Analysis of localized cAMP perturbations within a tissue reveal the effects of a local, dynamic gap junction state on ERK signaling.

Beyond natural stimuli such as growth factors and stresses, the ability to experimentally modulate at will the levels or activity of specific intracellular signaling molecule(s) in specified cells within a tissue can be a powerful tool for uncovering new regulation and tissue behaviors. Here we perturb the levels of cAMP within specific cells of an epithelial monolayer to probe the time-dynamic behavior of cell-cell communication protocols implemented by the cAMP/PKA pathway and its coupling to the ERK pathway. The time-dependent ERK responses we observe in the perturbed cells for spatially uniform cAMP perturbations (all cells) can be very different from those due to spatially localized perturbations (a few cells). Through a combination of pharmacological and genetic perturbations, signal analysis, and computational modeling, we infer how intracellular regulation and regulated cell-cell coupling each impact the intracellular ERK response in single cells. Our approach reveals how a dynamic gap junction state helps sculpt the intracellular ERK response over time in locally perturbed cells.

Optogenetic Control Reveals Differential Promoter Interpretation of Transcription Factor Nuclear Translocation Dynamics.

Gene expression is thought to be affected not only by the concentration of transcription factors (TFs) but also the dynamics of their nuclear translocation. Testing this hypothesis requires direct control of TF dynamics. Here, we engineer CLASP, an optogenetic tool for rapid and tunable translocation of a TF of interest. Using CLASP fused to Crz1, we observe that, for the same integrated concentration of nuclear TF over time, changing input dynamics changes target gene expression: pulsatile inputs yield higher expression than continuous inputs, or vice versa, depending on the target gene. Computational modeling reveals that a dose-response saturating at low TF input can yield higher gene expression for pulsatile versus continuous input, and that multi-state promoter activation can yield the opposite behavior. Our integrated tool development and modeling approach characterize promoter responses to Crz1 nuclear translocation dynamics, extracting quantitative features that may help explain the differential expression of target genes.

Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules.

The capability to engineer de novo feedback control with biological molecules is ushering in an era of robust functionality for many applications in biotechnology and medicine. To fulfill their potential, these control strategies need to be generalizable, modular, and operationally predictable. Proportional-integral-derivative (PID) control fulfills this role for technological systems. Integral feedback control allows a system to return to an invariant steady-state value after step disturbances. Proportional and derivative feedback control used with integral control modulate the dynamics of the return to steady state following perturbation. Recently, a biomolecular implementation of integral control was proposed based on an antithetic motif in which two molecules interact stoichiometrically to annihilate each other's function. In this work, we report how proportional and derivative implementations can be layered on top of this integral architecture to achieve a biochemical PID control design. We investigate computationally and analytically their properties and ability to improve performance.

The Impact of Different Sources of Fluctuations on Mutual Information in Biochemical Networks.

Stochastic fluctuations in signaling and gene expression limit the ability of cells to sense the state of their environment, transfer this information along cellular pathways, and respond to it with high precision. Mutual information is now often used to quantify the fidelity with which information is transmitted along a cellular pathway. Mutual information calculations from experimental data have mostly generated low values, suggesting that cells might have relatively low signal transmission fidelity. In this work, we demonstrate that mutual information calculations might be artificially lowered by cell-to-cell variability in both initial conditions and slowly fluctuating global factors across the population. We carry out our analysis computationally using a simple signaling pathway and demonstrate that in the presence of slow global fluctuations, every cell might have its own high information transmission capacity but that population averaging underestimates this value. We also construct a simple synthetic transcriptional network and demonstrate using experimental measurements coupled to computational modeling that its operation is dominated by slow global variability, and hence that its mutual information is underestimated by a population averaged calculation.

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.

Imaging of kiss-and-run exocytosis of surface receptors in neuronal cultures.

Transmembrane proteins are continuously shuttled from the endosomal compartment to the neuronal plasma membrane by highly regulated and complex trafficking steps. These events are involved in many homeostatic and physiological processes such as neuronal growth, signaling, learning and memory among others. We have previously shown that endosomal exocytosis of the B2 adrenergic receptor (B2AR) and the GluR1-containing AMPA receptor to the neuronal plasma membrane is mediated by two different types of vesicular fusion. A rapid type of exocytosis in which receptors are delivered to the plasma membrane in a single kinetic step, and a persistent mode in which receptors remain clustered at the insertion site for a variable period of time before delivery to the cell surface. Here, by comparing the exocytosis of multiple receptors in dissociated hippocampal and striatal cultures, we show that persistent events are a general mechanism of vesicular delivery. Persistent events were only observed after 10 days in vitro, and their frequency increased with use of the calcium ionophore A23187 and with depolarization induced by KCl. Finally, we determined that vesicles producing persistent events remain at the plasma membrane, closing and reopening their fusion pore for a consecutive release of cargo in a mechanism reminiscent of synaptic kiss-and-run. These results indicate that the delivery of transmembrane receptors to the cell surface can be dynamically regulated by kiss-and-run exocytosis.

Conformational biosensors reveal GPCR signalling from endosomes.

A long-held tenet of molecular pharmacology is that canonical signal transduction mediated by G-protein-coupled receptor (GPCR) coupling to heterotrimeric G proteins is confined to the plasma membrane. Evidence supporting this traditional view is based on analytical methods that provide limited or no subcellular resolution. It has been subsequently proposed that signalling by internalized GPCRs is restricted to G-protein-independent mechanisms such as scaffolding by arrestins, or GPCR activation elicits a discrete form of persistent G protein signalling, or that internalized GPCRs can indeed contribute to the acute G-protein-mediated response. Evidence supporting these various latter hypotheses is indirect or subject to alternative interpretation, and it remains unknown if endosome-localized GPCRs are even present in an active form. Here we describe the application of conformation-specific single-domain antibodies (nanobodies) to directly probe activation of the ß2-adrenoceptor, a prototypical GPCR, and its cognate G protein, Gs (ref. 12), in living mammalian cells. We show that the adrenergic agonist isoprenaline promotes receptor and G protein activation in the plasma membrane as expected, but also in the early endosome membrane, and that internalized receptors contribute to the overall cellular cyclic AMP response within several minutes after agonist application. These findings provide direct support for the hypothesis that canonical GPCR signalling occurs from endosomes as well as the plasma membrane, and suggest a versatile strategy for probing dynamic conformational change in vivo.

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.