Antibody i-Patch: Paratope prediction

  Paratope: Antibody i-Patch: Antibody contact residues prediction Binding likelihood score of each residue $latex a$: $latex p_a = \frac{\frac{f^{con}_a}{f^{non}_a}}{\frac{\sum f^{con}_b}{\sum f^{non}_b}}$ where $latex p_a $ is the propensity to be in contact, $latex f^{con}_a$ and $latex f^{non}_a$ are the surface frequency of residue $latex a$ to be in contact ($latex con$) and not to be in … Continue reading Antibody i-Patch: Paratope prediction

True stress, and relative stress (Finite Deformation)

I mean, stress tensor. Finite element analysis was, in its early days, proposed for engineering solutions to dam constructions - by discretising a continuous domain into smaller elements and approximating the displacements of each elements upon loading. A major advantage of FEM over FDM is its ability to handle complex geometry: in FEM, the domain … Continue reading True stress, and relative stress (Finite Deformation)

Finite Element Method (Weak form)

In order to apply Finite Element Method to solve PDEs, we need to convert the PDEs into an equivalent "weak form". Example: Axially loaded Elastic Bar Strong Form: $latex \frac{d}{dx}\big(AE\frac{du}{dx}\big)+b=0$ with boundary conditions: at $latex x=0$, traction/force per unit area $latex \bar{t}$, is prescribed: $latex \sigma(x=0) = \big(E\frac{du}{dx}\big)_{x=0}=\frac{p(0)}{A(0)}=-\bar{t}$ at $latex x=l$, displacement $latex \bar{u}$ is … Continue reading Finite Element Method (Weak form)

Finite Element Method (Simplex, Linear Elastic)

Finite Element method is a numerical method, rather than analytic method of solving PDEs. Interpolation function Defines the type of polynomials used approximate the real solution Higher order polynomials have some flexibilities to approximate the actual solution more accurately However it requires more information and operations to compute a higher order element. For example, in 1D, a … Continue reading Finite Element Method (Simplex, Linear Elastic)

Finite Element Method (Simplest case)

Motivation: Approximating solutions to ODE/PDE in a complex geometry Steps: Domain Discretisation Derivation of Equations Assemble Element Equations Boundary Conditions Solution Case: Assume a cylinder with radius $latex R$ and length $latex L$. Changes in Temperature: $latex \hat{\theta} = (T - T_{env})$ Position of node: $latex \eta = \frac{x}{L}$ Constant: $latex \mu^2 = L^2 \frac{2h}{kR}$ … Continue reading Finite Element Method (Simplest case)

An alternative perspective to differential equations systems

Foreword: In biological system modelling, often we are faced with a (huge) set of differential equations. They describe physical phenomena and are therefore relatively easy to construct and inspect if the system was constructed in the right way. However, solving these are computationally taxing and there is no way to predict the outcome just by … Continue reading An alternative perspective to differential equations systems