Ordinary Differential Equation (ODE), Model

2013 ◽  
pp. 1606-1608
Author(s):  
Rui-Sheng Wang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Ode Model

scholarly journals Effects of spatial heterogeneity on bacterial genetic circuits

2019 ◽  
Author(s):  
Carlos Barajas ◽  
Domitilla Del Vecchio
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Spatial Heterogeneity ◽  
Mixed Models ◽  
Mixed Model ◽  
Spatial Effects ◽  
Genetic Circuits ◽  
Association Rate Constant ◽  
Ode Model ◽  
Association Rate

AbstractIntracellular spatial heterogeneity is frequently observed in bacteria, where the chromosome occupies part of the cell’s volume and a circuit’s DNA often localizes within the cell. How this heterogeneity affects core processes and genetic circuits is still poorly understood. In fact, commonly used ordinary differential equation (ODE) models of genetic circuits assume a well-mixed ensemble of molecules and, as such, do not capture spatial aspects. Reaction-diffusion partial differential equation (PDE) models have been only occasionally used since they are difficult to integrate and do not provide mechanistic understanding of the effects of spatial heterogeneity. In this paper, we derive a reduced ODE model that captures spatial effects, yet has the same dimension as commonly used well-mixed models. In particular, the only difference with respect to a well-mixed ODE model is that the association rate constant of binding reactions is multiplied by a coefficient, which we refer to as the binding correction factor (BCF). The BCF depends on the size of interacting molecules and on their location when fixed in space and it is equal to unity in a well-mixed ODE model. The BCF can be used to investigate how spatial heterogeneity affects the behavior of core processes and genetic circuits. Specifically, our reduced model indicates that transcription and its regulation are more effective for genes located at the cell poles than for genes located on the chromosome. The extent of these effects depends on the value of the BCF, which we found to be close to unity. For translation, the value of the BCF is always greater than unity, it increases with mRNA size, and, with biologically relevant parameters, is substantially larger than unity. Our model has broad validity, has the same dimension as a well-mixed model, yet it incorporates spatial heterogeneity. This simple-to-use model can be used to both analyze and design genetic circuits while accounting for spatial intracellular effects.Abstract FigureHighlightsIntracellular spatial heterogeneity modulates the effective association rate constant of binding reactions through a binding correction factor (BCF) that fully captures spatial effectsThe BCF depends on molecules size and location (if fixed) and can be determined experimentallySpatial heterogeneity may be detrimental or exploited for genetic circuit designTraditional well-mixed models can be appropriate despite spatial heterogeneityStatement of significanceA general and simple modeling framework to determine how spatial heterogeneity modulates the dynamics of gene networks is currently lacking. To this end, this work provides a simple-to-use ordinary differential equation (ODE) model that can be used to both analyze and design genetic circuits while accounting for spatial intracellular effects. We apply our model to several core biological processes and determine that transcription and its regulation are more effective for genes located at the cell poles than for genes located on the chromosome and this difference increases with regulator size. For translation, we predict the effective binding between ribosomes and mRNA is higher than that predicted by a well-mixed model, and it increases with mRNA size. We provide examples where spatial effects are significant and should be considered but also where a traditional well-mixed model suffices despite severe spatial heterogeneity. Finally, we illustrate how the operation of well-known genetic circuits is impacted by spatial effects.

Grasp and Orientation Control of an Object by Two Euler–Bernoulli Arms With Rolling Constraints

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Takahiro Endo ◽  
Nobuhiro Shiratani ◽  
Kaiyo Yamaguchi ◽  
Fumitoshi Matsuno
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Lyapunov Functional ◽  
Bending Moment ◽  
Ode Model ◽  
Rotational Angle ◽  
Orientation Control ◽  
Grasping And Manipulation ◽  
Flexible Arms

Abstract This paper focuses on grasping and manipulation of an object by two one-link flexible arms. By taking rolling constraints between the arm tip and the grasped object, the arms have the potential to grasp and manipulate an object at the same time. To realize grasping and manipulation by two flexible arms, a boundary controller is derived from a Lyapunov functional related to the total energy of a dynamic model described by a hybrid partial differential equation-ordinary differential equation (PDE-ODE) model. The derived controller consists of the bending moment at the root of the arm, the rotational angle, and the angular velocity of the motor. In particular, the controller does not need the feedback of the information of the grasped object, and thus, it is easy to implement the controller. Further, it is shown that the derived controller realizes stable grasping and orientation control of the object as well as vibration control of the arms. Finally, experiments and numerical simulations are conducted to investigate the validity of the derived boundary controller.

scholarly journals On Nonlinear Profile Decompositions and Scattering for an NLS–ODE Model

2018 ◽  
Vol 2020 (18) ◽  
pp. 5679-5722
Author(s):  
Scipio Cuccagna ◽  
Masaya Maeda
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Hamiltonian System ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Golden Rule ◽  
Simplified Model ◽  
Radial Solutions ◽  
Fermi Golden Rule ◽  
Ode Model

Abstract In this paper, we consider a Hamiltonian system combining a nonlinear Schrödinger equation (NLS) and an ordinary differential equation. This system is a simplified model of the NLS around soliton solutions. Following Nakanishi [33], we show scattering of $L^2$ small $H^1$ radial solutions. The proof is based on Nakanishi’s framework and Fermi Golden Rule estimates on $L^4$ in time norms.

scholarly journals Reparametrizing the Sigmoid Model of Gene Regulation for Bayesian Inference

2018 ◽  
Author(s):  
Martin Modrák
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Monte Carlo ◽  
Gene Regulation ◽  
State Of The Art ◽  
Source Code ◽  
Linear Ordinary Differential Equation ◽  
Ode Model ◽  
Detailed Explanation ◽  
Fully Bayesian

AbstractThis poster describes a novel reparametrization of a fre-quently used non-linear ordinary differential equation (ODE) model of gene regulation. We show that in its commonly used form, the model cannot reliably distinguish between both quantitatively and qualitatively different parameter combinations. The proposed reparametrization makes inference over the model stable and amenable to fully Bayesian treatment with state of the art Hamiltonian Monte Carlo methods.Complete source code and a more detailed explanation of the model is available at https://github.com/cas-bioinf/genexpi-stan.

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