Research Interests:
Broad Research areas:
Chemical kinetics in Condensed phase.
Statistical view of Biological dynamics.
KEYWORDS : Rate kinetics, First Passage Time Distribution, Polymer Looping, End-to-End looping, Reaction Diffusion systems, energy-transfer processes in chemical reactions, Green's Function, Laplace domain, Time domain results
1. Thesis Title: Theoretical investigations of looping of a long chain polymer molecule in dilute solution
Supervisor : Dr. Aniruddha Chakraborty
Ph.D. Synopsis file
Thesis Chapters :
1. Introduction
2. Investigation of end-to-end irreversible looping process: point sink model
3. Investigation of end-to-end reversible looping process: point coupling model
4. Investigation of end-to-end looping and un-looping kinetics: point sink model and beyond
5. End-to-end looping dynamics: An exact study of a time-domain solution for Dirac delta function sink of
time dependent strength.
6. Summary and Future Scope
Flexible polymers:
Understanding the irreversible and reversible looping kinetics of a long flexible chain polymer molecules in solution has been an interesting problem for both experimentalists and theoreticians. In our model, the dynamics of end-to end distribution is mathematically represented by a Smoluchowski-like equation which considers the Brownian motion of the individual monomers on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface . Exact modelling of end-to-end looping process is ensured by adding a sink of finite strength for irreversible model and by using a coupling function in two state reversible models. Several experimentally important parameters governing the process is also incorporated. The Green's function method in absence of sink is used for modelling the phenomenon in Laplace domain . Furthermore we have incorporated the effect of all other chemical reactions involving either one or both of the end-group on rate of end-to-end loop formation.
References:
- Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delta function sink model, M. Ganguly* & A. Chakraborty, Physica A, 484, 163 (2017).
- Exploring the role of relaxation time, bond length and the length of the polymer chain in the end-to-end looping kinetics of a long polymer chain in solution. An exact analytical model, M Ganguly, A Chakraborty
Chemical Physics Letters 733, 136673 (2019) - Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delocalized sink model, M. Ganguly* & A. Chakraborty [revision] (2020).
- Understanding the reversible looping kinetics of a long chain polymer molecule in solution with Dirac Delta coupling. An exact analytical perspective. M. Ganguly, A. Chakraborty, Physica A, 536, 122509 (2019).
- Understanding reversible looping kinetics of a long polymer molecule in solution. Exact Solution for delocalized coupling model, M. Ganguly* & A. Chakraborty , Physica Scripta, 95 , 115006 (2020).
Unfortunately, the biopolymers like DNA, protein, actin, and microtubules have too much internal stiffness to be successfully modelled as flexible chains. Smith et al., have shown that a semiflexible polymer model is undistinguished while considering the case for a long ssDNA. Also it is seen in experiments that the reactive events concerning biopolymers like proteins follow strongly a nonexponential (power law) decay kinetics even in the long time. Then a flexible chain model can no longer adequately describe the dynamics where there is non-exponential survival probability only at small to intermediate times but exponential decay in the long-time limit. Therefore, we try to model the end-to-end distribution and also try to derive analytical expressions depicting the kinetics of looping of semiflexible polymers in solution . We use generalized random walks and give simple expression for the end-to-end distribution function that stands accurate over a wide range of stiffness. This study is important for further theoretical progress in understanding the properties of stiff chains.
References:
- Dynamics of semiflexible polymer end-to-end distribution and barrierless chemical reactions using Fractional diffusion equation. An exact analytical model., M.Ganguly, A. Chakraborty ,Physica Scripta. (under review)
I shall perform Brownian dynamics simulation studies of looping of a single polymer chains to to see how ' shape of the sink function' decides the looping dynamics. Also we have found the end-to-end autocorrelation function for the end-to-end distribution of a long chain polymer by Brownian Dynamics Simulation using Python environment.
References:
- Analytical expression for end-to-end- auto correlation function of a long chain polymer molecule in solution, M. Ganguly* & A. Chakraborty, Chem. Phys. Lett [revision] (2020)
3. Rate calculation for end-to -end polymer looping phenomenon in time domain
Obviously, even the most promising analytical model would also involve solving the equation in frequency domain due to simplicity in calculations, but in reality, the experimental data are commonly generated and inferred in the time domain. Since solving the Smoluchowski equation with a Dirac delta sink for harmonic potential is beyond the scope of standard analytical methods thus researchers have tried various alternative methods to solve such PDE's. One of such method involves the Laplace transform of Smoluchowski-like equation with a Dirac delta sink of infinite strength. The method of adding sink term where the sink is a Dirac delta function makes it analytically tractable. This has been an unsolved problem for a long time and holds immense importance as a method for not only understanding the rates of the polymer looping but also in understanding several other reaction diffusion scenarios. Our analytical procedure, based on the simplest manoeuvre of Galelei transformation, avoids the Laplace transformations used in previous analytical theories and is thus useful for fitting the molecular dynamics simulation data and force distribution data in real time domain. By using such transformation, the solution for the flat potential converges with the solution for harmonic potential. We use appropriate delta function sink with finite strength rather than pinhole sink with infinite decay, to obtain the solution of the Smoluchowski-like equation. This method provides an alternative and robust way to analytically solve the entire looping processes in time domain.
References
- Diffusion-reaction approach to polymer cyclization in solution: Exact time domain solution for Dirac delta function sink model, M.Ganguly , A. Chakraborty, Chemical Physics (under review)
5. Morphogen Gradient Analysis :
I derived an analytical solution to time dependent Smoluchowski- like equation for Bicoid morphogen gradient in Fruit fly patterning. Morphogen gradients provide embryonic tissues with positional information by inducing
target genes at different concentration thresholds and thus at different positions. The Bicoid protein gradient plays a crucial role in determining the anterior body pattern of Drosophila embryos. This gradient is the classic
example of morphogen-mediated patterning of a developing metazoan and serves as a major topic for mathematical modeling. Bicoid can be a simple case of reaction-diffusion system. The variation in morphogen concentration across the embryo defining the anterior posterior segments, obeys simple reaction diffusion equations. The reaction being the degradation of Bicoid protein with some rate which is produced at source
following which it diffuses along the anterior-posterior axis. I tried to model qualitatively and quantitatively the rate of morphogen diffusion by a simple model showing the entire distribution varying with time.
References:
- A time-dependent Morphogen Gradient Analysis: An Exact Analytical Method, M. Ganguly, A. Chakraborty , Chem. Phy. Lett.(under review)
6. Assessment of Oxidant and Antioxidant Status of Red Blood Cells In Bronchial Asthma And Alteration In Membrane Protein
In the present study we observed that in asthma there is no difference in the yield of number of erythrocytes. The total protein content of the membrane was significantly higher in asthmatics than the healthy controls.
In this study, patients with asthma have shown increased oxidative stress which was evidenced by increased protein carbonyls (P˂0.0001) and increased lipid peroxidation products (P˂0.0018) indicating increased free radical injury in asthmatics. This is accompanied by alterations in several antioxidants in blood. A compensatory increase in the level of total blood Glutathione (P˂0.0023) was observed after the increased free radical injury. In Red Blood Cells in asthmatic patients compared to healthy control subjects, statistically significant reduction in the glutathione peroxidase activity (P˂0.0035) was observed with a concomitant decrease in the red blood cell catalase activity (P˂0.0125).
The resolution of the membrane proteins on SDS-PAGE resolved different protein profile of asthmatics than healthy controls. This suggested qualitative and quantitative alteration in protein profile of asthma, which should be explored further in designing studies on a larger number of population involving various ethnic groups
7. Molecular Docking and Simulations study of phytoconstituents from medicinal plant compounds against tuberculosis, an in silico analysis. (ongoing, will be updated soon)