r)(j) = 10 , indicate that the first five concentration profiles are small with a short propagation length; nonetheless, the last concentration profile, c6, attains more than 90% of its full value with a relatively large propagation length as an indication of signal transduction. Signal transduction also occurred favourably in the kinetic regimes ii) and iii), but the signal was longer-ranged in the regime ii).

Early T cell activation: integrating biochemical, structural, and biophysical cues

T cells carry out the formidable task of identifying small numbers of foreign antigenic peptides rapidly and specifically against a very noisy environmental background of endogenous self-peptides. Early steps in T cell activation have thus fascinated biologists and are among the best-studied models of cell stimulation. This remarkable process, critical in adaptive immune responses, approaches and even seems to exceed the limitations set by the physical laws ruling molecular behavior. Despite the enormous amount of information concerning the nature of molecules involved in the T cell antigen receptor (TCR) signal transduction network, and the description of the nanoscale organization and real-time analysis of T cell responses, the general principles of information gathering and processing remain incompletely understood. Here we review currently accepted key data on TCR function, discuss the limitations of current research strategies, and suggest a novel model of TCR triggering and a few promising ways of going further into the integration of available data.

Single Particle Tracking Reveals that EGFR Signaling Activity Is Amplified in Clathrin-Coated Pits

Signaling from the epidermal growth factor receptor (EGFR) via phosphorylation on its C-terminal tyrosine residues requires self-association, which depends on the diffusional properties of the receptor and its density in the plasma membrane. Dimerization is a key event for EGFR activation, but the role of higher order clustering is unknown. We employed single particle tracking to relate the mobility and aggregation of EGFR to its signaling activity. EGFR mobility alternates between short-lived free, confined and immobile states. In the immobile state, EGFR tends to aggregate in clathrin-coated pits, which is further enhanced in a phosphorylation-dependent manner and does not require ligand binding. EGFR phosphorylation is further amplified by cross-phosphorylation in clathrin-coated pits. Because phosphorylated receptors can escape from the pits, local gradients of signaling active EGFR are formed. These results show that amplification of EGFR phosphorylation by receptor clustering in clathrin-coated pits supports signal activation at the plasma membrane.

PDE/ODE modeling and simulation to determine the role of diffusion in long-term and -range cellular signaling

Background

We study the relevance of diffusion for the dynamics of signaling pathways. Mathematical modeling of cellular diffusion leads to a coupled system of differential equations with Robin boundary conditions which requires a substantial knowledge in mathematical theory. Using our new developed analytical and numerical techniques together with modern experiments, we analyze and quantify various types of diffusive effects in intra- and inter-cellular signaling. The complexity of these models necessitates suitable numerical methods to perform the simulations precisely and within an acceptable period of time.

Methods

The numerical methods comprise a Galerkin finite element space discretization, an adaptive time stepping scheme and either an iterative operator splitting method or fully coupled multilevel algorithm as solver.

Results

The simulation outcome allows us to analyze different biological aspects. On the scale of a single cell, we showed the high cytoplasmic concentration gradients in irregular geometries. We found an 11 % maximum relative total STAT5-concentration variation in a fibroblast and a 70 % maximum relative pSTAT5-concentration variation in a fibroblast with an irregular cell shape. For pSMAD2 the maximum relative variation was 18 % in a hepatocyte with a box shape and 70 % in an irregular geometry. This result can be also obtained in a cell with a box shape if the molecules diffuse slowly (with D=1 μm²/s instead of D=15 μm²/s). On a scale of cell system in the lymph node, our simulations showed an inhomogeneous IL-2 pattern with an amount over three orders of magnitude (10⁻³−1 pM) and high gradients in face of its fast diffusivity. We observed that 20 out of 125 cells were activated after 9 h and 33 in the steady state. Our in-silico experiments showed that the insertion of 31 regulatory T cells in our cell system can completely downregulate the signal.

Conclusions

We quantify the concentration gradients evolving from the diffusion of the molecules in several signaling pathways. For intracellular signaling pathways with nuclear accumulation the size of cytoplasmic gradients does not indicate the change in gene expression which has to be analyzed separately in future. For intercellular signaling the high cytokine concentration gradients play an essential role in the regulation of the molecular mechanism of the immune response. Furthermore, our simulation results can give the information on which signaling pathway diffusion may play a role. We conclude that a PDE model has to be considered for cells with an irregular shape or for slow diffusing molecules. Also the high gradients inside a cell or in a cell system can play an essential role in the regulation of the molecular mechanisms.

Plasma membrane restricted RhoGEF activity is sufficient for RhoA-mediated actin polymerization

The small GTPase RhoA is involved in cell morphology and migration. RhoA activity is tightly regulated in time and space and depends on guanine exchange factors (GEFs). However, the kinetics and subcellular localization of GEF activity towards RhoA are poorly defined. To study the mechanism underlying the spatiotemporal control of RhoA activity by GEFs, we performed single cell imaging with an improved FRET sensor reporting on the nucleotide loading state of RhoA. By employing the FRET sensor we show that a plasma membrane located RhoGEF, p63RhoGEF, can rapidly activate RhoA through endogenous GPCRs and that localized RhoA activity at the cell periphery correlates with actin polymerization. Moreover, synthetic recruitment of the catalytic domain derived from p63RhoGEF to the plasma membrane, but not to the Golgi apparatus, is sufficient to activate RhoA. The synthetic system enables local activation of endogenous RhoA and effectively induces actin polymerization and changes in cellular morphology. Together, our data demonstrate that GEF activity at the plasma membrane is sufficient for actin polymerization via local RhoA signaling.

Spatial gradients controlling spindle assembly

The mitotic spindle is the macromolecular machine utilized to accurately segregate chromosomes in cells. How this self-organized structure assembles is a key aspect of understanding spindle morphogenesis. In the present review, we focus on understanding mechanisms of spindle self-assembly and address how subcellular signalling gradients, such as Ran-GTP and Aurora B, contribute to spindle organization and function.

Dynamics of gradient formation by intracellular shuttling

A number of important cellular functions rely on the formation of intracellular protein concentration gradients. Experimental studies discovered a number of mechanisms for the formation of such gradients. One of the mechanisms relies on the intracellular shuttling of a protein that interconverts between the two states with different diffusivities, under the action of two enzymes, one of which is localized to the plasma membrane, whereas the second is uniformly distributed in the cytoplasm. Recent work reported an analytical solution for the steady state gradient in this mechanism, obtained in the framework of a one-dimensional reaction-diffusion model. Here, we study the dynamics in this model and derive analytical expressions for the Laplace transforms of the time-dependent concentration profiles in terms of elementary transcendental functions. Inverting these transforms numerically, one can obtain time-dependent concentration profiles of the two forms of the protein.

Cytoplasmic localization and asymmetric division in the early embryo of Caenorhabditis elegans

During the initial cleavages of the Caenorhabditis elegans embryo, a series of rapid and invariant asymmetric cell divisions pattern the fate, size, and position of four somatic blastomeres and a single germline blastomere. These asymmetric divisions are orchestrated by a collection of maternally deposited factors that are initially symmetrically distributed in the newly fertilized embryo. Maturation of the sperm-derived centrosome in the posterior cytoplasm breaks this symmetry by triggering a dramatic and highly stereotyped partitioning of these maternal factors. A network of conserved cell polarity regulators, the PAR proteins, form distinct anterior and posterior domains at the cell cortex. From these domains, the PAR proteins direct the segregation of somatic and germline factors into opposing regions of the cytoplasm such that, upon cell division, they are preferentially inherited by the somatic blastomere or the germline blastomere, respectively. The segregation of these factors is controlled, at least in part, by a series of reaction-diffusion mechanisms that are asymmetrically deployed along the anterior/posterior axis. The characterization of these mechanisms has important implications for our understanding of how cells are polarized and how spatial organization is generated in the cytoplasm. For further resources related to this article, please visit the WIREs website.

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

Aggregation-fragmentation model of robust concentration gradient formation

Concentration gradients of signaling molecules are essential for patterning during development and they have been observed in both unicellular and multicellular systems. In subcellular systems, clustering of the signaling molecule has been observed. We develop a theoretical model of cluster-mediated concentration gradient formation based on the Becker-Döring equations of aggregation-fragmentation processes. We show that such a mechanism produces robust concentration gradients on realistic time and spatial scales so long as the process of clustering does not significantly stabilize the signaling molecule. Finally, we demonstrate that such a model is applicable to the pom1p subcellular gradient in fission yeast.

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

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

Enhancement of tunability of MAPK cascade due to coexistence of processive and distributive phosphorylation mechanisms

The processive phosphorylation mechanism becomes important when there is macromolecular crowding in the cytoplasm. Integrating the processive phosphorylation mechanism with the traditional distributive one, we propose a mixed dual-site phosphorylation (MDP) mechanism in a single-layer phosphorylation cycle. Further, we build a degree model by applying the MDP mechanism to a three-layer mitogen-activated protein kinase (MAPK) cascade. By bifurcation analysis, our study suggests that the crowded-environment-induced pseudoprocessive mechanism can qualitatively change the response of this biological network. By adjusting the degree of processivity in our model, we find that the MAPK cascade is able to switch between the ultrasensitivity, bistability, and oscillatory dynamical states. Sensitivity analysis shows that the theoretical results remain unchanged within a reasonably chosen variation of parameter perturbation. By scaling the reaction rates and also introducing new connections into the kinetic scheme, we further construct a proportion model of the MAPK cascade to validate our findings. Finally, it is illustrated that the spatial propagation of the activated MAPK signal can be improved (or attenuated) by increasing the degree of processivity of kinase (or phosphatase). Our research implies that the MDP mechanism makes the MAPK cascade become a flexible signal module, and the coexistence of processive and distributive phosphorylation mechanisms enhances the tunability of the MAPK cascade.

Covalent modification cycles through the spatial prism

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.

Cross talk between CD3 and CD28 is spatially modulated by protein lateral mobility

Functional convergence of CD28 costimulation and TCR signaling is critical to T-cell activation and adaptive immunity. These receptors form complex microscale patterns within the immune synapse, although the impact of this spatial organization on cell signaling remains unclear. We investigate this cross talk using micropatterned surfaces that present ligands to these membrane proteins in order to control the organization of signaling molecules within the cell-substrate interface. While primary human CD4(+) T cells were activated by features containing ligands to both CD3 and CD28, this functional convergence was curtailed on surfaces in which engagement of these two systems was separated by micrometer-scale distances. Moreover, phosphorylated Lck was concentrated to regions of CD3 engagement and exhibited a low diffusion rate, suggesting that costimulation is controlled by a balance between the transport of active Lck to CD28 and its deactivation. In support of this model, disruption of the actin cytoskeleton increased Lck mobility and allowed functional T-cell costimulation by spatially separated CD3 and CD28. In primary mouse CD4(+) T cells, a complementary system, reducing the membrane mobility increased the sensitivity to CD3-CD28 separation. These results demonstrate a subcellular reaction-diffusion system that allows cells to sense the microscale organization of the extracellular environment.

Development of a FRET biosensor with high specificity for Akt

The serine/threonine kinase Akt plays a critical role in cell proliferation, survival, and tumorigenesis. As a central kinase in the phosphatidylinositol 3-kinase pathway, its activation mechanism at the plasma membrane has been well characterized. However, the subcellular Akt activity in living cells is still largely unknown. Fluorescence resonance energy transfer (FRET)-based biosensors have emerged as indispensable tools to visualize the subcellular activities of signaling molecules. In this study, we developed a highly specific FRET biosensor for Akt based on the Eevee backbone, called Eevee-iAkt. Using inhibitors targeting kinases upstream and downstream of Akt, we showed that Eevee-iAkt specifically monitors Akt activity in living cells. To visualize Akt activity at different subcellular compartments, we targeted Eevee-iAkt to raft and non-raft regions of the plasma membrane, mitochondria, and nucleus in HeLa and Cos7 cells. Interestingly, we revealed substantial differences in Akt activation between HeLa and Cos7 cells upon epidermal growth factor (EGF) stimulation: Akt was transiently activated in HeLa cells with comparable levels at the plasma membrane, cytosol, and mitochondria. In contrast, sustained and spatially localized Akt activation was observed in EGF-stimulated Cos7 cells. We found high Akt activity at the plasma membrane, low activity in the cytosol, and no detectable activity at the mitochondria and nucleus in Cos7 cells. The Eevee-iAkt biosensor was shown to be a valuable tool to study the functional relationship between subcellular Akt activation and its anti-apoptotic role in living cells.

Complexity of receptor tyrosine kinase signal processing

Our knowledge of molecular mechanisms of receptor tyrosine kinase (RTK) signaling advances with ever-increasing pace. Yet our understanding of how the spatiotemporal dynamics of RTK signaling control specific cellular outcomes has lagged behind. Systems-centered experimental and computational approaches can help reveal how overlapping networks of signal transducers downstream of RTKs orchestrate specific cell-fate decisions. We discuss how RTK network regulatory structures, which involve the immediate posttranslational and delayed transcriptional controls by multiple feed forward and feedback loops together with pathway cross talk, adapt cells to the combinatorial variety of external cues and conditions. This intricate network circuitry endows cells with emerging capabilities for RTK signal processing and decoding. We illustrate how mathematical modeling facilitates our understanding of RTK network behaviors by unraveling specific systems properties, including bistability, oscillations, excitable responses, and generation of intricate landscapes of signaling activities.

Intracellular regulation of cell signaling cascades: how location makes a difference

Organelles such as endosomes and the Golgi apparatus play a critical role in regulating signal transmission to the nucleus. Recent experiments have shown that appropriate positioning of these organelles within the intracellular space is critical for effective signal regulation. To understand the mechanism behind this observation, we consider a reaction-diffusion model of an intracellular signaling cascade and investigate the effect on the signaling of intracellular regulation in the form of a small release of phosphorylated signaling protein, kinase, and/or phosphatase. Variational analysis is applied to characterize the most effective regions for the localization of this intracellular regulation. The results demonstrate that signals reaching the nucleus are most effectively regulated by localizing the release of phosphorylated substrate protein and kinase near the nucleus. Phosphatase release, on the other hand, is nearly equally effective throughout the intracellular space. The effectiveness of the intracellular regulation is affected strongly by the characteristics of signal propagation through the cascade. For signals that are amplified as they propagate through the cascade, reactions in the upstream levels of the cascade exhibit much larger sensitivities to regulation by release of phosphorylated substrate protein and kinase than downstream reactions. On the other hand, for signals that decay through the cascade, downstream reactions exhibit larger sensitivity than upstream reactions. For regulation by phosphatase release, all reactions within the cascade show large sensitivity for amplified signals but lose this sensitivity for decaying signals. We use the analysis to develop a simple model of endosome-mediated regulation of cell signaling. The results demonstrate that signal regulation by the modeled endosome is most effective when the endosome is positioned in the vicinity of the nucleus. The present findings may explain at least in part why endosomes in many cell types localize near the nucleus.