Critical role of DNA unwinding and Cas9 conformational changes in modelling off-target effects

CRISPR-Cas9 off-target effects interfere with the ability to accurately perform genetic edits. To predict off-target effects CRISPR-Cas9 researchers perform high throughput guide RNA mismatch and bulge experiments and then use the data to fit thermodynamic binding models. While impactful from an engineering perspective such models are not based on the experimentally observed target interrogation process and thus incorrectly measure the energetic effects mismatches have on the system. In this work we convert an experimentally deduced qualitive model of target interrogation to a linear ODE model and demonstrate that the mismatch tolerance patterns observed in experiments do not need to be caused by differences in energetic penalties of mismatches but rather are emergent effects of the timing and coordination of target DNA unwinding and Cas9 conformational changes.

Helicoidal surfaces with prescribed curvatures in a conformally flat 3-space

In this paper, we study a conformally flat 3-space 𝔽 3 {\mathbb{F}_{3}} which is an Euclidean 3-space with a conformally flat metric with the conformal factor 1 F 2 {\frac{1}{F^{2}}} , where F ⁢ ( x ) = e - x 1 2 - x 2 2 {F(x)=e^{-x_{1}^{2}-x_{2}^{2}}} for x = ( x 1 , x 2 , x 3 ) ∈ ℝ 3 {x=(x_{1},x_{2},x_{3})\in\mathbb{R}^{3}} . In particular, we construct all helicoidal surfaces in 𝔽 3 {\mathbb{F}_{3}} by solving the second-order non-linear ODE with extrinsic curvature and mean curvature functions. As a result, we give classification of minimal helicoidal surfaces as well as examples for helicoidal surfaces with some extrinsic curvature and mean curvature functions in 𝔽 3 {\mathbb{F}_{3}} .

Reproducing kernel functions and homogenizing transforms

A lot of problems of the physical world can be modeled by non-linear ODE with their initial and boundary conditions. Especially higher order differential equations play a vital role in this process. The method for solution and its effectiveness are as important as the modelling. In this paper, on the basis of reproducing kernel theory, the reproducing kernel functions have been obtained for solving some non-linear higher order differential equations. Additionally, for each problem the homogenizing transforms have been obtained.

Rapid exponential stabilization by boundary state feedback for a class of coupled nonlinear ODE and $ 1-d $ heat diffusion equation

<p style='text-indent:20px;'>In this paper, we solve the problem of rapid exponential stabilization for coupled nonlinear ordinary differential equation (ODE) and <inline-formula><tex-math id="M2">\begin{document}$ 1-d $\end{document}</tex-math></inline-formula> unstable linear heat diffusion. The control acts at a boundary of the heat domain and the heat equation enters in the ODE by Dirichlet connection. We show that the infinite dimensional backstepping transformation introduced recently for stabilization of coupled linear ODE-PDE can deal with a nonlinear ODE and obtain a global stabilization result. Our result is innovative and no similar result can be found in the literature as it combines the three following factors, i) nonlinear term in the ODE subsystem, ii) unstable PDE subsystem and iii) mixed boundary condition. Not only this, the techniques used in this work can provide answers to fundamental questions, such as the stabilization of coupled systems where both subsystems may contain nonlinear terms.</p>

Graphene-based Newtonian nanoliquid flows over an inclined permeable moving cylinder due to thermal stratification

Heat flux enhancement due to utilization of graphene, graphene nanoplatelets, and graphene oxides in water/ethylene-glycol based nanofluids over an inclined permeable cylinder is focused in the present study. The governing PDE are reformulated into non-linear ODE by applying similarity expressions. A shooting procedure is opted to reformulate the equations into boundary value problems which are solved by employing a numerical finite difference code in MATLAB. The effects of constructive parameters toward the model on non-dimensional velocity and temperature dissemination, reduced skin friction coefficient and reduced Nusselt number are graphically reported and discussed in details. It is observed that by in-creasing the thermal stratification and inclination angle, the temperature profile and Nusselt number for the selected nanofluids will be decreased.

Overview of Gene Regulatory Network Inference Based on Differential Equation Models

: Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.

SOLVING SOME IMPORTANT NONLINEAR TIME-FRACTIONAL EVOLUTION EQUATIONS BY USING THE (G’/G)-EXPANSION METHOD

The aim of the present study is to find the exact solutions for three generalized nonlinear time-fractional evolution equations, Kaup-Kupershmidt equation, Burgers-Fisher equation and, Shallow Water Wave equation. By using the (G’/G)-expansion method and depending on second order linear ODE as well as the complex transformation, three kinds of solutions (hyperbolic, trigonometric, and rational) are obtained. With the help of Mathematica software package, difficult algebraic systems are solved and surfaces of some particular solutions of the equations under study are plotted.

Linear ODE with nonlocal boundary conditions and Green’s functions for such problems

In this article we investigate a formula for the Green’s function for the n-orderlinear differential equation with n additional conditions. We use this formula for calculatingthe Green’s function for problems with nonlocal boundary conditions.