Using dynamic noise propagation to infer causal regulatory relationships in biochemical networks.

Cellular decision making is accomplished by complex networks, the structure of which has traditionally been inferred from mean gene expression data. In addition to mean data, quantitative measures of distributions across a population can be obtained using techniques such as flow cytometry that measure expression in single cells. The resulting distributions, which reflect a population's variability or noise, constitute a potentially rich source of information for network reconstruction. A significant portion of molecular noise in a biological process is propagated from the upstream regulators. This propagated component provides additional information about causal network connections. Here, we devise a procedure in which we exploit equations for dynamic noise propagation in a network under nonsteady state conditions to distinguish between alternate gene regulatory relationships. We test our approach in silico using data obtained from stochastic simulations as well as in vivo using experimental data collected from synthetic circuits constructed in yeast.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions.

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes.

Diffusion of biological molecules on 2D biological membranes can play an important role in the behavior of stochastic biochemical reaction systems. Yet, we still lack a fundamental understanding of circumstances where explicit accounting of the diffusion and spatial coordinates of molecules is necessary. In this work, we illustrate how time-dependent, non-exponential reaction probabilities naturally arise when explicitly accounting for the diffusion of molecules. We use the analytical expression of these probabilities to derive a novel algorithm which, while ignoring the exact position of the molecules, can still accurately capture diffusion effects. We investigate the regions of validity of the algorithm and show that for most parameter regimes, it constitutes an accurate framework for studying these systems. We also document scenarios where large spatial fluctuation effects mandate explicit consideration of all the molecules and their positions. Taken together, our results derive a fundamental understanding of the role of diffusion and spatial fluctuations in these systems. Simultaneously, they provide a general computational methodology for analyzing a broad class of biological networks whose behavior is influenced by diffusion on membranes.

A data-integrated method for analyzing stochastic biochemical networks.

Variability and fluctuations among genetically identical cells under uniform experimental conditions stem from the stochastic nature of biochemical reactions. Understanding network function for endogenous biological systems or designing robust synthetic genetic circuits requires accounting for and analyzing this variability. Stochasticity in biological networks is usually represented using a continuous-time discrete-state Markov formalism, where the chemical master equation (CME) and its kinetic Monte Carlo equivalent, the stochastic simulation algorithm (SSA), are used. These two representations are computationally intractable for many realistic biological problems. Fitting parameters in the context of these stochastic models is particularly challenging and has not been accomplished for any but very simple systems. In this work, we propose that moment equations derived from the CME, when treated appropriately in terms of higher order moment contributions, represent a computationally efficient framework for estimating the kinetic rate constants of stochastic network models and subsequent analysis of their dynamics. To do so, we present a practical data-derived moment closure method for these equations. In contrast to previous work, this method does not rely on any assumptions about the shape of the stochastic distributions or a functional relationship among their moments. We use this method to analyze a stochastic model of a biological oscillator and demonstrate its accuracy through excellent agreement with CME/SSA calculations. By coupling this moment-closure method with a parameter search procedure, we further demonstrate how a model's kinetic parameters can be iteratively determined in order to fit measured distribution data.

Rapid delivery of internalized signaling receptors to the somatodendritic surface by sequence-specific local insertion.

The recycling pathway is a major route for delivering signaling receptors to the somatodendritic plasma membrane. We investigated the cell biological basis for the remarkable selectivity and speed of this process. We focused on the mu-opioid neuropeptide receptor and the beta(2)-adrenergic catecholamine receptor, two seven-transmembrane signaling receptors that traverse the recycling pathway efficiently after ligand-induced endocytosis and localize at steady state throughout the postsynaptic surface. Rapid recycling of each receptor in dissociated neuronal cultures was mediated by a receptor-specific cytoplasmic sorting sequence. Total internal reflection fluorescence microscopy imaging revealed that both sequences drive recycling via discrete vesicular fusion events in the cell body and dendritic shaft. Both sequences promoted recycling via "transient"-type events characterized by nearly immediate lateral spread of receptors after vesicular insertion resembling receptor insertion events observed previously in non-neural cells. The sequences differed in their abilities to produce distinct "persistent"-type events at which inserted receptors lingered for a variable time period before lateral spread. Both types of insertion event generated a uniform distribution of receptors in the somatodendritic plasma membrane when imaged over a 1 min interval, but persistent events uniquely generated a punctate surface distribution over a 10 s interval. These results establish sequence-directed recycling of signaling receptors in CNS neurons and show that this mechanism has the ability to generate receptor-specific patterns of local surface distribution on a timescale overlapping that of rapid physiological signaling.

BiP binding to the ER-stress sensor Ire1 tunes the homeostatic behavior of the unfolded protein response.

The unfolded protein response (UPR) is an intracellular signaling pathway that counteracts variable stresses that impair protein folding in the endoplasmic reticulum (ER). As such, the UPR is thought to be a homeostat that finely tunes ER protein folding capacity and ER abundance according to need. The mechanism by which the ER stress sensor Ire1 is activated by unfolded proteins and the role that the ER chaperone protein BiP plays in Ire1 regulation have remained unclear. Here we show that the UPR matches its output to the magnitude of the stress by regulating the duration of Ire1 signaling. BiP binding to Ire1 serves to desensitize Ire1 to low levels of stress and promotes its deactivation when favorable folding conditions are restored to the ER. We propose that, mechanistically, BiP achieves these functions by sequestering inactive Ire1 molecules, thereby providing a barrier to oligomerization and activation, and a stabilizing interaction that facilitates de-oligomerization and deactivation. Thus BiP binding to or release from Ire1 is not instrumental for switching the UPR on and off as previously posed. By contrast, BiP provides a buffer for inactive Ire1 molecules that ensures an appropriate response to restore protein folding homeostasis to the ER by modulating the sensitivity and dynamics of Ire1 activity.

A rigorous framework for multiscale simulation of stochastic cellular networks.

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-cell variability even in clonal populations. Stochastic biochemical networks are modeled as continuous time discrete state Markov processes whose probability density functions evolve according to a chemical master equation (CME). The CME is not solvable but for the simplest cases, and one has to resort to kinetic Monte Carlo techniques to simulate the stochastic trajectories of the biochemical network under study. A commonly used such algorithm is the stochastic simulation algorithm (SSA). Because it tracks every biochemical reaction that occurs in a given system, the SSA presents computational difficulties especially when there is a vast disparity in the timescales of the reactions or in the number of molecules involved in these reactions. This is common in cellular networks, and many approximation algorithms have evolved to alleviate the computational burdens of the SSA. Here, we present a rigorously derived modified CME framework based on the partition of a biochemically reacting system into restricted and unrestricted reactions. Although this modified CME decomposition is as analytically difficult as the original CME, it can be naturally used to generate a hierarchy of approximations at different levels of accuracy. Most importantly, some previously derived algorithms are demonstrated to be limiting cases of our formulation. We apply our methods to biologically relevant test systems to demonstrate their accuracy and efficiency.