A quantitative model of ERK MAP kinase phosphorylation in crowded media

Viscosity-dependent control of protein synthesis and degradation

It has been proposed that the concentration of proteins in the cytoplasm maximizes the speed of important biochemical reactions. Here we have used Xenopus egg extracts, which can be diluted or concentrated to yield a range of cytoplasmic protein concentrations, to test the effect of cytoplasmic concentration on mRNA translation and protein degradation. We find that protein synthesis rates are maximal in ~1x cytoplasm, whereas protein degradation continues to rise to a higher optimal concentration of ~1.8x. We show that this difference in optima can be attributed to a greater sensitivity of translation to cytoplasmic viscosity. The different concentration optima could produce a negative feedback homeostatic system, where increasing the cytoplasmic protein concentration above the 1x physiological level increases the viscosity of the cytoplasm, which selectively inhibits translation and drives the system back toward the 1x set point.

A unified approach to dissecting biphasic responses in cell signaling

Biphasic responses are encountered at all levels in biological systems. At the cellular level, biphasic dose-responses are widely encountered in cell signaling and post-translational modification systems and represent safeguards against overactivation or overexpression of species. In this paper, we provide a unified theoretical synthesis of biphasic responses in cell signaling systems, by assessing signaling systems ranging from basic biochemical building blocks to canonical network structures to well-characterized exemplars on one hand, and examining different types of doses on the other. By using analytical and computational approaches applied to a range of systems across levels (described by broadly employed models), we reveal (i) design principles enabling the presence of biphasic responses, including in almost all instances, an explicit characterization of the parameter space (ii) structural factors which preclude the possibility of biphasic responses (iii) different combinations of the presence or absence of enzyme-biphasic and substrate-biphasic responses, representing safeguards against overactivation and overexpression, respectively (iv) the possibility of broadly robust biphasic responses (v) the complete alteration of signaling behavior in a network due to biphasic interactions between species (biphasic regulation) (vi) the propensity of different co-existing biphasic responses in the Erk signaling network. These results both individually and in totality have a number of important consequences for systems and synthetic biology.

Architecture of the MKK6-p38α complex defines the basis of MAPK specificity and activation

The mitogen-activated protein kinase (MAPK) p38α is a central component of signaling in inflammation and the immune response and is, therefore, an important drug target. Little is known about the molecular mechanism of its activation by double phosphorylation from MAPK kinases (MAP2Ks), because of the challenge of trapping a transient and dynamic heterokinase complex. We applied a multidisciplinary approach to generate a structural model of p38α in complex with its MAP2K, MKK6, and to understand the activation mechanism. Integrating cryo-electron microscopy with molecular dynamics simulations, hydrogen-deuterium exchange mass spectrometry, and experiments in cells, we demonstrate a dynamic, multistep phosphorylation mechanism, identify catalytically relevant interactions, and show that MAP2K-disordered amino termini determine pathway specificity. Our work captures a fundamental step of cell signaling: a kinase phosphorylating its downstream target kinase.

Optimal density of bacterial cells

A substantial fraction of the bacterial cytosol is occupied by catalysts and their substrates. While a higher volume density of catalysts and substrates might boost biochemical fluxes, the resulting molecular crowding can slow down diffusion, perturb the reactions' Gibbs free energies, and reduce the catalytic efficiency of proteins. Due to these tradeoffs, dry mass density likely possesses an optimum that facilitates maximal cellular growth and that is interdependent on the cytosolic molecule size distribution. Here, we analyze the balanced growth of a model cell, accounting systematically for crowding effects on reaction kinetics. Its optimal cytosolic volume occupancy depends on the nutrient-dependent resource allocation into large ribosomal vs. small metabolic macromolecules, reflecting a tradeoff between the saturation of metabolic enzymes, favoring larger occupancies with higher encounter rates, and the inhibition of the ribosomes, favoring lower occupancies with unhindered diffusion of tRNAs. Our predictions across growth rates are quantitatively consistent with the experimentally observed reduction in volume occupancy on rich media compared to minimal media in E. coli. Strong deviations from optimal cytosolic occupancy only lead to minute reductions in growth rate, which are nevertheless evolutionarily relevant due to large bacterial population sizes. In sum, cytosolic density variation in bacterial cells appears to be consistent with an optimality principle of cellular efficiency.

Protein homeostasis from diffusion-dependent control of protein synthesis and degradation

It has been proposed that the concentration of proteins in the cytoplasm maximizes the speed of important biochemical reactions. Here we have used the Xenopus extract system, which can be diluted or concentrated to yield a range of cytoplasmic protein concentrations, to test the effect of cytoplasmic concentration on mRNA translation and protein degradation. We found that protein synthesis rates are maximal in ~1x cytoplasm, whereas protein degradation continues to rise to an optimal concentration of ~1.8x. This can be attributed to the greater sensitivity of translation to cytoplasmic viscosity, perhaps because it involves unusually large macromolecular complexes like polyribosomes. The different concentration optima sets up a negative feedback homeostatic system, where increasing the cytoplasmic protein concentration above the 1x physiological level increases the viscosity of the cytoplasm, which selectively inhibits translation and drives the system back toward the 1x set point.

The Golgi-resident protein ACBD3 concentrates STING at ER-Golgi contact sites to drive export from the ER

STING, an endoplasmic reticulum (ER)-resident receptor for cyclic di-nucleotides (CDNs), is essential for innate immune responses. Upon CDN binding, STING moves from the ER to the Golgi, where it activates downstream type-I interferon (IFN) signaling. General cargo proteins exit from the ER via concentration at ER exit sites. However, the mechanism of STING concentration is poorly understood. Here, we visualize the ER exit sites of STING by blocking its transport at low temperature or by live-cell imaging with the cell-permeable ligand bis-^pivSATE-2'F-c-di-dAMP, which we have developed. After ligand binding, STING forms punctate foci at non-canonical ER exit sites. Unbiased proteomic screens and super-resolution microscopy show that the Golgi-resident protein ACBD3/GCP60 recognizes and concentrates ligand-bound STING at specialized ER-Golgi contact sites. Depletion of ACBD3 impairs STING ER-to-Golgi trafficking and type-I IFN responses. Our results identify the ACBD3-mediated non-canonical cargo concentration system that drives the ER exit of STING.

Precise timing of ERK phosphorylation/dephosphorylation determines the outcome of trial repetition during long-term memory formation

Two-trial learning in Aplysia reveals nonlinear interactions between training trials: A single trial has no effect, but two precisely spaced trials induce long-term memory. Extracellularly regulated kinase (ERK) activity is essential for intertrial interactions, but the mechanism remains unresolved. A combination of immunochemical and optogenetic tools reveals unexpected complexity of ERK signaling during the induction of long-term synaptic facilitation by two spaced pulses of serotonin (5-hydroxytryptamine, 5HT). Specifically, dual ERK phosphorylation at its activating TxY motif is accompanied by dephosphorylation at the pT position, leading to a buildup of inactive, singly phosphorylated pY-ERK. Phosphorylation and dephosphorylation occur concurrently but scale differently with varying 5HT concentrations, predicting that mixed two-trial protocols involving both "strong" and "weak" 5HT pulses should be sensitive to the precise order and timing of trials. Indeed, long-term synaptic facilitation is induced only when weak pulses precede strong, not vice versa. This may represent a physiological mechanism to prioritize memory of escalating threats.

On the parameter combinations that matter and on those that do not: data-driven studies of parameter (non)identifiability

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.

Oncogenic mutant RAS signaling activity is rescaled by the ERK/MAPK pathway

Activating mutations in RAS are present in ~ 30% of human tumors, and the resulting aberrations in ERK/MAPK signaling play a central role in oncogenesis. However, the form of these signaling changes is uncertain, with activating RAS mutants linked to both increased and decreased ERK activation in vivo. Rationally targeting the kinase activity of this pathway requires clarification of the quantitative effects of RAS mutations. Here, we use live‐cell imaging in cells expressing only one RAS isoform to quantify ERK activity with a new level of accuracy. We find that despite large differences in their biochemical activity, mutant KRAS isoforms within cells have similar ranges of ERK output. We identify roles for pathway‐level effects, including variation in feedback strength and feedforward modulation of phosphatase activity, that act to rescale pathway sensitivity, ultimately resisting changes in the dynamic range of ERK activity while preserving responsiveness to growth factor stimuli. Our results reconcile seemingly inconsistent reports within the literature and imply that the signaling changes induced by RAS mutations early in oncogenesis are subtle.

Symmetry breaking meets multisite modification

Multisite modification is a basic way of conferring functionality to proteins and a key component of post-translational modification networks. Additional interest in multisite modification stems from its capability of acting as complex information processors. In this paper, we connect two seemingly disparate themes: symmetry and multisite modification. We examine different classes of random modification networks of substrates involving separate or common enzymes. We demonstrate that under different instances of symmetry of the modification network (invoked explicitly or implicitly and discussed in the literature), the biochemistry of multisite modification can lead to the symmetry being broken. This is shown computationally and consolidated analytically, revealing parameter regions where this can (and in fact does) happen, and characteristics of the symmetry-broken state. We discuss the relevance of these results in situations where exact symmetry is not present. Overall, through our study we show how symmetry breaking (i) can confer new capabilities to protein networks, including concentration robustness of different combinations of species (in conjunction with multiple steady states); (ii) could have been the basis for ordering of multisite modification, which is widely observed in cells; (iii) can significantly impact information processing in multisite modification and in cell signalling networks/pathways where multisite modification is present; and (iv) can be a fruitful new angle for engineering in synthetic biology and chemistry. All in all, the emerging conceptual synthesis provides a new vantage point for the elucidation and the engineering of molecular systems at the junction of chemical and biological systems.

Proteins help our cells perform the chemical reactions necessary for life. Once proteins are made, they can also be modified in different ways. This can simply change their activity, or otherwise make them better suited for their specific jobs within the cell. Biological ‘catalysts’ called enzymes carry out protein modifications by reversibly adding (or removing) chemical groups, such as phosphate groups.

‘Multisite modifications’ occur when a protein has two or more modifications in different areas, which can be added randomly or in a specific sequence. The combination of all the modifications attached to a protein acts like a chemical barcode and confers a specific function to the protein.

Modification networks add levels of complexity above individual proteins. These encompass not only the proteins in a cell or tissue, but also the different enzymes that can modify them, and how they all interact with each other. Although our knowledge of these networks is substantial, basic aspects, such as how the ordering of multisite modification systems emerges, is still not well understood.

Using a simple set of multisite modifications, Ramesh and Krishnan set out to study the potential mechanisms allowing the creation of order in this context. Symmetry is a pervasive theme across the sciences. In biology, symmetry and how it may be broken, is important to understand, for example, how organism develop. Ramesh and Krishnan used the perspective of symmetry in protein networks to uncover the origins of ordering.

First, mathematical models of simple modification networks were created based on their basic descriptions. This system centred on proteins that could have phosphate modifications at two possible sites. The network was ‘symmetric’, meaning that the rate of different sets of chemical reactions was identical, as were the amounts of all the enzymes involved.

Dissecting the simulated network using a variety of mathematical approaches showed that its initial symmetry could break, giving rise to sets of ordered multisite modifications. Breaking symmetry did not require any additional features or factors; the basic chemical ‘ingredients’ of protein modification were all that was needed. The prism of symmetry also revealed other aspects of these multisite modification networks, such as robustness and oscillations.

This study sheds new light on the mechanism behind ordering of protein modifications. In the future, Ramesh and Krishnan hope that this approach can be applied to the study of not just proteins but also a wider range of biochemical networks.

Transcription and Translation in Cytomimetic Protocells Perform Most Efficiently at Distinct Macromolecular Crowding Conditions

The formation of cytomimetic protocells that capture the physicochemical aspects of living cells is an important goal in bottom-up synthetic biology. Here, we recreated the crowded cytoplasm in liposome-based protocells and studied the kinetics of cell-free gene expression in these crowded containers. We found that diffusion of key components is affected not only by macromolecular crowding but also by enzymatic activity in the protocell. Surprisingly, size-dependent diffusion in crowded conditions yielded two distinct maxima for protein synthesis, reflecting the differential impact of crowding on transcription and translation. Our experimental data show, for the first time, that macromolecular crowding induces a switch from reaction to diffusion control and that this switch depends on the sizes of the macromolecules involved. These results highlight the need to control the physical environment in the design of synthetic cells.

Dehydration entropy drives liquid-liquid phase separation by molecular crowding

Complex coacervation driven liquid-liquid phase separation (LLPS) of biopolymers has been attracting attention as a novel phase in living cells. Studies of LLPS in this context are typically of proteins harboring chemical and structural complexity, leaving unclear which properties are fundamental to complex coacervation versus protein-specific. This study focuses on the role of polyethylene glycol (PEG)-a widely used molecular crowder-in LLPS. Significantly, entropy-driven LLPS is recapitulated with charged polymers lacking hydrophobicity and sequence complexity, and its propensity dramatically enhanced by PEG. Experimental and field-theoretic simulation results are consistent with PEG driving LLPS by dehydration of polymers, and show that PEG exerts its effect without partitioning into the dense coacervate phase. It is then up to biology to impose additional variations of functional significance to the LLPS of biological systems.

Inference of Multisite Phosphorylation Rate Constants and Their Modulation by Pathogenic Mutations

Multisite protein phosphorylation plays a critical role in cell regulation [1-3]. It is widely appreciated that the functional capabilities of multisite phosphorylation depend on the order and kinetics of phosphorylation steps, but kinetic aspects of multisite phosphorylation remain poorly understood [4-6]. Here, we focus on what appears to be the simplest scenario, when a protein is phosphorylated on only two sites in a strict, well-defined order. This scenario describes the activation of ERK, a highly conserved cell-signaling enzyme. We use Bayesian parameter inference in a structurally identifiable kinetic model to dissect dual phosphorylation of ERK by MEK, a kinase that is mutated in a large number of human diseases [7-12]. Our results reveal how enzyme processivity and efficiencies of individual phosphorylation steps are altered by pathogenic mutations. The presented approach, which connects specific mutations to kinetic parameters of multisite phosphorylation mechanisms, provides a systematic framework for closing the gap between studies with purified enzymes and their effects in the living organism.

Quantification of the Dynamic Phosphorylation Process of ERK Using Stable Isotope Dilution Selective Reaction Monitoring Mass Spectrometry

Mitogen-activated protein (MAP) kinase signaling is critical for various cellular responses, including cell proliferation, differentiation, and cell death. The MAP kinase cascade is conserved in the eukaryotic kingdom as a three-tiered kinase module-MAP kinase kinase kinase, MAP kinase kinase, and MAP kinase-that transduces signals via sequential phosphorylation upon stimulation. Dual phosphorylation of MAP kinase on the conserved threonine-glutamic acid-tyrosine (TEY) motif is essential for its catalytic activity and signal activation; however, the molecular mechanism by which the two residues are phosphorylated remains elusive. In the present study, the pattern of dual phosphorylation of extracellular signal-regulated kinase (ERK) is profiled on the TEY motif using stable isotope dilution (SID)-selective reaction monitoring (SRM) mass spectrometry (MS) to elucidate the order and magnitude of endogenous ERK phosphorylation in cellular model systems. The SID-SRM-MS analysis of phosphopeptides demonstrates that tyrosine phosphorylation in the TEY motif is dynamic, while threonine phosphorylation is static. Analyses of the mono-phosphorylatable mutants ERK^T202A and ERK^Y204F indicate that phosphorylation of tyrosine is not affected by the phosphorylation state of threonine, while threonine phosphorylation depends on tyrosine phosphorylation. The data suggest that dual phosphorylation of ERK is a highly ordered and restricted mechanism determined by tyrosine phosphorylation.

Single-cell quantification of the concentrations and dissociation constants of endogenous proteins

Kinetic simulation is a useful approach for elucidating complex cell-signaling systems. The numerical simulations required for kinetic modeling in live cells critically require parameters such as protein concentrations and dissociation constants (K_d ). However, only a limited number of parameters have been measured experimentally in living cells. Here we describe an approach for quantifying the concentration and K_d of endogenous proteins at the single-cell level with CRISPR/Cas9-mediated knock-in and fluorescence cross-correlation spectroscopy. First, the mEGFP gene was knocked in at the end of the mitogen-activated protein kinase 1 (MAPK1) gene, encoding extracellular signal-regulated kinase 2 (ERK2), through homology-directed repair or microhomology-mediated end joining. Next, the HaloTag gene was knocked in at the end of the ribosomal S6 kinase 2 (RSK2) gene. We then used fluorescence correlation spectroscopy to measure the protein concentrations of endogenous ERK2-mEGFP and RSK2-HaloTag fusion constructs in living cells, revealing substantial heterogeneities. Moreover, fluorescence cross-correlation spectroscopy analyses revealed temporal changes in the apparent K_d values of the binding between ERK2-mEGFP and RSK2-HaloTag in response to epidermal growth factor stimulation. Our approach presented here provides a robust and efficient method for quantifying endogenous protein concentrations and dissociation constants in living cells.

When More Is Less: Dual Phosphorylation Protects Signaling Off State against Overexpression

Kinases in signaling pathways are commonly activated by multisite phosphorylation. For example, the mitogen-activated protein kinase Erk is activated by its kinase Mek by two consecutive phosphorylations within its activation loop. In this article, we use kinetic models to study how the activation of Erk is coupled to its abundance. Intuitively, Erk activity should rise with increasing amounts of Erk protein. However, a mathematical model shows that the signaling off state is robust to increasing amounts of Erk, and Erk activity may even decline with increasing amounts of Erk. This counterintuitive, bell-shaped response of Erk activity to increasing amounts of Erk arises from the competition of the unmodified and single phosphorylated form of Erk for access to its kinase Mek. This shows that phosphorylation cycles can contain an intrinsic robustness mechanism that protects signaling from aberrant activation e.g., by gene expression noise or kinase overexpression after gene duplication events in diseases like cancer.

Crowding, Entropic Forces, and Confinement: Crucial Factors for Structures and Functions in the Cell Nucleus

The view of the cell nucleus as a crowded system of colloid particles and that chromosomes are giant self-avoiding polymers is stimulating rapid advances in our understanding of its structure and activities, thanks to concepts and experimental methods from colloid, polymer, soft matter, and nano sciences and to increased computational power for simulating macromolecules and polymers. This review summarizes current understanding of some characteristics of the molecular environment in the nucleus, of how intranuclear compartments are formed, and of how the genome is highly but precisely compacted, and underlines the crucial, subtle, and sometimes unintuitive effects on structures and reactions of entropic forces caused by the high concentration of macromolecules in the nucleus.

Dual Specificity Phosphatase 5-Substrate Interaction: A Mechanistic Perspective

The mammalian genome contains approximately 200 phosphatases that are responsible for catalytically removing phosphate groups from proteins. In this review, we discuss dual specificity phosphatase 5 (DUSP5). DUSP5 belongs to the dual specificity phosphatase (DUSP) family, so named after the family members' abilities to remove phosphate groups from serine/threonine and tyrosine residues. We provide a comparison of DUSP5's structure to other DUSPs and, using molecular modeling studies, provide an explanation for DUSP5's mechanistic interaction and specificity toward phospho-extracellular regulated kinase, its only known substrate. We also discuss new insights from molecular modeling studies that will influence our current thinking of mitogen-activated protein kinase signaling. Finally, we discuss the lessons learned from identifying small molecules that target DUSP5, which might benefit targeting efforts for other phosphatases. © 2017 American Physiological Society. Compr Physiol 7:1449-1461, 2017.

Kinase Inhibition Leads to Hormesis in a Dual Phosphorylation-Dephosphorylation Cycle

Many antimicrobial and anti-tumour drugs elicit hormetic responses characterised by low-dose stimulation and high-dose inhibition. While this can have profound consequences for human health, with low drug concentrations actually stimulating pathogen or tumour growth, the mechanistic understanding behind such responses is still lacking. We propose a novel, simple but general mechanism that could give rise to hormesis in systems where an inhibitor acts on an enzyme. At its core is one of the basic building blocks in intracellular signalling, the dual phosphorylation-dephosphorylation motif, found in diverse regulatory processes including control of cell proliferation and programmed cell death. Our analytically-derived conditions for observing hormesis provide clues as to why this mechanism has not been previously identified. Current mathematical models regularly make simplifying assumptions that lack empirical support but inadvertently preclude the observation of hormesis. In addition, due to the inherent population heterogeneities, the presence of hormesis is likely to be masked in empirical population-level studies. Therefore, examining hormetic responses at single-cell level coupled with improved mathematical models could substantially enhance detection and mechanistic understanding of hormesis.

Hormesis is a highly controversial and poorly understood phenomenon. It describes the idea that an inhibitor molecule, like an anti-cancer or anti-microbial drug, can inadvertently stimulate cell growth instead of suppressing it. This can have a profound effect on human health leading to failures in clinical treatments. Therefore, getting at the mechanistic basis of hormesis is critical for drug development and clinical practice, however molecular mechanisms underpinning hormesis remain poorly understood. In this paper we use a mathematical model to propose a simple and yet general mechanism that could explain why we find hormesis so widely in living systems. In particular, we discover that hormesis is present within a fundamental structure that forms a basic building block of many intracellular signalling pathways found in diverse processes including control of cell reproduction and programmed cell death. The benefits of our study are two-fold. Having simple molecular understanding of the causes of hormetic responses can greatly improve the design of new drug compounds that avoid such responses. Moreover, due to the fundamental nature of the newly proposed mechanism, our findings have a potential broad applicability to both anti-cancer and anti-microbial drugs.

DNA binding proteins explore multiple local configurations during docking via rapid rebinding

Finding the target site and associating in a specific orientation are essential tasks for DNA-binding proteins. In order to make the target search process as efficient as possible, proteins should not only rapidly diffuse to the target site but also dynamically explore multiple local configurations before diffusing away. Protein flipping is an example of this second process that has been observed previously, but the underlying mechanism of flipping remains unclear. Here, we probed the mechanism of protein flipping at the single molecule level, using HIV-1 reverse transcriptase (RT) as a model system. In order to test the effects of long-range attractive forces on flipping efficiency, we varied the salt concentration and macromolecular crowding conditions. As expected, increased salt concentrations weaken the binding of RT to DNA while increased crowding strengthens the binding. Moreover, when we analyzed the flipping kinetics, i.e. the rate and probability of flipping, at each condition we found that flipping was more efficient when RT bound more strongly. Our data are consistent with a view that DNA bound proteins undergo multiple rapid re-binding events, or short hops, that allow the protein to explore other configurations without completely dissociating from the DNA.

Effect of crowding and confinement on first-passage times: A model study

We study the "color dynamics" of a hard-disk fluid confined in an annulus, as well as the corresponding hard-sphere system in three dimensions, using event-driven simulation in order to explore the effect of confinement and self-crowding on the search for targets. We compute the mean first-passage times (MFPTs) of red particles transiting from the outer to the inner boundary as well as those of blue particles passing from the inner to the outer boundary for different packing fractions and geometries. In the steady state the reaction rate, defined as the rate of collision of red particles with the inner boundary, is inversely proportional to the sum of the MFPTs. The reaction rate is wall mediated (ballistic) at low densities and diffusion controlled at higher densities and displays a maximum at intermediate densities. At moderate to high densities, the presence of layering has a strong influence on the search process. The numerical results for the reaction rate and MFPTs are compared with a ballistic model at low densities and a Smoluchowski approach with uniform diffusivities at higher densities. We discuss the reasons for the limited validity of the theoretical approaches. The maximum in the reaction rate is qualitatively well rendered by a Bosanquet-like approach that interpolates between the two regimes. Finally, we compute the position-dependent diffusivity from the MFPTs and observe that it is out of phase with the radial density.

Long-term dynamics of multisite phosphorylation

A systematic framework for exploring the long-term dynamics of a reaction network is applied to a minimal model of ERK regulation that distinguishes both monophosphorylated forms and allows for nonzero enzyme processivity. Bistability and oscillations can be observed at high levels of processivity.

Multisite phosphorylation cycles are ubiquitous in cell regulation systems and are studied at multiple levels of complexity, from molecules to organisms, with the ultimate goal of establishing predictive understanding of the effects of genetic and pharmacological perturbations of protein phosphorylation in vivo. Achieving this goal is essentially impossible without mathematical models, which provide a systematic framework for exploring dynamic interactions of multiple network components. Most of the models studied to date do not discriminate between the distinct partially phosphorylated forms and focus on two limiting reaction regimes, distributive and processive, which differ in the number of enzyme–substrate binding events needed for complete phosphorylation or dephosphorylation. Here we use a minimal model of extracellular signal-related kinase regulation to explore the dynamics of a reaction network that includes all essential phosphorylation forms and arbitrary levels of reaction processivity. In addition to bistability, which has been studied extensively in distributive mechanisms, this network can generate periodic oscillations. Both bistability and oscillations can be realized at high levels of reaction processivity. Our work provides a general framework for systematic analysis of dynamics in multisite phosphorylation systems.

Mixed mechanisms of multi-site phosphorylation

Multi-site phosphorylation is ubiquitous in cell biology and has been widely studied experimentally and theoretically. The underlying chemical modification mechanisms are typically assumed to be distributive or processive. In this paper, we study the behaviour of mixed mechanisms that can arise either because phosphorylation and dephosphorylation involve different mechanisms or because phosphorylation and/or dephosphorylation can occur through a combination of mechanisms. We examine a hierarchy of models to assess chemical information processing through different mixed mechanisms, using simulations, bifurcation analysis and analytical work. We demonstrate how mixed mechanisms can show important and unintuitive differences from pure distributive and processive mechanisms, in some cases resulting in monostable behaviour with simple dose-response behaviour, while in other cases generating new behaviour-like oscillations. Our results also suggest patterns of information processing that are relevant as the number of modification sites increases. Overall, our work creates a framework to examine information processing arising from complexities of multi-site modification mechanisms and their impact on signal transduction.

Context-specific flow through the MEK/ERK module produces cell- and ligand-specific patterns of ERK single and double phosphorylation

The same pathway, such as the mitogen-activated protein kinase (MAPK) pathway, can produce different cellular responses, depending on stimulus or cell type. We examined the phosphorylation dynamics of the MAPK kinase MEK and its targets extracellular signal-regulated kinase 1 and 2 (ERK1/2) in primary hepatocytes and the transformed keratinocyte cell line HaCaT A5 exposed to either hepatocyte growth factor or interleukin-6. By combining quantitative mass spectrometry with dynamic modeling, we elucidated network structures for the reversible threonine and tyrosine phosphorylation of ERK in both cell types. In addition to differences in the phosphorylation and dephosphorylation reactions, the HaCaT network model required two feedback mechanisms, which, as the experimental data suggested, involved the induction of the dual-specificity phosphatase DUSP6 and the scaffold paxillin. We assayed and modeled the accumulation of the double-phosphorylated and active form of ERK1/2, as well as the dynamics of the changes in the monophosphorylated forms of ERK1/2. Modeling the differences in the dynamics of the changes in the distributions of the phosphorylated forms of ERK1/2 suggested that different amounts of MEK activity triggered context-specific responses, with primary hepatocytes favoring the formation of double-phosphorylated ERK1/2 and HaCaT A5 cells that produce both the threonine-phosphorylated and the double-phosphorylated form. These differences in phosphorylation distributions explained the threshold, sensitivity, and saturation of the ERK response. We extended the findings of differential ERK phosphorylation profiles to five additional cultured cell systems and matched liver tumor and normal tissue, which revealed context-specific patterns of the various forms of phosphorylated ERK.

The robustness of proofreading to crowding-induced pseudo-processivity in the MAPK pathway

Double phosphorylation of protein kinases is a common feature of signaling cascades. This motif may reduce cross-talk between signaling pathways because the second phosphorylation site allows for proofreading, especially when phosphorylation is distributive rather than processive. Recent studies suggest that phosphorylation can be pseudo-processive in the crowded cellular environment, since rebinding after the first phosphorylation is enhanced by slow diffusion. Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive behavior becomes possible. However, this loss of specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e., when the system is necessarily distributive. Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself. We also show that proofreading can remain effective when the intended signaling pathway exhibits high levels of rebinding-induced pseudo-processivity, unlike other proposed advantages of the dual phosphorylation motif.

Influence of diffusion on the kinetics of multisite phosphorylation

When an enzyme modifies multiple sites on a substrate, the influence of the relative diffusive motion of the reactants cannot be described by simply altering the rate constants in the rate equations of chemical kinetics. We have recently shown that, even as a first approximation, new transitions between the appropriate species must also be introduced. The physical reason for this is that a kinase, after phosphorylating one site, can rebind and modify another site instead of diffusing away. The corresponding new rate constants depend on the capture or rebinding probabilities that an enzyme-substrate pair, which is formed after dissociation from one site, reacts at the other site rather than diffusing apart. Here we generalize our previous work to describe both random and sequential phosphorylation by considering inequivalent modification sites. In addition, anisotropic reactive sites (instead of uniformly reactive spheres) are explicitly treated by using localized sink and source terms in the reaction-diffusion equations for the enzyme-substrate pair distribution function. Finally, we show that our results can be rederived using a phenomenological approach based on introducing transient encounter complexes into the standard kinetic scheme and then eliminating them using the steady-state approximation.

Parameter-free methods distinguish Wnt pathway models and guide design of experiments

The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.

Bioinformatics in protein kinases regulatory network and drug discovery

Protein kinases have been implicated in a number of diseases, where kinases participate many aspects that control cell growth, movement and death. The deregulated kinase activities and the knowledge of these disorders are of great clinical interest of drug discovery. The most critical issue is the development of safe and efficient disease diagnosis and treatment for less cost and in less time. It is critical to develop innovative approaches that aim at the root cause of a disease, not just its symptoms. Bioinformatics including genetic, genomic, mathematics and computational technologies, has become the most promising option for effective drug discovery, and has showed its potential in early stage of drug-target identification and target validation. It is essential that these aspects are understood and integrated into new methods used in drug discovery for diseases arisen from deregulated kinase activity. This article reviews bioinformatics techniques for protein kinase data management and analysis, kinase pathways and drug targets and describes their potential application in pharma ceutical industry.

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.

Sensitive targeted quantification of ERK phosphorylation dynamics and stoichiometry in human cells without affinity enrichment

Targeted mass spectrometry is a promising technology for site-specific quantification of posttranslational modifications. However, a major constraint is the limited sensitivity for quantifying low-abundance PTMs, requiring the use of affinity reagents for enrichment. Herein, we demonstrate the direct site-specific quantification of ERK phosphorylation isoforms (pT, pY, pTpY) and their relative stoichiometry using a sensitive targeted MS approach termed high-pressure, high-resolution separations with intelligent selection, and multiplexing (PRISM). PRISM provides effective enrichment of target peptides into a given fraction from complex mixture, followed by selected reaction monitoring quantification. Direct quantification of ERK phosphorylation in human mammary epithelial cells (HMEC) was demonstrated from as little as 25 μg tryptic peptides from whole cell lysates. Compared to immobilized metal-ion affinity chromatography, PRISM provided ∼10-fold higher signal intensities, presumably due to the better peptide recovery of PRISM. This approach was applied to quantify ERK phosphorylation dynamics in HMEC treated by different doses of epidermal growth factor at both the peak activation (10 min) and steady state (2 h). The maximal ERK activation was observed with 0.3 and 3 ng/mL doses for 10 min and 2 h time points, respectively. The dose-response profiles of individual phosphorylated isoforms showed that singly phosphorylated pT-ERK never increases significantly, while the increase of pY-ERK paralleled that of pTpY-ERK. This data supports for a processive, rather than distributed model of ERK phosphorylation. The PRISM-SRM quantification of protein phosphorylation illustrates the potential for simultaneous quantification of multiple PTMs.

What macromolecular crowding can do to a protein

The intracellular environment represents an extremely crowded milieu, with a limited amount of free water and an almost complete lack of unoccupied space. Obviously, slightly salted aqueous solutions containing low concentrations of a biomolecule of interest are too simplistic to mimic the “real life” situation, where the biomolecule of interest scrambles and wades through the tightly packed crowd. In laboratory practice, such macromolecular crowding is typically mimicked by concentrated solutions of various polymers that serve as model “crowding agents”. Studies under these conditions revealed that macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, protein-protein interactions, protein-nucleic acid interactions, and pathological aggregation. The goal of this review is to systematically analyze currently available experimental data on the variety of effects of macromolecular crowding on a protein molecule. The review covers more than 320 papers and therefore represents one of the most comprehensive compendia of the current knowledge in this exciting area.

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.

Importance of crowding in signaling, genetic, and metabolic networks

It is now well established that the cell is a highly crowded environment. Yet, the effects of crowding on the dynamics of signaling pathways, gene regulation networks, and metabolic networks are still largely unknown. Crowding can alter both molecular diffusion and the equilibria of biomolecular reactions. In this chapter, we first discuss how diffusion can affect biochemical networks. Diffusion of transcription factors can increase noise in gene expression, while diffusion of proteins between intracellular compartments or between cells can reduce concentration fluctuations. In push-pull networks diffusion can impede information transmission, while in multisite protein modification networks diffusion can qualitatively change the macroscopic response of the system, such as the loss or emergence of bistability. Moreover, diffusion can directly change the metabolic flux. We describe how crowding affects diffusion, and thus how all these phenomena are influenced by crowding. Yet, a potentially more important effect of crowding on biochemical networks is mediated via the shift in the equilibria of bimolecular reactions, and we provide computational evidence that supports this idea. Finally, we discuss how the effects of crowding can be incorporated in models of biochemical networks.

Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis

The simplest way to describe the influence of the relative diffusion of the reactants on the time course of bimolecular reactions is to modify or renormalize the phenomenological rate constants that enter into the rate equations of conventional chemical kinetics. However, for macromolecules with multiple inequivalent reactive sites, this is no longer sufficient, even in the low concentration limit. The physical reason is that an enzyme (or a ligand) that has just modified (or dissociated from) one site can bind to a neighboring site rather than diffuse away. This process is not described by the conventional chemical kinetics, which is only valid in the limit that diffusion is fast compared with reaction. Using an exactly solvable many-particle reaction-diffusion model, we show that the influence of diffusion on the kinetics of multisite binding and catalysis can be accounted for by not only scaling the rates, but also by introducing new connections into the kinetic scheme. The rate constants that describe these new transitions or reaction channels turn out to have a transparent physical interpretation: The chemical rates are scaled by the appropriate probabilities that a pair of reactants, which are initially in contact, bind rather than diffuse apart. The theory is illustrated by application to phosphorylation of a multisite substrate.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.