Muhammad Shahzad

Free energy calculations of protein-water complexes with Gromacs

We used GFP(Green Fluorescent Protein) to understand its basic structure, adding solvent water around the GFP, minimize and equilibrating it using molecular dynamics simulation with Gromacs. Gromacs is an open source software and widely used in molecular dynamics simulation of biological molecules such as proteins, and nucleic acids (DNA AND RNA-molecules). We employ the CHARMM (Chemistry at HARvard Molecular Mechanics) program for the force fields which enable the potential energy of a molecular system to be calculated rapidly. In this particular simple molecular mechanics interaction fields (CHARMM), the force fields consists of stretching energy, bending energy and torsion energy. The non-bond interaction energy is modeled by Lennard-Jones potential. The pdb2gmx gromacs command is implemented to obtained the basic coordinate file and topology for the particular system from the GFP PDB file (1gfl.pdb). We enclosed water molecule in a rhombic dodecahedron box having size 0.5nm, and protein are embedded in solvent water. The steepest descent method (first-order minimization) are implemented to calculate the local energy minimum with 104-steps. The stability of protein with solvent water molecule are analyzed by measuring the root-mean square displacement (RMSD) of all atoms. It was shown with help of figure that RMSD initially increases rapidly in the first part of simulation, but become stable around 0.14nm, roughly the resolution of the X-ray structure. The difference is partly due to the moving and vibration of atoms around an equilibrium structure. Secondary structure of GFP protein is presented with the help of DSSP-program.

Computer simulation of knotted proteins unfold and translocation through nano-pores

We study the unfold and translocation of knotted protein, YibK and YbeA, through α-hemolysin nano-pore via a coarse grained computational model. We observe that knot of protein unfold in advance before the translocation take place. We also characterized the translocation mechanism by studying the thermodynamical and kinetic properties of the process. In particular, we study the average of translocation time, and the translocation probability as a function of pulling force F acting in the channel. In limit of low pulling inward constant force acting along the axis of the pore, the YibK knotted protein takes longer average translocation time as compare to YbeA knotted protein.

Translocation of structured biomolecule through a vibrating nanopore

We study the effect of fluctuating environment in protein transport dynamics. In particular, we investigate the translocation of a structured biomolecule (protein) across a temporally modulated nano-pore. We allow the radius of the cylindrical pore to oscillate harmonically with certain frequency and amplitude about an average radius. The protein is imported inside the pore whose dynamics is influences by the fluctuating nature of the pore. We investigate the dynamic and thermodynamical properties of the translocation process by revealing the statistics of translocation time as a function of the pulling inward force acting along the axis of the pore, and the frequency of the time dependent radius of the channel. We also examine the distribution of translocation time in the intermediate frequency regime. We observe that the shaking mechanism of pore leads to accelerate the translocation process as compared to the static channel that has a radius equal to the mean radius of oscillating pore. Moreover, the translocation time shows a global maximum as a function of frequency of the oscillating radius, hence revealing a resonant activation phenomenon in the dynamics of protein translocation.

Mechanical unfold and transport of Green Florescent Protein through a nanopore

We report the unfold and trans-location of Green Fluorescent protein (GFP) mechanically by a constant force acting parallel along the axis of nanopore. A coarse-grained numerical model (Go-model) were implemented both for the protein and the nanopore. Detail description of each peptide unfold by the constant force is presented. Depending on the GFP topological structure, β-sheet barrel, the protein unfold and transport as a double loop conformation in the confinement geometry. The result is compared with maltose binding protein (MBP), having majority of alpha helix, which unfold and trans-locate as single profile conformation through nanopore. The result emphasis that protein with different topological structure unfold and trans-locate in different fashion depending on their native fold structure.

Polymer translocation through nano-pores: influence of pore and polymer deformation

We have simulated polymer translocation across the a α-hemolysin nano-pore via a coarse grained computational model for both the polymer and the pore. We simulate the translocation process by allowing the protein cross a free-energy barrier from a metastable state, in the presence of thermal fluctuations. The deformation in the channel, which we model by making the radius of pore change from large to small size, can be originated by the random and non-random (systematic) cellular environment, drive out the polymer out of equilibrium during the transport dynamics. We expect that in more realistic conditions, effects originating on the translocation phenomena due to the deformability of the nano-pore can either decrease or increase the transport time of biomolecule passing through the channel. Deformation in channel can occurred because the structure of α-hemolysin channel is not completely immobile, hence a small pore deformation can be occurred during translocation process. We also discuss the effects of polymer deformation on the translocation process, which we achieve by varying the value of the empirical and dihedral potential constants. We investigate the dynamic and thermodynamical properties of the translocation process by revealing the statistics of translocation time as a function of the pulling inward force acting along the axis of the pore under the influence of small and large pore. We observed that a pore with small size can speed down the polymer translocation process, especially at the limit of small pulling force. A drastic increase in translocation time at the limit of low force for small pore clearly illustrate the strong interaction between the transport polymer and pore. Our results can be of fundamental importance for those experiments on DNA-RNA sorting and sequencing and drug delivery mechanism for anti-cancer therapy.

Time-Periodically Driven Brownian Motion of Rigid Rod in one dimensional space

In this paper we discuss a simple theoretical approach, taken from the theory of stochastic processes to understand the basic phenomenology of protein translocation through a flickering pore. In this theoretical approach we investigate the dynamics of Brownian particle driven by a periodically driving force. This toy model is further extended by considering the Langevin equation with constants drift and time dependent variance. Using the first passage time theory we derived the formalism for probability density function to comprehend the translocation process occurring in the presence of fluctuating environment.

Computational Analysis of Complex Population Dynamical Model with Arbitrary Order

This paper considers the approximation of solution for a fractional order biological population model. The fractional derivative is considered in the Caputo sense. By using Laplace Adomian decomposition method (LADM), we construct a base function and provide deformation equation of higher order in a simple equation. The considered scheme gives us a solution in the form of rapidly convergent infinite series. Some examples are used to show the efficiency of the method. The results show that LADM is efficient and accurate for solving such types of nonlinear problems.

The Application of Homotopy Analysis Method to Non-linear Reaction Diffusion System

In this paper, the homotopy analysis method is applied to non-linear reaction diffusion system of Lotka-Volterra type subject of extensive numerical and analytical studies. The comparisons of the other analytical techniques are presented in tables to show the accuracy of this method. The results show that the homotopy analysis method is more reliable than the other available techniques giving the advantage of the choice of some quantities such as initial guess, auxiliary function, auxiliary parameter that play an important role in the convergence of the series solution.

Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

The fractional order Susceptible-Infected-Recovered (SIR) epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.

Fuzzy soft set over a fuzzy topological space

AbstractThe aim of this article, we combine the fuzzy soft set and fuzzy topological space. We introduce the notion of fuzzy soft set over common universe of fuzzy topological space. We defined quasi-open fuzzy soft set over fuzzy topological space and we study the properties of extended union of two quasi-open fuzzy soft set over fuzzy topological space. We study “OR” and “AND” operations of quasi-open fuzzy soft set over fuzzy topological space. We also define open fuzzy soft set, b-open fuzzy soft set and b-closed fuzzy soft set over fuzzy topological space. We give some characterizations of these concepts.