Quantification of Circadian Rhythms in Single Cells

Bioluminescence techniques allow accurate monitoring of the circadian clock in single cells. We have analyzed bioluminescence data of Per gene expression in mouse SCN neurons and fibroblasts. From these data, we extracted parameters such as damping rate and noise intensity using two simple mathematical models, one describing a damped oscillator driven by noise, and one describing a self-sustained noisy oscillator. Both models describe the data well and enabled us to quantitatively characterize both wild-type cells and several mutants. It has been suggested that the circadian clock is self-sustained at the single cell level, but we conclude that present data are not sufficient to determine whether the circadian clock of single SCN neurons and fibroblasts is a damped or a self-sustained oscillator. We show how to settle this question, however, by testing the models' predictions of different phases and amplitudes in response to a periodic entrainment signal (zeitgeber)

Robustness from flexibility in the fungal circadian clock

Background Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa. Results The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure. Conclusions Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators

Adaptive intermittent control: A computational model explaining motor intermittency observed in human behavior

It is a fundamental question how our brain performs a given motor task in a real-time fashion with the slow sensorimotor system. Computational theory proposed an influential idea of feed-forward control, but it has mainly treated the case that the movement is ballistic (such as reaching) because the motor commands should be calculated in advance of movement execution. As a possible mechanism for operating feed-forward control in continuous motor tasks (such as target tracking), we propose a control model called "adaptive intermittent control" or "segmented control," that brain adaptively divides the continuous time axis into discrete segments and executes feed-forward control in each segment. The idea of intermittent control has been proposed in the fields of control theory, biological modeling and nonlinear dynamical system. Compared with these previous models, the key of the proposed model is that the system speculatively determines the segmentation based on the future prediction and its uncertainty. The result of computer simulation showed that the proposed model realized faithful visuo-manual tracking with realistic sensorimotor delays and with less computational costs (i.e., with fewer number of segments). Furthermore, it replicated "motor intermittency", that is, intermittent discontinuities commonly observed in human movement trajectories. We discuss that the temporally segmented control is an inevitable strategy for brain which has to achieve a given task with small computational (or cognitive) cost, using a slow control system in an uncertain variable environment, and the motor intermittency is the side-effect of this strategy

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of Computational Neuroscience, in press (2007

DAMNED: A Distributed and Multithreaded Neural Event-Driven simulation framework

In a Spiking Neural Networks (SNN), spike emissions are sparsely and irregularly distributed both in time and in the network architecture. Since a current feature of SNNs is a low average activity, efficient implementations of SNNs are usually based on an Event-Driven Simulation (EDS). On the other hand, simulations of large scale neural networks can take advantage of distributing the neurons on a set of processors (either workstation cluster or parallel computer). This article presents DAMNED, a large scale SNN simulation framework able to gather the benefits of EDS and parallel computing. Two levels of parallelism are combined: Distributed mapping of the neural topology, at the network level, and local multithreaded allocation of resources for simultaneous processing of events, at the neuron level. Based on the causality of events, a distributed solution is proposed for solving the complex problem of scheduling without synchronization barrier.Comment: 6 page

Rotating states in driven clock- and XY-models

We consider 3D active plane rotators, where the interaction between the spins is of XY-type and where each spin is driven to rotate. For the clock-model, when the spins take N\gg1 possible values, we conjecture that there are two low-temperature regimes. At very low temperatures and for small enough drift the phase diagram is a small perturbation of the equilibrium case. At larger temperatures the massless modes appear and the spins start to rotate synchronously for arbitrary small drift. For the driven XY-model we prove that there is essentially a unique translation-invariant and stationary distribution despite the fact that the dynamics is not ergodic

Timing models for high-level synthesis

In this paper, we describe a timing model for clock estimation during high-level synthesis. In order to obtain realistic timing estimates, the proposed model considers all delay elements, including datapath, control and wire delays, and several technology factors, such as layout architecture, technology mapping, buffers insertion and loading effects. The experimental results show that this model can provide much better estimates than previous models. This model is well suited for automatic and interactive synthesis as well as feedback-driven synthesis where performance matrices must be rapidly and incrementally calculated