Analysis of the lactose metabolism in E. coli using sum-of-squares decomposition

We provide a system-theoretic analysis of the mathematical model of lactose induction in E.coli which predicts the level of lactose induction into the cell for specified values of external lactose. Depending on the levels of external lactose and other parameters, the Lac operon is known to have a low steady state in which it is said to be turned off and high steady state where it is said to be turned on. Furthermore, the model has been shown experimentally to exhibit a bi-stable behavior. Using ideas from Lyapunov stability theory and sum-of-squares decomposition, we characterize the reachable state space for different sets of initial conditions, calculating estimates of the regions of attraction of the biologically relevant equilibria of this system. The changes in the basins of attraction with changes in model parameters can be used to provide biological insight. Specifically, we explain the crucial role played by a small basal transcription rate in the Lac operon. We show that if the basal rate is below a threshold, the region of attraction of the low steady state grows significantly, indicating that system is trapped in the (off) mode, showing the importance of the basal rate of transcription

Optimized Stochastic Policies for Task Allocation in Swarms of Robots

We present a scalable approach to dynamically allocating a swarm of homogeneous robots to multiple tasks, which are to be performed in parallel, following a desired distribution. We employ a decentralized strategy that requires no communication among robots. It is based on the development of a continuous abstraction of the swarm obtained by modeling population fractions and defining the task allocation problem as the selection of rates of robot ingress and egress to and from each task. These rates are used to determine probabilities that define stochastic control policies for individual robots, which, in turn, produce the desired collective behavior. We address the problem of computing rates to achieve fast redistribution of the swarm subject to constraint(s) on switching between tasks at equilibrium. We present several formulations of this optimization problem that vary in the precedence constraints between tasks and in their dependence on the initial robot distribution. We use each formulation to optimize the rates for a scenario with four tasks and compare the resulting control policies using a simulation in which 250 robots redistribute themselves among four buildings to survey the perimeters

Effect of Spatial Inhomogeneities on the Membrane Surface on Receptor Dimerization and Signal Initiation

Important signal transduction pathways originate on the plasma membrane, where microdomains may transiently entrap diffusing receptors. This results in a non-random distribution of receptors even in the resting state, which can be visualized as “clusters” by high resolution imaging methods. Here, we explore how spatial in-homogeneities in the plasma membrane might influence the dimerization and phosphorylation status of ErbB2 and ErbB3, two receptor tyrosine kinases that preferentially heterodimerize and are often co-expressed in cancer. This theoretical study is based upon spatial stochastic simulations of the two-dimensional membrane landscape, where variables include differential distributions and overlap of transient confinement zones (“domains”) for the two receptor species. The in silico model is parameterized and validated using data from single particle tracking experiments. We report key differences in signaling output based on the degree of overlap between domains and the relative retention of receptors in such domains, expressed as escape probability. Results predict that a high overlap of domains, which favors transient co-confinement of both receptor species, will enhance the rate of hetero-interactions. Where domains do not overlap, simulations confirm expectations that homo-interactions are favored. Since ErbB3 is uniquely dependent on ErbB2 interactions for activation of its catalytic activity, variations in domain overlap or escape probability markedly alter the predicted patterns and time course of ErbB3 and ErbB2 phosphorylation. Taken together, these results implicate membrane domain organization as an important modulator of signal initiation, motivating the design of novel experimental approaches to measure these important parameters across a wider range of receptor systems

Specialization as an Optimal Strategy Under Varying External Conditions

We present an investigation of specialization when considering the execution of collaborative tasks by a robot swarm. Specifically, we consider the stick-pulling problem first proposed by Martinoli et al. [1], [2] and develop a macroscopic analytical model for the swarm executing a set of tasks that require the collaboration of two robots. We show, for constant external conditions, maximum productivity can be achieved by a single species swarm with carefully chosen operational parameters. While the same applies for a two species swarm, we show how specialization is a strategy best employed for changing external conditions

From sleep spindles of natural sleep to spike and wave discharges of typical absence seizures: is the hypothesis still valid?

The temporal coincidence of sleep spindles and spike-and-wave discharges (SWDs) in patients with idiopathic generalized epilepsies, together with the transformation of spindles into SWDs following intramuscular injection of the weak GABAA receptor (GABAAR) antagonist, penicillin, in an experimental model, brought about the view that SWDs may represent ‘perverted’ sleep spindles. Over the last 20 years, this hypothesis has received considerable support, in particular by in vitro studies of thalamic oscillations following pharmacological/genetic manipulations of GABAARs. However, from a critical appraisal of the evidence in absence epilepsy patients and well-established models of absence epilepsy it emerges that SWDs can occur as frequently during wakefulness as during sleep, with their preferential occurrence in either one of these behavioural states often being patient dependent. Moreover, whereas the EEG expression of both SWDs and sleep spindles requires the integrity of the entire cortico-thalamo-cortical network, SWDs initiates in cortex while sleep spindles in thalamus. Furthermore, the hypothesis of a reduction in GABAAR function across the entire cortico-thalamo-cortical network as the basis for the transformation of sleep spindles into SWDs is no longer tenable. In fact, while a decreased GABAAR function may be present in some cortical layers and in the reticular thalamic nucleus, both phasic and tonic GABAAR inhibitions of thalamo-cortical neurons are either unchanged or increased in this epileptic phenotype. In summary, these differences between SWDs and sleep spindles question the view that the EEG hallmark of absence seizures results from a transformation of this EEG oscillation of natural sleep