Kinetic proofreading model

Autoactivation of small GTPases by the GEF-effector positive feedback modules

Small GTPases are organizers of a plethora of cellular processes. The time and place of their activation are tightly controlled by the localization and activation of their regulators, guanine-nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs). Remarkably, in some systems, the upstream regulators of GTPases are also found downstream of their activity. Resulting feedback loops can generate complex spatiotemporal dynamics of GTPases with important functional consequences. Here we discuss the concept of positive autoregulation of small GTPases by the GEF-effector feedback modules and survey recent developments in this exciting area of cell biology.

T-Cell Mechanobiology: Force Sensation, Potentiation, and Translation

A T cell is a sensitive self-referential mechanical sensor. Mechanical forces influence the recognition, activation, differentiation, and function throughout the lifetime of a T cell. T cells constantly perceive and respond to physical stimuli through their surface receptors, cytoskeleton, and subcellular structures. Surface receptors receive physical cues in the form of forces generated through receptor-ligand binding events, which are dynamically regulated by contact tension, shear stress, and substrate rigidity. The resulting mechanotransduction not only influences T-cell recognition and signaling but also possibly modulates cell metabolism and gene expression. Moreover, forces also dynamically regulate the deformation, organization, and translocation of cytoskeleton and subcellular structures, leading to changes in T-cell mobility, migration, and infiltration. However, the roles and mechanisms of how mechanical forces modulate T-cell recognition, signaling, metabolism, and gene expression, are largely unknown and underappreciated. Here, we review recent technological and scientific advances in T-cell mechanobiology, discuss possible roles and mechanisms of T-cell mechanotransduction, and propose new research directions of this emerging field in health and disease.

Simple biochemical networks allow accurate sensing of multiple ligands with a single receptor

Cells use surface receptors to estimate concentrations of external ligands. Limits on the accuracy of such estimations have been well studied for pairs of ligand and receptor species. However, the environment typically contains many ligands, which can bind to the same receptors with different affinities, resulting in cross-talk. In traditional rate models, such cross-talk prevents accurate inference of concentrations of individual ligands. In contrast, here we show that knowing the precise timing sequence of stochastic binding and unbinding events allows one receptor to provide information about multiple ligands simultaneously and with a high accuracy. We show that such high-accuracy estimation of multiple concentrations can be realized with simple structural modifications of the familiar kinetic proofreading biochemical network diagram. We give two specific examples of such modifications. We argue that structural and functional features of real cellular biochemical sensory networks in immune cells, such as feedforward and feedback loops or ligand antagonism, sometimes can be understood as solutions to the accurate multi-ligand estimation problem.

Cells live in chemically complex environments with many different chemical ligands around them. Can cells estimate concentrations of more ligands than they have receptor types? In this paper, we show that, surprisingly, the answer is “yes”, and the estimation can be implemented with simple biochemical components already present in many cells. Therefore, cells may “know” a lot more about their environment and thus may be able to implement more complex and accurate response strategies than was previously thought.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

A large number of receptors may reduce cellular response time variation

Cells often have tens of thousands of receptors, even though only a few activated receptors can trigger full cellular responses. Reasons for the overabundance of receptors remain unclear. We suggest that, under certain conditions, the large number of receptors can result in a competition among receptors to be the first to activate the cell. The competition decreases the variability of the time to cellular activation, and hence results in a more synchronous activation of cells. We argue that, in simple models, this variability reduction does not necessarily interfere with the receptor specificity to ligands achieved by the kinetic proofreading mechanism. Thus cells can be activated accurately in time and specifically to certain signals. We predict the minimum number of receptors needed to reduce the coefficient of variation for the time to activation following binding of a specific ligand. Furthermore, we predict the maximum number of receptors so that the kinetic proofreading mechanism still can improve the specificity of the activation. These predictions fall in line with experimentally reported receptor numbers for multiple systems.

Population-expression models of immune response

The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an initial naive phenotype to an effector phenotype which controls the pathogen, and subsequently to a memory phenotype that is maintained and responsible for long-term protection. The expansion and the differentiation have been considered largely independently. Changes in cell populations are typically described using ecologically based ordinary differential equation models. In contrast, differentiation of single cells is studied within systems biology and is frequently modeled by considering changes in gene and protein expression in individual cells. Recent advances in experimental systems biology make available for the first time data to allow the coupling of population and high dimensional expression data of immune cells during infections. Here we describe and develop population-expression models which integrate these two processes into systems biology on the multicellular level. When translated into mathematical equations, these models result in non-conservative, non-local advection-diffusion equations. We describe situations where the population-expression approach can make correct inference from data while previous modeling approaches based on common simplifying assumptions would fail. We also explore how model reduction techniques can be used to build population-expression models, minimizing the complexity of the model while keeping the essential features of the system. While we consider problems in immunology in this paper, we expect population-expression models to be more broadly applicable.

Stochastic ensembles, conformationally adaptive teamwork, and enzymatic detoxification

It has been appreciated for a long time that enzymes exist as conformational ensembles throughout multiple stages of the reactions they catalyze, but there is renewed interest in the functional implications. The energy landscape that results from conformationlly diverse poteins is a complex surface with an energetic topography in multiple dimensions, even at the transition state(s) leading to product formation, and this represents a new paradigm. At the same time there has been renewed interest in conformational ensembles, a new paradigm concerning enzyme function has emerged, wherein catalytic promiscuity has clear biological advantages in some cases. "Useful", or biologically functional, promiscuity or the related behavior of "multifunctionality" can be found in the immune system, enzymatic detoxification, signal transduction, and the evolution of new function from an existing pool of folded protein scaffolds. Experimental evidence supports the widely held assumption that conformational heterogeneity promotes functional promiscuity. The common link between these coevolving paradigms is the inherent structural plasticity and conformational dynamics of proteins that, on one hand, lead to complex but evolutionarily selected energy landscapes and, on the other hand, promote functional promiscuity. Here we consider a logical extension of the overlap between these two nascent paradigms: functionally promiscuous and multifunctional enzymes such as detoxification enzymes are expected to have an ensemble landscape with more states accessible on multiple time scales than substrate specific enzymes. Two attributes of detoxification enzymes become important in the context of conformational ensembles: these enzymes metabolize multiple substrates, often in substrate mixtures, and they can form multiple products from a single substrate. These properties, combined with complex conformational landscapes, lead to the possibility of interesting time-dependent, or emergent, properties. Here we demonstrate these properties with kinetic simulations of nonequilibrium steady state (NESS) behavior resulting from energy landscapes expected for detoxification enzymes. Analogous scenarios with other promiscuous enzymes may be worthy of consideration.

Activation or tolerance of natural killer cells is modulated by ligand quality in a nonmonotonic manner

Natural killer (NK) cells extend important immune resistance in vertebrates by lysing infected and tumor cells. A fine balance between opposing signals generated by a diverse set of stimulatory and inhibitory NK-cell receptors determines the fate of target cells interacting with the NK cells. We have developed a mathematical model involving membrane proximal initial signaling events that provides novel mechanistic insights into how activation of NK cells is modulated by the half-life of receptor-ligand interaction and ligand concentrations. We show that strong stimulatory ligands produce digital activation, whereas weaker stimulatory ligands can mediate inhibition by strengthening the signals generated by inhibitory ligands, as indicated in experiments in knockout mice. We find under certain conditions, counterintuitively, inhibitory receptors can help mediate activation instead of inhibition. Mechanistic insights gained from NK-cell signaling can facilitate understanding of complex signaling responses that occur due to cross talk between dueling signaling pathways in other cell types.

A detailed mathematical model predicts that serial engagement of IgE-Fc epsilon RI complexes can enhance Syk activation in mast cells

The term serial engagement was introduced to describe the ability of a single peptide, bound to a MHC molecule, to sequentially interact with TCRs within the contact region between a T cell and an APC. In addition to ligands on surfaces, soluble multivalent ligands can serially engage cell surface receptors with sites on the ligand, binding and dissociating from receptors many times before all ligand sites become free and the ligand leaves the surface. To evaluate the role of serial engagement in Syk activation, we use a detailed mathematical model of the initial signaling cascade that is triggered when FcepsilonRI is aggregated on mast cells by multivalent Ags. Although serial engagement is not required for mast cell signaling, it can influence the recruitment of Syk to the receptor and subsequent Syk phosphorylation. Simulating the response of mast cells to ligands that serially engage receptors at different rates shows that increasing the rate of serial engagement by increasing the rate of dissociation of the ligand-receptor bond decreases Syk phosphorylation. Increasing serial engagement by increasing the rate at which receptors are cross-linked (for example by increasing the forward rate constant for cross-linking or increasing the valence of the ligand) increases Syk phosphorylation. When serial engagement enhances Syk phosphorylation, it does so by partially reversing the effects of kinetic proofreading. Serial engagement rapidly returns receptors that have dissociated from aggregates to new aggregates before the receptors have fully returned to their basal state.

The SCHOOL of nature: I. Transmembrane signaling

Receptor-mediated transmembrane signaling plays an important role in health and disease. Recent significant advances in our understanding of the molecular mechanisms linking ligand binding to receptor activation revealed previously unrecognized striking similarities in the basic structural principles of function of numerous cell surface receptors. In this work, I demonstrate that the Signaling Chain Homooligomerization (SCHOOL)-based mechanism represents a general biological mechanism of transmembrane signal transduction mediated by a variety of functionally unrelated single- and multichain activating receptors. within the SCHOOL platform, ligand binding-induced receptor clustering is translated across the membrane into protein oligomerization in cytoplasmic milieu. This platform resolves a long-standing puzzle in transmembrane signal transduction and reveals the major driving forces coupling recognition and activation functions at the level of protein-protein interactions-biochemical processes that can be influenced and controlled. The basic principles of transmembrane signaling learned from the SCHOOL model can be used in different fields of immunology, virology, molecular and cell biology and others to describe, explain and predict various phenomena and processes mediated by a variety of functionally diverse and unrelated receptors. Beyond providing novel perspectives for fundamental research, the platform opens new avenues for drug discovery and development.