Multiple Scenarios of Transition to Chaos in the Alternative Splicing Model

2017 ◽  
Vol 27 (02) ◽  
pp. 1730006 ◽  
Author(s):  
Vladislav V. Kogai ◽  
Vitaly A. Likhoshvai ◽  
Stanislav I. Fadeev ◽  
Tamara M. Khlebodarova

We have investigated the scenarios of transition to chaos in the mathematical model of a genetic system constituted by a single transcription factor-encoding gene, the expression of which is self-regulated by a feedback loop that involves protein isoforms. Alternative splicing results in the synthesis of protein isoforms providing opposite regulatory outcomes — activation or repression. The model is represented by a differential equation with two delayed arguments. The possibility of transition to chaos dynamics via all classical scenarios: a cascade of period-doubling bifurcations, quasiperiodicity and type-I, type-II and type-III intermittencies, has been numerically demonstrated. The parametric features of each type of transition to chaos have been described.

1999 ◽  
Vol 09 (02) ◽  
pp. 383-396 ◽  
Author(s):  
J.-M. MALASOMA ◽  
P. WERNY ◽  
C.-H. LAMARQUE

Numerical investigations of the global behavior of a model of the convective flow of a binary mixture in a porous medium are reported. We find a complex behavior characterized by the presence of coexisting periodic, quasiperiodic and chaotic attractors. Bifurcations of periodic solutions and routes to chaos via type-I intermittency and period-doubling bifurcations are described. Boundary crises and band merging crises have also been observed.


2018 ◽  
Author(s):  
Chrissie Lim

Immune responses require the tight control of dose, location, strength and duration through genetic, epigenetic or biochemical regulation. Of these, the generation of alternatively-spliced constructs increases transcriptional and proteomic diversity in post-transcriptional modification, localization and functional domain integrity. Specifically, this thesis explores how splice variation engenders profound differences in the biological functions of interleukin-22 (IL-22) binding protein (IL-22BP) and interferon lambda 4 (IFNλ4), which are both central components of distinct cytokine pathways in mucosal immunity and inflammation. IL-22BP is a soluble receptor for IL-22 that is expressed as three isoforms in humans, though the physiological relevance of the three human isoforms has remained a mystery due to the absence of this variation in mice. We present novel findings that IL-22BPi1 is inactive due to intracellular retention by its unique exon, while IL-22BPi3 is also an antagonist but with differential activity from IL-22BPi2. Importantly, while IL-22BPi3 has widespread expression in steady-state homeostatic conditions, IL-22BPi2 is the only isoform induced by inflammatory TLR2/retinoic acid stimulation, highlighting important spatiotemporal control of the two isoforms that exploit their differential activities. IFNλ4 presents a different mystery in which the protein-coding variant is genetically associated with poorer clearance, but the mechanism for this association remains unclear. We investigated several non-canonical functions proposed by the field, including intrinsic differences in activity of the three protein isoforms and their interference with antiviral activites of other type I or III interferons. Establishing an overexpression system and purifying recombinant proteins, we found that only the full-length isoform is active and exhibits similar effects to canonical type III IFN IFNλ3, without any blockade of other IFN signaling. Simultaneously, functional IFNλ4 expression is suppressed in hepatocytes and dendritic cells through preferential splicing to increase intron retention and expression of inactive isoforms. Therefore, alternative splicing in IFNλ4 is an important mechanism to control IFNλ4 bioactivity. The divergent manners in which alternative splice forms impact the activity of both IL-22BP and IFNλ4 highlight the important contributions of this process to cytokine biology and bigger implications that escape detection by genomic analyses.


2005 ◽  
Vol 2005 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Terence R. Blows ◽  
Barry J. Wimmer

A simple mathematical model is presented for Batesian mimicry, which occurs when a harmless species (mimic) is morphologically similar to another species (model) that is noxious or distasteful to predators, thus gaining a measure of protection. Although mathematical models for species interaction, such as predator-prey or competition, are well known, there is no similar literature on mimicry. The mathematical model developed here is a one-dimensional iterated map which has the full range of dynamic behavior present in the logistic map, depending on the values of its parameters. The dynamics ranges from a stable fixed point and stable cycles through chaotic dynamics achieved through a sequence of period doubling bifurcations.


1992 ◽  
Vol 02 (01) ◽  
pp. 93-100 ◽  
Author(s):  
A.S. DMITRIEV ◽  
U.A. KOMLEV ◽  
D.V. TURAEV

This paper presents the 1:1 resonant horn bifurcation phenomena for the forced van der Pol—Duffing equation. It is shown that the transition to chaos in the case of small dissipation evolves in two parallel processes: a sequence of period-doubling bifurcations and the birth, growth and merging of homoclinic structures.


1995 ◽  
Vol 62 (4) ◽  
pp. 903-907 ◽  
Author(s):  
C. Semler ◽  
M. P. Pai¨doussis

The nonlinear equations for planar motions of a vertical cantilevered pipe conveying fluid are modified to take into account a small lumped mass added at the free end. The resultant equations contain nonlinear inertial terms; by discretizing the system first and inverting the inertia matrix, these terms are transferred into other matrices. In this paper, the dynamics of the system is examined when the added mass is negative (a mass defect), by means of numerical computations and by the software package AUTO. The system loses stability by a Hopf bifurcation, and the resultant limit cycle undergoes pitchfork and period-doubling bifurcations. Subsequently, as shown by the computation of Floquet multipliers, a type I intermittency route to chaos is followed—as illustrated further by a Lorenz return map, revealing the well-known normal form for this type of bifurcation. The period between “turbulent bursts” of nonperiodic oscillations is computed numerically, as well as Lyapunov exponents. Remarkable qualitative agreement, in both cases, is obtained with analytical results.


2003 ◽  
Vol 9 (6) ◽  
pp. 665-684 ◽  
Author(s):  
A. A. Al-Qaisia ◽  
A. M. Harb ◽  
A. A. Zaher ◽  
M. A. Zohdy

In this paper, we study the dynamics of a forced nonlinear oscillator with inertial and elastic symmetric nonlinearities using modern nonlinear, bifurcation and chaos theories. The results for the response have shown that, for a certain combination of physical parameters, this oscillator exhibits a chaotic behavior or a transition to chaos through a sequence of period doubling bifurcations. The main objective of this paper is to control the chaotic behavior for this type of oscillator. A nonlinear estimation-based controller is proposed and the transient performance is investigated. The design of the parameter update mechanism is analyzed while discussing ways to extend its performance to further account for other types of uncertainties. We examine robustness problems as well as ways to tune the controller parameters. Simulation results are presented for the uncontrolled and controlled cases, verifying the effectiveness and the capability of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.


1994 ◽  
Vol 04 (06) ◽  
pp. 1525-1534
Author(s):  
S.G. DOLINCHUK ◽  
V.I. ZADOROZHNII ◽  
A.M. FEDORCHENKO

We have considered the hierarchy of instabilities, the transition to chaos, and the periodic generation of three-wave solitons in an acoustic distributed system with additional feedback and pumping. At positive feedback only steady-state conditions are shown to be stable. Self-oscillations, period-doubling bifurcations, and transition from quasiperiodicity to chaos of parametrically coupled waves have been found at negative feedback. “Hard” excitation of the generator leads to the formation of solitons. Established effects have been studied on dependence with physical parameters of a TeO 2 crystal.


2010 ◽  
Vol 20 (05) ◽  
pp. 1439-1450 ◽  
Author(s):  
IRINA BASHKIRTSEVA ◽  
GUANRONG CHEN ◽  
LEV RYASHKO

We study the stochastically forced Chen system in its parameter zone under the transition to chaos via period-doubling bifurcations. We suggest a stochastic sensitivity function technique for the analysis of stochastic cycles. We show that this approach allows to construct the dispersion ellipses of random trajectories for any Poincaré sections, and these ellipses reflect the essential features of a spatial arrangement of random trajectories near deterministic cycles. For the Chen system, we demonstrate a growth of stochastic sensitivity of the forced cycles under transition to chaos.


Cells ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1720
Author(s):  
Kuo-Chieh Liao ◽  
Mariano A. Garcia-Blanco

The importance of transcriptional regulation of host genes in innate immunity against viral infection has been widely recognized. More recently, post-transcriptional regulatory mechanisms have gained appreciation as an additional and important layer of regulation to fine-tune host immune responses. Here, we review the functional significance of alternative splicing in innate immune responses to viral infection. We describe how several central components of the Type I and III interferon pathways encode spliced isoforms to regulate IFN activation and function. Additionally, the functional roles of splicing factors and modulators in antiviral immunity are discussed. Lastly, we discuss how cell death pathways are regulated by alternative splicing as well as the potential role of this regulation on host immunity and viral infection. Altogether, these studies highlight the importance of RNA splicing in regulating host–virus interactions and suggest a role in downregulating antiviral innate immunity; this may be critical to prevent pathological inflammation.


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