scholarly journals Remarks on GRN-type systems

4open ◽  
2020 ◽  
Vol 3 ◽  
pp. 8
Author(s):  
Eduard Brokan ◽  
Felix Sadyrbaev
Keyword(s):  
Gene Regulatory Networks ◽  
Critical Points ◽  
Regulatory Networks ◽  
Three Dimensional ◽  
Type Systems ◽  
Dimensional System ◽  
Two Dimensional ◽  
Multiple Parameters ◽  
Gene Regulatory ◽  
Two Dimensional System

Systems of ordinary differential equations that appear in gene regulatory networks theory are considered. We are focused on asymptotical behavior of solutions. There are stable critical points as well as attractive periodic solutions in two-dimensional and three-dimensional systems. Instead of considering multiple parameters (10 in a two-dimensional system) we focus on typical behaviors of nullclines. Conclusions about possible attractors are made.

scholarly journals Modelling Three Dimensional Gene Regulatory Networks

2021 ◽  
Vol 16 ◽  
pp. 755-763
Author(s):  
Inna Samuilik ◽  
Felix Sadyrbaev
Keyword(s):  
Differential Equations ◽  
Gene Regulatory Networks ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Linear Part ◽  
Three Dimensional ◽  
Special Kind ◽  
Sigmoidal Function ◽  
Solution Vector ◽  
Gene Regulatory

We consider the three-dimensional gene regulatory network (GRN in short). This model consists of ordinary differential equations of a special kind, where the nonlinearity is represented by a sigmoidal function and the linear part is present also. The evolution of GRN is described by the solution vector X(t), depending on time. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way.

Homology, neocortex, and the evolution of developmental mechanisms

Science ◽  
2018 ◽  
Vol 362 (6411) ◽  
pp. 190-193 ◽  
Author(s):  
Steven D. Briscoe ◽  
Clifton W. Ragsdale
Keyword(s):  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Three Dimensional ◽  
Neuronal Cell ◽  
Brain Evolution ◽  
Cell Types ◽  
Biological Organization ◽  
Developmental Evolution ◽  
Processing Pathways ◽  
Gene Regulatory

The six-layered neocortex of the mammalian pallium has no clear homolog in birds or non-avian reptiles. Recent research indicates that although these extant amniotes possess a variety of divergent and nonhomologous pallial structures, they share a conserved set of neuronal cell types and circuitries. These findings suggest a principle of brain evolution: that natural selection preferentially preserves the integrity of information-processing pathways, whereas other levels of biological organization, such as the three-dimensional architectures of neuronal assemblies, are less constrained. We review the similarities of pallial neuronal cell types in amniotes, delineate candidate gene regulatory networks for their cellular identities, and propose a model of developmental evolution for the divergence of amniote pallial structures.

scholarly journals Networks Describing Dynamical Systems

2018 ◽  
Vol 71 (1) ◽  
pp. 39-52
Author(s):  
Eduard Brokan ◽  
Felix Sadyrbaev
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Gene Regulatory Networks ◽  
Critical Points ◽  
Regulatory Networks ◽  
Decisive Role ◽  
Arbitrary Size ◽  
Definite Structure ◽  
Gene Regulatory

Abstract We consider systems of ordinary differential equations that arise in the theory of gene regulatory networks. These systems can be of arbitrary size but of definite structure that depends on the choice of regulatory matrices. Attractors play the decisive role in behaviour of elements of such systems. We study the structure of simple attractors that consist of a number of critical points for several choices of regulatory matrices.

MORPHOLOGICAL EVOLUTION OF DROPLETS IN OSTWALD RIPENING

1991 ◽  
Vol 05 (01) ◽  
pp. 57-63 ◽  
Author(s):  
TATSUHIRO IMAEDA ◽  
KYOZI KAWASAKI
Keyword(s):  
Ostwald Ripening ◽  
Morphological Evolution ◽  
Three Dimensional ◽  
Computation Time ◽  
Multipole Expansion ◽  
Dimensional System ◽  
Two Dimensional ◽  
Ripening Process ◽  
Expansion Theory ◽  
Two Dimensional System

The multipole expansion theory presented recently by the authors for Ostwald ripening in a two-dimensional system is extended to apply to the three-dimensional ripening process. A fairly reasonable computation time is enough to simulate the morphological evolution of many droplets.

HALF-SKYRMION IN SPINOR BOSE–EINSTEIN CONDENSATES

2013 ◽  
Vol 27 (25) ◽  
pp. 1350183 ◽  
Author(s):  
YONG-KAI LIU ◽  
CONG ZHANG ◽  
SHI-JIE YANG
Keyword(s):  
Exact Solutions ◽  
Topological Charge ◽  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System ◽  
Bose Einstein ◽  
Nontrivial Topology

In this paper, we present exact solutions to the F = 1 spinor Bose–Einstein condensates with only spin-independent energy by adopting a method of separating the variables, which exhibit nontrivial topology. These solutions can form solitonic fractional vortex and solitonic half-skyrmion with a Q = 1/2 topological charge in the two-dimensional system. We further address a three-dimensional prototype solution.

Open-framework sodium uranyl selenate and sodium uranyl sulfate with protonated morpholino-N-acetic acid

2019 ◽  
Vol 234 (2) ◽  
pp. 109-118 ◽  
Author(s):  
Oleg I. Siidra ◽  
Evgeny V. Nazarchuk ◽  
Dmitry O. Charkin ◽  
Nikita V. Chukanov ◽  
Alexander Yu. Zakharov ◽  
...  
Keyword(s):  
Acetic Acid ◽  
Sulfuric Acid ◽  
Ir Spectroscopy ◽  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Uranyl Sulfate ◽  
Open Framework ◽  
Two Dimensional System ◽  
Framework Compounds

Abstract The reaction of sodium N-morpholine acetate with selenic and sulfuric acid and uranyl nitrate results in the formation of two novel open-framework compounds, |Na(Hmfa)|[(UO2)2(SeO4)3(H2O)](H2O)2 (NaUSe) and [Na2(SO3OH)(Hmfa)]|(UO2)(SO4)2| (NaUS), respectively. Despite identical synthetic procedures, sulfate structure dramatically differs from selenate compound. Their common feature is an open-framework featuring two-dimensional system of channels occupied by protonated morpholino-N-acetic acid species. Coordination of Na atoms is different. In NaUSe, [(UO2)2 (SeO4)3(H2O)]2− layers are pillared by {Na2O8(H2O)2(Hmfa)2} complexes to form a microporous framework. In NaUS, UO7 and SO4 polyhedra of [(UO2)(SO4)2]2− chains share common oxygen atoms with Na-centered tetrameric complexes providing a three-dimensional integrity of the structure. Both of the compounds are characterized by IR spectroscopy.

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