Benjamin Pfeuty

The Combined Effects of Inhibitory and Electrical Synapses in Synchrony

Recent experimental results have shown that GABAergic interneurons in the central nervous system are frequently connected via electrical synapses. Hence, depending on the area or the subpopulation, interneurons interact via inhibitory synapses or electrical synapses alone or via both types of interactions. The theoretical work presented here addresses the significance of these different modes of interactions for the interneuron networks dynamics. We consider the simplest system in which this issue can be investigated in models or in experiments: a pair of neurons, interacting via electrical synapses, inhibitory synapses, or both, and activated by the injection of a noisy external current. Assuming that the couplings and the noise are weak, we derive an analytical expression relating the cross-correlation (CC) of the activity of the two neurons to the phase response function of the neurons. When electrical and inhibitory interactions are not too strong, they combine their effect in a linear manner. In this regime, the effect of electrical and inhibitory interactions when combined can be deduced knowing the effects of each of the interactions separately. As a consequence, depending on intrinsic neuronal proper-ties, electrical and inhibitory synapses may cooperate, both promoting synchrony, or may compete, with one promoting synchrony while the other impedes it. In contrast, for sufficiently strong couplings, the two types of synapses combine in a nonlinear fashion. Remarkably, we find that in this regime, combining electrical synapses with inhibition ampli-fies synchrony, whereas electrical synapses alone would desynchronize the activity of the neurons. We apply our theory to predict how the shape of the CC of two neurons changes as a function of ionic channel conduc-tances, focusing on the effect of persistent sodium conductance, of the firing rate of the neurons and the nature and the strength of their interac-tions. These predictions may be tested using dynamic clamp techniques.

The combination of positive and negative feedback loops confers exquisite flexibility to biochemical switches

A wide range of cellular processes require molecular regulatory pathways to convert a graded signal into a discrete response. One prevalent switching mechanism relies on the coexistence of two stable states (bistability) caused by positive feedback regulations. Intriguingly, positive feedback is often supplemented with negative feedback, raising the question of whether and how these two types of feedback can cooperate to control discrete cellular responses. To address this issue, we formulate a canonical model of a protein-protein interaction network and analyze the dynamics of a prototypical two-component circuit. The appropriate combination of negative and positive feedback loops can bring a bistable circuit close to the oscillatory regime. Notably, sharply activated negative feedback can give rise to a bistable regime wherein two stable fixed points coexist and may collide pairwise with two saddle points. This specific type of bistability is found to allow for separate and flexible control of switch-on and switch-off events, for example (i) to combine fast and reversible transitions, (ii) to enable transient switching responses and (iii) to display tunable noise-induced transition rates. Finally, we discuss the relevance of such bistable switching behavior, and the circuit topologies considered, to specific biological processes such as adaptive metabolic responses, stochastic fate decisions and cell-cycle transitions. Taken together, our results suggest an efficient mechanism by which positive and negative feedback loops cooperate to drive the flexible and multifaceted switching behaviors arising in biological systems.

Underlying principles of cell fate determination during G1 phase of the mammalian cell cycle

Upon their exit from mitosis, mammalian cells enter a G1 phase during which they acutely sense all sorts of environmental stimuli. On the basis of these signals that they first need to decipher and integrate, they decide whether to undergo division, differentiation, senescence or apoptosis. We questioned whether, despite the complexity of the G1 regulatory network, simple organizing principles might be identified that could explain how specific input signals are converted into appropriate cell fates. For this purpose, we formulated a mathematical model of the G1 regulatory network using a simplified description of activities linked to signal transduction, cell growth, cell division and cell death. Bifurcation analysis of the model revealed the existence of multistability between several attractor states corresponding to G0-arrest, G1-arrest, S-phase entry and apoptosis cell fates. We further unravelled interlinked feedback and feedforward loops within the G1 regulatory network that drive the signal-dependent transition between G0 arrest and the other cell fates. Initially, exit from G0 and progression in early G1 entail growth factor-dependent activation of an upstream positive feedback loop that activates the cell-growth machinery. Once ribosome synthesis is restored in G1, a competition develops between a downstream positive feedback loop, which, upon activation, triggers S-phase entry, and stress-activated pathways that promote G1 arrest. If S-phase entry prevails over G1 arrest, cells are sensitized to apoptosis due to stress-induced activation of pro-apoptotic pathways or repression of pro-survival pathways. Thus, the choice between the four possible cell fates in the G1 phase relies on the flexibly interlinked growth-activatory and division-activatory modules, certain components of which have antagonistic effects on pathways involved in driving apoptosis and G1 arrest. The final outcome ultimately depends on the context-dependent coordination between the cell-growth and cell-division processes.

Strategic Cell-Cycle Regulatory Features That Provide Mammalian Cells with Tunable G1 Length and Reversible G1 Arrest

Transitions between consecutive phases of the eukaryotic cell cycle are driven by the catalytic activity of selected sets of cyclin-dependent kinases (Cdks). Yet, their occurrence and precise timing is tightly scheduled by a variety of means including Cdk association with inhibitory/adaptor proteins (CKIs). Here we focus on the regulation of G1-phase duration by the end of which cells of multicelled organisms must decide whether to enter S phase or halt, and eventually then, differentiate, senesce or die to obey the homeostatic rules of their host. In mammalian cells, entry in and progression through G1 phase involve sequential phosphorylation and inactivation of the retinoblastoma Rb proteins, first, by cyclin D-Cdk4,6 with the help of CKIs of the Cip/Kip family and, next, by the cyclin E-Cdk2 complexes that are negatively regulated by Cip/Kip proteins. Using a dynamical modeling approach, we show that the very way how the Rb and Cip/Kip regulatory modules interact differentially with cyclin D-Cdk4,6 and cyclin E-Cdk2 provides to mammalian cells a powerful means to achieve an exquisitely-sensitive control of G1-phase duration and fully reversible G1 arrests. Consistently, corruption of either one of these two modules precludes G1 phase elongation and is able to convert G1 arrests from reversible to irreversible. This study unveils fundamental design principles of mammalian G1-phase regulation that are likely to confer to mammalian cells the ability to faithfully control the occurrence and timing of their division process in various conditions.

Robust and flexible response of the Ostreococcus tauri circadian clock to light/dark cycles of varying photoperiod

The green microscopic alga Ostreococcus tauri has recently emerged as a promising model for understanding how circadian clocks, which drive the daily biological rhythms of many organisms, synchronize to the day/night cycle in changing weather and seasons. Here, we analyze translational reporter time series data for the central clock genes CCA1 and TOC1 for a wide range of daylight durations (photoperiods). The variation of temporal expression profiles with day duration is complex, with the two protein peaks tracking different times of the day. Nevertheless, all profiles are accurately reproduced by a simple two‐gene transcriptional loop model whose parameters depend on light only through the photoperiod value. We show that this non‐intuitive behavior allows the circadian clock to combine flexibility and robustness with respect to daylight fluctuations.

Circadian clocks in changing weather and seasons: lessons from the picoalga Ostreococcus tauri.

Daylight is the primary cue used by circadian clocks to entrain to the day/night cycle so as to synchronize physiological processes with periodic environmental changes induced by Earth rotation.

Minimal requirements for robust cell size control in eukaryotic cells

Most cell types living in a stable environment tend to keep a constant characteristic size over successive generations. Size homeostasis requires that cells exert a tight control over the size at which they divide. Cell size control is not only robust against various noises, but also highly flexible since cell sizes can vary tremendously, notably as a function of nutrient levels. We formulated a minimal mathematical model of the eukaryotic cell cycle in which the cell size control operates through a cell growth-dependent bifurcation in the cell cycle dynamics. Such a bifurcation mechanism can readily explain the occurrence of a minimum critical size at division under limiting growth conditions. However, it also predicts that cells should become progressively larger and larger under prolific growth conditions. We argue that the cell size control can be reinforced at fast growth rates by adding a new cell cycle inhibitory activity whose strength would increase with the cell growth rate. We further show that various sources of noise may also generate a large variability in cell size at division and interdivision time that exhibit characteristic exponential tail distributions, without compromising the robustness of the cell size control.

A computational model for the coordination of neural progenitor self-renewal and differentiation through Hes1 dynamics.

Proper tissue development requires that stem/progenitor cells precisely coordinate cell division and differentiation in space and time. Notch-Hes1 intercellular signaling, which affects both differentiation and cell cycle progression and directs cell fate decisions at various developmental stages in many cell types, is central to this process. This study explored whether the pattern of connections among the cell cycle regulatory module, the Notch effector Hes1 and the proneural factor Ngn2 could explain salient aspects of cell fate determination in neural progenitors. A mathematical model that includes mutual interactions between Hes1, Ngn2 and G1-phase regulators was constructed and simulated at the single- and two-cell levels. By differentially regulating G1-phase progression, Hes1 and Ngn2 are shown to induce two contrasting cell cycle arrest states in early and late G1, respectively. Indeed, steady Hes1 overexpression promotes reversible quiescence by downregulating activators of G0/G1 exit and Ngn2. Ngn2 also downregulates activators of G0/G1 exit, but cooperates with Cip/Kip proteins to prevent G1/S transit, whereby it promotes G1-phase lengthening and, ultimately, contributes to reinforcing an irreversible late G1 arrest coincident with terminal differentiation. In this scheme, Hes1 oscillation in single cells is able to maintain a labile proliferation state in dynamic balance with two competing cell fate outputs associated with Hes1-mediated and Ngn2-mediated cell cycle arrest states. In Delta/Notch-connected cells, Hes1 oscillations and a lateral inhibition mechanism combine to establish heterogeneous Hes1, Ngn2 and cell cycle dynamics between proliferating neural progenitors, thereby increasing the chances of asymmetric cell fate decisions and improving the reliability of commitment to differentiation. Summary: Computational modelling deciphers the connections between the cell-cycle machinery and Notch signalling which govern whether neural stem cells proliferate, differentiate or enter quiescence.

The Role of Intrinsic Cell Properties in Synchrony of Neurons Interacting via Electrical Synapses

The study of the synchronization of neural activity has to deal with the existence of a great diversity of neuronal and synaptic properties, which both may influence the collective behavior of neurons. In this chapter, we present an approach that allows to disentangle the respective role of neuronal and synaptic properties in synchronization. It relies on the theory of weakly coupled oscillators and on the concept of infinitesimal Phase Response Curve (iPRC) which is relevant for systems where neurons fire periodically. Applying this theory to networks of neurons coupled with electrical synapses provides a unifying framework explaining how their synchronization behavior depends on the shape of the iPRC. It reveals that synchronization mediated by electrical synapses is more versatile than previously considered. It depends on the intrinsic currents and morphology of neurons as well as on their combination with inhibitory synapses.

Minimal model of transcriptional elongation processes with pauses.

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.