Browsing by Subject "physics, mathematical"

Now showing 1 - 5 of 5

Open Access
Bifurcation Analysis of Gene Regulatory Circuits Subject to Copy Number Variation
(2010) Mileyko, Yuriy; Weitz, Joshua S
Gene regulatory networks are comprised of many small gene circuits. Understanding expression dynamics of gene circuits for broad ranges of parameter space may provide insight into the behavior of larger regulatory networks as well as facilitate the use of circuits as autonomous units performing specific regulatory tasks. In this paper, we consider three common gene circuits and investigate the dependence of gene expression dynamics on the circuit copy number. In particular, we perform a detailed bifurcation analysis of the circuits' corresponding nonlinear gene regulatory models restricted to protein-only dynamics. Employing a geometric approach to bifurcation theory, we are able to derive closed form expressions for conditions which guarantee existence of saddle-node bifurcations caused by variation in the circuit copy number or copy number concentration. This result shows that the drastic effect of copy number variation on equilibrium behavior of gene circuits is highly robust to variation in other parameters in the circuits. We discuss a possibility of extending the current results to higher dimensional models which incorporate more details of the gene regulatory process.
Open Access
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans
(2010) Dai, Shu; Schaeffer, David G
Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria-Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456058]
Open Access
Computational and Analytic Perspectives on the Drift Paradox
(2010) Pasour, VB; Ellner, SP
The fact that many small aquatic and marine organisms manage to persist in their native environments in the presence of constant advection into unfavorable habitat is known as the "drift paradox." Although advection may determine large scale biological patterns, individual behavior such as predation or vertical/horizontal migration can dominate at smaller scales. Using both computational and analytical methods to model flow in an idealized channel, we explore the extent to which biological processes can counteract physical drivers. In particular, we investigate how different zooplankton migration behaviors affect biological retention time under a variety of flow regimes and whether a combination of physical/biological regimes exists that can resolve the drift paradox, i.e., allow the zooplankton to avoid washout for time periods much greater than the hydrologic retention time. The computational model is a three-dimensional semi-implicit hydrodynamic model which is coupled with an individual-based model for zooplankton behavior, while the analytical model is a simple partial differential equation containing both advective and behavioral components. The only behavior exhibited by the zooplankton is diel vertical migration. Our studies show that the interaction of zooplankton behavior and exchange flow can significantly influence zooplankton residence time. For a channel without vegetation, the analytical methods give biological residence times that vary by at most a day from the computational results.
Open Access
Dynamics of electroencephalogram entropy and pitfalls of scaling detection
(2010) Ignaccolo, M; Latka, M; Jernajczyk, W; Grigolini, P; West, BJ
In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein we study the time evolution of diffusion entropy to elucidate the scaling of EEG time series. For a cohort of 20 awake healthy volunteers with closed eyes, we find that the diffusion entropy of EEG increments (obtained from EEG waveforms by differencing) exhibits three features: short-time growth, an alpha wave related oscillation whose amplitude gradually decays in time, and asymptotic saturation which is achieved after approximately 1 s. This analysis suggests a linear, stochastic Ornstein-Uhlenbeck Langevin equation with a quasiperiodic forcing (whose frequency and/or amplitude may vary in time) as the model for the underlying dynamics. This model captures the salient properties of EEG dynamics. In particular, both the experimental and simulated EEG time series exhibit short-time scaling which is broken by a strong periodic component, such as alpha waves. The saturation of EEG diffusion entropy precludes the existence of asymptotic scaling. We find that the crossover between two scaling regions seen in detrended fluctuation analysis (DFA) of EEG increments does not originate from the underlying dynamics but is merely an artifact of the algorithm. This artifact is rooted in the failure of the "trend plus signal" paradigm of DFA.
Open Access
Spontaneous brain activity as a source of ideal 1/f noise
(2009) Allegrini, Paolo; Menicucci, Danilo; Bedini, Remo; Fronzoni, Leone; Gemignani, Angelo; Grigolini, Paolo; West, Bruce J; Paradisi, Paolo
We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we study global properties of events simultaneously occurring among two or more electrodes termed coincidences. We convert the coincidences into a diffusion process with three distinct rules that can yield the same mu only in the case where the coincidences are driven by a renewal process. We establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index mu approximate to 2 corresponding to ideal 1/f noise. We argue that this discovery, shared by all subjects of our study, supports the conviction that 1/f noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them.