Cooperative maintenance of cellular identity in systems with intercellular communication defects.

The cooperative dynamics of cellular populations emerging from the underlying interactions determines cellular functions and thereby their identity in tissues. Global deviations from this dynamics, on the other hand, reflect pathological conditions. However, how these conditions are stabilized from dysregulation on the level of the single entities is still unclear. Here, we tackle this question using the generic Hodgkin-Huxley type of models that describe physiological bursting dynamics of pancreatic ß-cells and introduce channel dysfunction to mimic pathological silent dynamics. The probability for pathological behavior in ß-cell populations is ∼100% when all cells have these defects, despite the negligible size of the silent state basin of attraction for single cells. In stark contrast, in a more realistic scenario for a mixed population, stabilization of the pathological state depends on the size of the subpopulation which acquired the defects. However, the probability to exhibit stable pathological dynamics in this case is less than 10%. These results, therefore, suggest that the physiological bursting dynamics of a population of ß-cells is cooperatively maintained, even under intercellular communication defects induced by dysfunctional channels of single cells.

Dimensionality reduction of bistable biological systems.

Time hierarchies, arising as a result of interactions between system's components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novel method, which allows investigation of the time hierarchies in systems exhibiting bistability. The proposed method is in turn used in identifying the components, other than reactions, which determine the systemic dynamical properties. We demonstrate that in biological systems of varying levels of complexity and spanning different biological levels, the method can be effectively employed for model simplification while ensuring preservation of qualitative dynamical properties (i.e., bistability). Finally, by establishing a connection between techniques from nonlinear dynamics and multivariate statistics, the proposed approach provides the basis for extending reference-based analysis to bistable systems.

Inner composition alignment for inferring directed networks from short time series.

Identifying causal links (couplings) is a fundamental problem that facilitates the understanding of emerging structures in complex networks. We propose and analyze inner composition alignment-a novel, permutation-based asymmetric association measure to detect regulatory links from very short time series, currently applied to gene expression. The measure can be used to infer the direction of couplings, detect indirect (superfluous) links, and account for autoregulation. Applications to the gene regulatory network of E. coli are presented.

Parameter mismatches and oscillation death in coupled oscillators.

We use a set of qualitatively different models of coupled oscillators (genetic, membrane, Ca-metabolism, and chemical oscillators) to study dynamical regimes in the presence of small detuning. In particular, we focus on a distinct oscillation quenching mechanism, the oscillation death phenomenon. Using bifurcation analysis in general, we demonstrate that under strong coupling via slow variable detuning can eliminate standard oscillatory solutions from a large region of the parameter space, establishing the dominance of oscillation death. We argue furthermore that the oscillation death dominance effect provides a reliable dynamical control mechanism in the general case of N coupled oscillators.

Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator.

We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.

Topological structures enhance the presence of dynamical regimes in synthetic networks.

Genetic and protein networks, through their underlying dynamical behavior, characterize structural and functional cellular processes, and are thus regarded as "driving forces" of all living systems. Understanding the rhythm generation mechanisms that emerge from such complex networks has benefited in recent years by synthetic approaches, through which simpler network modules (e.g., switches and oscillators) have been built. In this manner, a significant attention to date has been focused on the dynamical behavior of these isolated synthetic circuits, and the occurrence of unifying rhythms in systems of globally coupled genetic units. In contrast to this, we address here the question: Could topologically distinct structures enhance the presence of various dynamical regimes in synthetic networks? We show that an intercellular mechanism, engineered to operate on a local scale, will inevitably lead to multirhythmicity, and to the appearance of several coexisting (complex) dynamical regimes, if certain preconditions regarding the dynamical structure of the synthetic circuits are met. Moreover, we discuss the importance of regime enhancement in synthetic structures in terms of memory storage and computation capabilities.

Cooperative differentiation through clustering in multicellular populations.

The coordinated development of multicellular organisms is driven by intercellular communication. Differentiation into diverse cell types is usually associated with the existence of distinct attractors of gene regulatory networks, but how these attractors emerge from cell-cell coupling is still an open question. In order to understand and characterize the mechanisms through which coexisting attractors arise in multicellular systems, here we systematically investigate the dynamical behavior of a population of synthetic genetic oscillators coupled by chemical means. Using bifurcation analysis and numerical simulations, we identify various attractors and attempt to deduce from these findings a way to predict the organized collective behavior of growing populations. Our results show that dynamical clustering is a generic property of multicellular systems. We argue that such clustering might provide a basis for functional differentiation and variability in biological systems.

Inherent multistability in arrays of autoinducer coupled genetic oscillators.

Rhythm generation mechanisms are very important for genetic network functions as well as for the design of synthetic genetic circuits. A significant attention to date has been focused on the synchronization of communicating genetic units, which results in the production of an unified rhythm. In contrast to this we address the question: what mechanisms of intercell communication can be responsible for multirhythmicity in globally coupled genetic units? Here, we show that an autoinducer intercell communication system that provides coupling between synthetic genetic oscillators will inherently lead to multirhythmicity and the appearance of several coexisting dynamical regimes, if the time evolution of the genetic network can be split in two well-separated time scales. We investigate in detail a variety of dynamical regimes in a genetic population and show the possibility for multiple element distributions between clusters, as well as the possibility of generating complex oscillations with different return times in one limit cycle.

Stochastic suppression of gene expression oscillators under intercell coupling.

This paper examines the dynamics of an ensemble of hysteresis-based genetic relaxation oscillators, focusing on the influence of noise and cell-to-cell coupling on the appearance of new dynamical regimes. In particular, we show that control of the coupling strength and noise can effectively change the dynamics of the system leading to behaviors such as clustering, synchronous and asynchronous oscillations, and suppression. Moreover, under certain conditions an optimal amount of noise can lead to increased order in the system. The results obtained are correlated with relevant biological processes that occur in living organisms.