Multisite phosphorylation of CDK target proteins provides the requisite nonlinearity for cell cycle modeling using elementary reaction mechanisms.Stochastic simulations, based on Gillespie's algorithm and using realistic numbers of protein and mRNA molecules, compare favorably with single-cell measurements in budding yeast.The role of transcription–translation coupling is critical in the robust operation of protein regulatory networks in yeast cells.

Variability within isogenic T cell populations yields heterogeneous ‘local’ signaling responses to shared antigenic stimuli, but responding clones may communicate ‘global’ antigen load through paracrine messengers, such as cytokines. Such coordination of individual cell responses within multicellular populations is critical for accurate collective reactions to shared environmental cues. However, cytokine production may saturate as a function of antigen input, or be dominated by the precursor frequency of antigen-specific T cells. Surprisingly, we found that T cells scale their collective output of IL-2 to total antigen input over a large dynamic range, independently of population size. Through experimental quantitation and computational modeling, we demonstrate that this scaling is enforced by an inhibitory cross-talk between antigen and IL-2 signaling, and a nonlinear acceleration of IL-2 secretion per cell. Our study reveals how time-integration of these regulatory loops within individual cell signaling generates scaled collective responses and can be leveraged for immune monitoring.DOI: http://dx.doi.org/10.7554/eLife.01944.001

The activity of a protein can be reversibly modulated by post-translational, covalent modifications, such as phosphorylation and dephosphorylation. In many cases, the modulated protein may be phosphorylated by the same kinase on many different amino acid residues. Such multisite phosphorylations may occur progressively (during a single binding event of kinase to substrate) or distributively (the kinase dissociates from its substrate after each phosphorylation reaction). If a protein is phosphorylated by a distributive multisite mechanism, then the net activity of a population of these protein molecules can be a highly nonlinear function of the ratio of activities of the kinase and phosphatase enzymes. If the multiply phosphorylated protein is embedded in a positive feedback loop with its kinase and/or phosphatase, then the network may exhibit robust bistable behavior. Using numerical simulations and bifurcation theory, we study the properties of a particular bistable reaction network motivated by the antagonistic relationship between cyclin-dependent kinase and its multiply phosphorylated target, Cdh1, which is involved in the degradation of cyclin molecules. We characterize the bistable switch in terms of (i) the mechanism of distributive phosphorylation (ordered or disordered), (ii) the number of phosphorylation sites on the target protein, (iii) the effect of phosphorylation on the target protein (abrupt or progressive inactivation), and (iv) the effects of stochastic fluctuations in small cells with limited numbers of kinase, phosphatase and target proteins.

Many physiological characteristics of living cells are regulated by protein interaction networks. Because the total numbers of these protein species can be small, molecular noise can have significant effects on the dynamical properties of a regulatory network. Computing these stochastic effects is made difficult by the large timescale separations typical of protein interactions (e.g., complex formation may occur in fractions of a second, whereas catalytic conversions may take minutes). Exact stochastic simulation may be very inefficient under these circumstances, and methods for speeding up the simulation without sacrificing accuracy have been widely studied. We show that the "total quasi-steady-state approximation" for enzyme-catalyzed reactions provides a useful framework for efficient and accurate stochastic simulations. The method is applied to three examples: a simple enzyme-catalyzed reaction where enzyme and substrate have comparable abundances, a Goldbeter-Koshland switch, where a kinase and phosphatase regulate the phosphorylation state of a common substrate, and coupled Goldbeter-Koshland switches that exhibit bistability. Simulations based on the total quasi-steady-state approximation accurately capture the steady-state probability distributions of all components of these reaction networks. In many respects, the approximation also faithfully reproduces time-dependent aspects of the fluctuations. The method is accurate even under conditions of poor timescale separation.

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a systemreservoir nonlinear coupling model we present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Markovian Langevin description and an associated Fokker-Planck equation in position space in the overdamped limit. We examine the thermodynamic consistency and explore the possibility of observing a quantum current, a generic quantum effect, as a consequence of this state-dependent diffusion similar to one proposed by Büttiker [Z. Phys. B 68, 161 (1987)] in a classical context several years ago.