Edmilson Roque

Synchronous long-term oscillations in a synthetic gene circuit

Nature 538, 7626 (2016). doi:10.1038/nature19841

Authors: Laurent Potvin-Trottier, Nathan D. Lord, Glenn Vinnicombe & Johan Paulsson

Synthetically engineered genetic circuits can perform a wide variety of tasks but are generally less accurate than natural systems. Here we revisit the first synthetic genetic oscillator, the repressilator, and modify it using principles from stochastic chemistry in single cells. Specifically, we sought to reduce error propagation and information losses, not by adding control loops, but by simply removing existing features. We show that this modification created highly regular and robust oscillations. Furthermore, some streamlined circuits kept 14 generation periods over a range of growth conditions and kept phase for hundreds of generations in single cells, allowing cells in flasks and colonies to oscillate synchronously without any coupling between them. Our results suggest that even the simplest synthetic genetic networks can achieve a precision that rivals natural systems, and emphasize the importance of noise analyses for circuit design in synthetic biology.

We describe the phenomenon of localization in the epidemic SIS model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp localization transition, instead there is a smooth crossover from localized to delocalized states as we approach the epidemic threshold from below. Analyzing these long-lasting local outbreaks for a random regular graph with a hub, we show how this localization can be detected from the shape of the distribution of the number of infective nodes.

Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component connecting large portion of the network would emerge. Assessing the percolation threshold of networks has wide applications in network reliability, information spread, epidemic control, etc. The theoretical approach so far to assess the percolation threshold is mainly based on spectral radius of adjacency matrix or non-backtracking matrix, which is limited to dense graphs or locally treelike graphs, and is less effective for sparse networks with non-negligible amount of triangles and loops. In this paper, we study high-order non-backtracking matrices and their application to assessing percolation threshold. We first define high-order non-backtracking matrices and study the properties of their spectral radii. Then we focus on 2nd-order non-backtracking matrix and demonstrate analytically that the reciprocal of its spectral radius gives a tighter lower bound than those of adjacency and standard non-backtracking matrices. We further build a smaller size matrix with the same largest eigenvalue as the 2nd-order non-backtracking matrix to improve computation efficiency. Finally, we use both synthetic networks and 42 real networks to illustrate that the use of 2nd-order non-backtracking matrix does give better lower bound for assessing percolation threshold than adjacency and standard non-backtracking matrices.

Author(s): Marcel Wellner

This two-dimensional study is motivated by cardiac electrophysiology, and focuses on rotating spiral waves in reaction-diffusion (RD) models. Here we deal with a spiral's translational drift under a constant externally imposed gradient G. A long-standing problem may be stated as follows: Given the d…

[Phys. Rev. E 94, 042421] Published Wed Oct 26, 2016

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space.For illustration we consider a generalized model of ecological meta-foodwebs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions are sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Author(s): Haider Hasan Jafri, R. K. Brojen Singh, and Ramakrishna Ramaswamy

We study the effect of multiplicative noise in dynamical flows arising from the coupling of stochastic processes with intrinsic noise. Situations wherein such systems arise naturally are in chemical or biological oscillators that are coupled to each other in a drive--response configuration. Above a …

[Phys. Rev. E] Published Thu Oct 20, 2016

Author(s): Alexander Kuczala and Tatyana O. Sharpee

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each other. The analytical results are confirmed by numerical sim…

[Phys. Rev. E] Published Thu Oct 20, 2016

We found that a network-organized metapopulation of cooperators, defectors and destructive agents playing the public goods game with mutations, can collectively reach global synchronization or chimera states. Global synchronization is accompanied by a collective periodic burst of cooperation, whereas chimera states reflect the tendency of the networked metapopulation to be fragmented in clusters of synchronous and incoherent bursts of cooperation. Numerical simulations have shown that the system's dynamics alternates between these two steady states through a first order transition. Depending on the parameters determining the dynamical and topological properties, chimera states with different numbers of coherent and incoherent clusters are observed. Our results present the first systematic study of chimera states and their characterization in the context of evolutionary game theory. This provides a valuable insight into the details of their occurrence, extending the relevance of such states to natural and social systems.

In this note we describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional asynchronous networks gives a factorization of dynamics in terms of constituent subnetworks. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network and thereby answer a question originally raised by Alon in the context of biological networks.

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties of static and fluctuating networks, we find that random network alternations can enhance the synchronizability. Synchronized states appear to be maximally stable when fluctuations are much faster than the time-delay, even when the instantaneous state of the network does not allow synchronization. This enhancing effect disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, a desynchronizing resonance is reported. Moreover, we observe characteristic oscillations, with a periodicity related to the coupling delay, as the system approaches or drifts away from the synchronized state.

Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a "carrot and stick" approach towards symbionts with a stabilizing effect on their symbiosis. In open human societies, a mutualistic relationship arises when a native insider population attracts outsiders with benevolent incentives in hope that the additional labor will improve the standard of all. A lingering question, however, is the extent to which insiders are willing to tolerate outsiders before mutualism slips into antagonism. To test the assertion by Karl Popper that unlimited tolerance leads to the demise of tolerance, we model a society under a growing incursion from the outside. Guided by their traditions of maintaining the social fabric and prizing tolerance, the insiders reduce their benevolence toward the growing subpopulation of outsiders but do not invoke punishment. This reduction of benevolence intensifies as less tolerant insiders (e.g., "radicals") openly renounce benevolence. Although more tolerant insiders maintain some level of benevolence, they may also tacitly support radicals out of fear for the future. If radicals and their tacit supporters achieve a critical majority, herd behavior ensues and the relation between the insider and outsider subpopulations turns antagonistic. To control the risk of unwanted social dynamics, we map the parameter space within which the tolerance of insiders is in balance with the assimilation of outsiders, the tolerant insiders maintain a sustainable majority, and any reduction in benevolence occurs smoothly. We also identify the circumstances that cause the relations between insiders and outsiders to collapse or that lead to the dominance of the outsiders.

This paper has incorporated the stochasticity into the Newell car following model. Three stochastic driving factors have been considered: (i) Driver's acceleration is stochastic and bounded. (ii) Driver's deceleration includes stochastic component, which is depicted by a deceleration with the randomization probability that is assumed to increase with the speed. (iii) Vehicles in the jam state have a larger randomization probability. Two simulation scenarios are conducted to test the model. In the first scenario, traffic flow on a circular road is investigated, and the empirical characteristics of the synchronized traffic flow can be simulated. In the second scenario, traffic flow pattern induced by a rubberneck bottleneck is studied, and the simulated traffic oscillations are consistent with that in the NGSIM data. Moreover, two experiments of model calibration and validation are conducted. The first is to calibrate and validate using experimental data, which illustrates that the concave growth pattern has been simulated successfully. The second is to calibrate and cross validate vehicles'trajectories using NGISM data, which also exhibits good performance of the model. Therefore, our study highlights the importance of speed dependent stochasticity in traffic flow modeling, which cannot be ignored as in most car-following studies.

Multilayer networks are a useful way to capture and model multiple, binary relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the development of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set by comparison with a multilayer fixed degree random graph model. Unlike existing detection methods, Multilayer Extraction handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure is able to capture overlapping communities, and it identifies background vertex-layer pairs that do not belong to any community. We establish large-graph consistency of the vertex-layer set optimizer of our proposed multilayer score under the multilayer stochastic block model. We investigate the performance of Multilayer Extraction empirically on three applications, as well as a test bed of simulations. Our theoretical and numerical evaluations suggest that Multilayer Extraction is an effective exploratory tool for analyzing complex multilayer networks. Publicly available R software for Multilayer Extraction is available at https://github.com/jdwilson4/MultilayerExtraction.

Epidemic propagation on complex networks has been widely investigated, mostly with invariant parameters. However, the process of epidemic propagation is not always constant. Epidemics can be affected by various perturbations, and may bounce back to its original state, which is considered resilient. Here, we study the resilience of epidemics on networks, by introducing a different infection rate ${\lambda_{2}}$ during SIS (susceptible-infected-susceptible) epidemic propagation to model perturbations (control state), whereas the infection rate is ${\lambda_{1}}$ in the rest of time. Through simulations and theoretical analysis, we find that even for ${\lambda_{2}<\lambda_{c}}$, epidemics eventually could bounce back if control duration is below a threshold. This critical control time for epidemic resilience, i.e., ${cd_{max}}$ can be predicted by the diameter (${d}$) of the underlying network, with the quantitative relation ${cd_{max}\sim d^{\alpha}}$. Our findings can help to design a better mitigation strategy for epidemics.

Synchronized human skeletal myotubes of lean, obese and type 2 diabetic patients maintain circadian oscillation of clock genes

Scientific Reports, Published online: 19 October 2016; doi:10.1038/srep35047

Author(s): S. Risau-Gusman

Most self-sustained oscillations in biological systems and in technical applications are based on a feedback loop, and it is usually important to know how they will react when an external oscillatory force is applied. Here we investigate the effects that the introduction of a time delay in the feedb…

[Phys. Rev. E 94, 042212] Published Tue Oct 18, 2016

Author(s): Ghazal Montaseri and Michael Meyer-Hermann

The heterogeneity of coupled oscillators is important for the degree of their synchronization. According to the classical Kuramoto model, larger heterogeneity reduces synchronization. Here, we show that in a model for coupled pancreatic β-cells, higher diversity of the cells induces higher synchrony…

[Phys. Rev. E 94, 042213] Published Tue Oct 18, 2016

Author(s): Bastian Pietras, Nicolás Deschle, and Andreas Daffertshofer

Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled, symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are iden…

[Phys. Rev. E] Published Tue Oct 18, 2016

The sensitivity (i.e. dynamic response) of complex networked systems has not been well understood, making difficult to predict whether new macroscopic dynamic behavior will emerge even if we know exactly how individual nodes behave and how they are coupled. Here we build a framework to quantify the sensitivity of complex networked system of coupled dynamic units. We characterize necessary and sufficient conditions for the emergence of new macroscopic dynamic behavior in the thermodynamic limit. We prove that these conditions are satisfied only for architectures with power-law degree distributions. Surprisingly, we find that highly connected nodes (i.e. hubs) only dominate the sensitivity of the network up to certain critical frequency.

We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension and stability as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function which yields more evenly distributed approximating finite point sets and perform corresponding numerical experiments.

An accurate approximate formula of the die-out probability in a SIS epidemic process on a network is proposed. The formula contains only three essential parameters: the largest eigenvalue of the adjacency matrix of the network, the effective infection rate of the virus, and the initial number of infected nodes in the network. The die-out probability formula is compared with the exact die-out probability in complete graphs, Erd\H{o}s-R\'enyi graphs, and a power-law graph. Furthermore, as an example, the formula is applied to the $N$-Intertwined Mean-Field Approximation, to explicitly incorporate the die-out.

Clustering network is one of which complex network attracting plenty of scholars to discuss and study the structures and cascading process. We primarily analyzed the effect of clustering coefficient to other various of the single clustering network under localized attack. These network models including double clustering network and star-like NON with clustering and random regular (RR) NON of ER networks with clustering are made up of at least two networks among which exist interdependent relation among whose degree of dependence is measured by coupling strength. We show both analytically and numerically, how the coupling strength and clustering coefficient effect the percolation threshold, size of giant component, critical coupling point where the behavior of phase transition changes from second order to first order with the increase of coupling strength between the networks. Last, we study the two types of clustering network: one type is same with double clustering network in which each subnetwork satisfies identical degree distribution and the other is that their subnetwork satisfies different degree distribution. The former type is treated both analytically and numerically while the latter is treated only numerically. In each section, we compared two results obtained from localized attack and random attack according to Shao et al:[22].

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erd\"os-R\'enyi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective synchronization. We demonstrate by exact results and numerics a surprisingly rich long-time behavior, in which the system settles into either a stationary state that could be in or out of equilibrium and supports either global synchrony or absence of it, or, in a time-periodic synchronized state. The system shows both continuous and discontinuous phase transitions, as well as an interesting reentrant transition in which the system successively loses and gains synchrony on steady increase of the relevant tuning parameter.

Author(s): Pau Clusella, Peter Grassberger, Francisco J. Pérez-Reche, and Antonio Politi

A new method (`explosive immunization' (EI)) is proposed for immunization and targeted destruction of networks. It combines the explosive percolation (EP) paradigm with the idea of maintaining a fragmented distribution of clusters. The ability of each node to block the spread of an infection (or to …

[Phys. Rev. Lett.] Published Thu Oct 13, 2016

Author(s): Yup Kim, Seokjong Park, and Soon-Hyung Yook

We study the mean first passage time (MFPT) of true self-avoiding walks (TSAWs) on various networks as a measure of searching efficiency. From the numerical analysis, we find that the MFPT of TSAWs, τTSAW, approaches the theoretical minimum τth/N=12 on synthetic networks whose degree-degree correlat…

[Phys. Rev. E 94, 042309] Published Fri Oct 14, 2016

Author(s): Alfonso Allen-Perkins, Javier Galeano, and Juan Manuel Pastor

Complex networks are a recent type of frameworks used to study complex systems with many interacting elements, such as Self-Organized Criticality (SOC). The network nodes's tendency to link to other nodes of similar type is characterized by assortative mixing. Real networks exhibit assortative mixin…

[Phys. Rev. E] Published Thu Oct 13, 2016