172 research outputs found
Ca2+ Alternans in a Cardiac Myocyte Model that Uses Moment Equations to Represent Heterogeneous Junctional SR Ca2+
AbstractMultiscale whole-cell models that accurately represent local control of Ca2+-induced Ca2+ release in cardiac myocytes can reproduce high-gain Ca2+ release that is graded with changes in membrane potential. Using a recently introduced formalism that represents heterogeneous local Ca2+ using moment equations, we present a model of cardiac myocyte Ca2+ cycling that exhibits alternating sarcoplasmic reticulum (SR) Ca2+ release when periodically stimulated by depolarizing voltage pulses. The model predicts that the distribution of junctional SR [Ca2+] across a large population of Ca2+ release units is distinct on alternating cycles. Load-release and release-uptake functions computed from this model give insight into how Ca2+ fluxes and stimulation frequency combine to determine the presence or absence of Ca2+ alternans. Our results show that the conditions for the onset of Ca2+ alternans cannot be explained solely by the steepness of the load-release function, but that changes in the release-uptake process also play an important role. We analyze the effect of the junctional SR refilling time constant on Ca2+ alternans and conclude that physiologically realistic models of defective Ca2+ cycling must represent the dynamics of heterogeneous junctional SR [Ca2+] without assuming rapid equilibration of junctional and network SR [Ca2+]
Nonlinear Dynamics, Synchronisation and Chaos in Coupled FHN Cardiac and Neural Cells
Physiological systems are amongst the most challenging systems to investigate from a
mathematically based approach. The eld of mathematical biology is a relatively recent
one when compared to physics. In this thesis I present an introduction to the physiological
aspects needed to gain access to both cardiac and neural systems for a researcher trained
in a mathematically based discipline. By using techniques from nonlinear dynamical
systems theory I show a number of results that have implications for both neural and
cardiac cells. Examining a reduced model of an excitable biological oscillator I show how
rich the dynamical behaviour of such systems can be when coupled together. Quantifying
the dynamics of coupled cells in terms of synchronisation measures is treated at length.
Most notably it is shown that for cells that themselves cannot admit chaotic solutions,
communication between cells be it through electrical coupling or synaptic like coupling,
can lead to the emergence of chaotic behaviour. I also show that in the presence of
emergent chaos one nds great variability in intervals of activity between the constituent
cells. This implies that chaos in both cardiac and neural systems can be a direct result
of interactions between the constituent cells rather than intrinsic to the cells themselves.
Furthermore the ubiquity of chaotic solutions in the coupled systems may be a means of
information production and signaling in neural systems
Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]
An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u
Tricritical points in a Vicsek model of self-propelled particles with bounded confidence
We study the orientational ordering in systems of self-propelled particles
with selective interactions. To introduce the selectivity we augment the
standard Vicsek model with a bounded-confidence collision rule: a given
particle only aligns to neighbors who have directions quite similar to its own.
Neighbors whose directions deviate more than a fixed restriction angle
are ignored. The collective dynamics of this systems is studied by agent-based
simulations and kinetic mean field theory. We demonstrate that the reduction of
the restriction angle leads to a critical noise amplitude decreasing
monotonically with that angle, turning into a power law with exponent 3/2 for
small angles. Moreover, for small system sizes we show that upon decreasing the
restriction angle, the kind of the transition to polar collective motion
changes from continuous to discontinuous. Thus, an apparent tricritical point
is identified and calculated analytically. We also find that at very small
interaction angles the polar ordered phase becomes unstable with respect to the
apolar phase. We show that the mean-field kinetic theory permits stationary
nematic states below a restriction angle of . We calculate the
critical noise, at which the disordered state bifurcates to a nematic state,
and find that it is always smaller than the threshold noise for the transition
from disorder to polar order. The disordered-nematic transition features two
tricritical points: At low and high restriction angle the transition is
discontinuous but continuous at intermediate . We generalize our
results to systems that show fragmentation into more than two groups and obtain
scaling laws for the transition lines and the corresponding tricritical points.
A novel numerical method to evaluate the nonlinear Fredholm integral equation
for the stationary distribution function is also presented.Comment: 20 pages, 18 figure
Nonlinear switching and solitons in PT-symmetric photonic systems
One of the challenges of the modern photonics is to develop all-optical
devices enabling increased speed and energy efficiency for transmitting and
processing information on an optical chip. It is believed that the recently
suggested Parity-Time (PT) symmetric photonic systems with alternating regions
of gain and loss can bring novel functionalities. In such systems, losses are
as important as gain and, depending on the structural parameters, gain
compensates losses. Generally, PT systems demonstrate nontrivial
non-conservative wave interactions and phase transitions, which can be employed
for signal filtering and switching, opening new prospects for active control of
light. In this review, we discuss a broad range of problems involving nonlinear
PT-symmetric photonic systems with an intensity-dependent refractive index.
Nonlinearity in such PT symmetric systems provides a basis for many effects
such as the formation of localized modes, nonlinearly-induced PT-symmetry
breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve
as powerful building blocks for the development of novel photonic devices
targeting an active light control.Comment: 33 pages, 33 figure
Recommended from our members
Feedback for neuronal system identification
In order to estimate reliable models from noisy input-output data, system identification techniques usually require that the data be generated by a process with a fading memory. Non-equilibrium systems such as neuronal and chaotic models lack a fading memory. Their identification is challenging, in particular in the presence of input noise. In this thesis, we propose a methodology based on the prediction-error method for the identification of neuronal systems subject to input-additive noise. We build on the fundamental observation that while a neuronal model does not have a fading memory, it can be transformed into a fading memory system by output feedback. Our ideas can be generalized to any non-equilibrium system sharing this property.
At the core of the methodology is the use of output feedback in experiment design. We provide a theoretical justification for this design choice, which has been exploited in neurophysiology since the invention of the voltage-clamp experiment. To investigate the problem of feedback for identification, we first address the estimation of simple non-equilibrium systems in Lure form, and show that feedback allows estimating the nonlinearity in a static experiment. We then address the estimation of conductance-based models. Assuming that an informed choice can be made on the elements of the model structure, we show that consistent parameter estimates can be obtained when noise is only present at the system input. Finally, we approach the problem from a black-box perspective, and propose identifying the neuronal internal dynamics using a universal approximator with Generalized Orthogonal Basis Functions.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – Brasil (Finance Code 001
Being in Uncertainties: An Inquiry-based Model Leveraging Complexity in Teaching-Learning
Education is traditionally structured as a closed system, privileging result-driven methods that offer control and predictability. In recent decades this reductionist approach has been effectively challenged by interdisciplinary work in complex systems theory, revealing myriad levels of orderly disorder that make either-or, linear instruction an inadequate norm. Narrowing the broad implications of a complexity lens on education, this paper focuses on generative uncertainty in teaching-learning, a paradoxical state of epistemological and creative growth described by English poet John Keats as the negative capability of being in uncertainties, mysteries, doubts. Opportunities to advance this potentiating capacity are especially abundant in constructivist curricula, for example the Methods of Inquiry (MoI) program discussed herein. MoI\u27s open, complexity-based approach foregrounds uncertainty-tolerance and other interactive dispositions, providing a fluid structure for the emergent, often turbulent nature of meaning production. Such dynamic attitudes and strategies are seen as essential for any classroom practice that seeks to transform as well as inform, to guide and also empower
- …