Control of Spatially Heterogeneous and Time-Varying Cellular Reaction Networks: A New Summation Law

A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control Analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient, cannot be applied to spatially separated protein networks. The present paper unravels the principles that govern the control over the fluxes and intermediate concentrations in spatially heterogeneous reaction networks. Our main results are two types of the control summation theorems. The first type is a non-trivial generalization of the classical theorems to systems with spatially and temporally varying concentrations. In this generalization, the process of diffusion, which enters as the result of spatial concentration gradients, plays a role similar to other processes such as chemical reactions and membrane transport. The second summation theorem is completely novel. It states that the control by the membrane transport, the diffusion control coefficient multiplied by two, and a newly introduced control coefficient associated with changes in the spatial size of a system (e.g., cell), all add up to one and zero for the control over flux and concentration. Using a simple example of a kinase/phosphatase system in a spherical cell, we speculate that unless active mechanisms of intracellular transport are involved, the threshold cell size is limited by the diffusion control, when it is beginning to exceed the spatial control coefficient significantly.Comment: 19 pages, AMS-LaTeX, 6 eps figures included with geompsfi.st

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

Signalling ballet in space and time.

Although we have amassed extensive catalogues of signalling network components, our understanding of the spatiotemporal control of emergent network structures has lagged behind. Dynamic behaviour is starting to be explored throughout the genome, but analysis of spatial behaviours is still confined to individual proteins. The challenge is to reveal how cells integrate temporal and spatial information to determine specific biological functions. Key findings are the discovery of molecular signalling machines such as Ras nanoclusters, spatial activity gradients and flexible network circuitries that involve transcriptional feedback. They reveal design principles of spatiotemporal organization that are crucial for network function and cell fate decisions

Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades

Mitogen-activated protein kinase (MAPK) cascades can operate as bistable switches residing in either of two different stable states. MAPK cascades are often embedded in positive feedback loops, which are considered to be a prerequisite for bistable behavior. Here we demonstrate that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation. Importantly, the reported kinetic properties of the kinase (MEK) and phosphatase (MKP3) of extracellular signal–regulated kinase (ERK) fulfill the essential requirements for generating a bistable switch at a single MAPK cascade level. Likewise, a cycle where multisite phosphorylations are performed by different kinases, but dephosphorylation reactions are catalyzed by the same phosphatase, can also exhibit bistability and hysteresis. Hence, bistability induced by multisite covalent modification may be a widespread mechanism of the control of protein activity

Polyubiquitin chain assembly and organization determine the dynamics of protein activation and degradation

Protein degradation via ubiquitination is a major proteolytic mechanism in cells. Once a protein is destined for degradation, it is tagged by multiple ubiquitin (Ub) molecules. The synthesized polyubiquitin chains can be recognized by the 26S proteosome where proteins are degraded. These chains form through multiple ubiquitination cycles that are similar to multi-site phosphorylation cycles. As kinases and phosphatases, two opposing enzymes (E3 ligases and deubiquitinases DUBs) catalyze (de)ubiquitination cycles. Although multi-ubiquitination cycles are fundamental mechanisms of controlling protein concentrations within a cell, their dynamics have never been explored. Here, we fill this knowledge gap. We show that under permissive physiological conditions, the formation of polyubiquitin chain of length greater than two and subsequent degradation of the ubiquitinated protein, which is balanced by protein synthesis, can display bistable, switch-like responses. Interestingly, the occurrence of bistability becomes pronounced, as the chain grows, giving rise to “all-or-none” regulation at the protein levels. We give predictions of protein distributions under bistable regime awaiting experimental verification. Importantly, we show for the first time that sustained oscillations can robustly arise in the process of formation of ubiquitin chain, largely due to the degradation of the target protein. This new feature is opposite to the properties of multi-site phosphorylation cycles, which are incapable of generating oscillation if the total abundance of interconverted protein forms is conserved. We derive structural and kinetic constraints for the emergence of oscillations, indicating that a competition between different substrate forms and the E3 and DUB is critical for oscillation. Our work provides the first detailed elucidation of the dynamical features brought about by different molecular setups of the polyubiquitin chain assembly process responsible for protein degradation

Domain-Oriented Reduction of Rule-Based Network Models

The coupling of membrane-bound receptors to transcriptional regulators and other effector functions is mediated by multi-domain proteins that form complex assemblies. The modularity of protein interactions lends itself to a rule-based description, in which species and reactions are generated by rules that encode the necessary context for an interaction to occur, but also can produce a combinatorial explosion in the number of chemical species that make up the signaling network. We have shown previously that exact network reduction can be achieved using hierarchical control relationships between sites/domains on proteins to dissect multi-domain proteins into sets of non-interacting sites, allowing the replacement of each “full” (progenitor) protein with a set of derived auxiliary (offspring) proteins. The description of a network in terms of auxiliary proteins that have fewer sites than progenitor proteins often greatly reduces network size. We describe here a method for automating domain-oriented model reduction and its implementation as a module in the BioNetGen modeling package. It takes as input a standard BioNetGen model and automatically performs the following steps: 1) detecting the hierarchical control relationships between sites; 2) building up the auxiliary proteins; 3) generating a raw reduced model; and 4) cleaning up the raw model to provide the correct mass balance for each chemical species in the reduced network. We tested the performance of this module on models representing portions of growth factor receptor and immunoreceptor-mediated signaling networks, and confirmed its ability to reduce the model size and simulation cost by at least one or two orders of magnitude. Limitations of the current algorithm include the inability to reduce models based on implicit site dependencies or heterodimerization, and loss of accuracy when dynamics are computed stochastically

Trading the micro-world of combinatorial complexity for the macro-world of protein interaction domains

Membrane receptors and proteins involved in signal transduction display numerous binding domains and operate as molecular scaffolds generating a variety of parallel reactions and protein complexes. The resulting combinatorial explosion of the number of feasible chemical species and, hence, different states of a network greatly impedes mechanistic modeling of signaling systems. Here we present novel general principles and identify kinetic requirements that allow us to replace a mechanistic picture of all possible micro-states and transitions by a macro-description of states of separate binding sites of network proteins. This domain-oriented approach dramatically reduces computational models of cellular signaling networks by dissecting mechanistic trajectories into the dynamics of macro- and meso-variables. We specify the conditions when the temporal dynamics of micro-states can be exactly or approximately expressed in terms of the product of the relative concentrations of separate domains. We prove that our macro-modeling approach equally applies to signaling systems with low population levels, analyzed by stochastic rather than deterministic equations. Thus, our results greatly facilitate quantitative analysis and computational modeling of multi-protein signaling networks