AWAITED
1. M. Ganguly and A. Chakraborty, Diffusion-reaction approach to polymer cyclization in solution: Exact time domain solution for Dirac delta function sink model, Chem. Phys. 2020. (submitted)
- Brief: We use the Smoluchowski equation for the harmonic-like potential to represent the distribution of the end-to-end distance of the polymer in this model, wherein the looping process is ensured by adding a Dirac delta function sink (reactive channel) with time-dependent strength (reaction area) at any arbitrary distance. Looping is believed to occur as a result of the creation of at least one bond between the polymer's ends. The electrostatic force between the end atoms is determined by the orientation of surrounding water molecules as well as the structure of the actual polymer molecule. Although the functional form of how this sink’s strength varies with time is unknown, different time-dependent functions are likely to describe the strength of this Dirac delta function sink for different systems. We use the exponential function to model the time dependence of the Dirac delta function sink strength in this paper. It is important to note that using this most generalized version of the end-to-end looping model of a polymer in solution, we can fit published time- domain experimental data from other research groups that would otherwise be difficult to fit satisfactorily.
- Brief: Experiments and simulations have recently indicated that a few of the contributing factors for intra-chain loop formation are solvent quality, solvent friction, hydrodynamic interactions, temperature, etc. They play a significant role in protein folding by influencing the looping kinetics. However, we propose that self-organized criticality phenomena may be employed to explain the source of stochastic variation in the end-to-end distribution, which leads to polymer molecule looping in the solvent. We study this phenomenon and build an analytical model to calculate the survival probability framework to understand the nature of self-organized criticality and see how interactions at different concentrations alter the diffusion of a single long-chain polymer. This model may describe the nature of fluctuation spreading across the polymer system and model. Using our model, we see that as a result of this occurrence, the system adjusts to its looping situation without any external modulation. An analytical expression is presented for the probability distribution of the duration of disturbances traversing the system. This distribution is scale-invariant, resulting in a power law over multiple orders of magnitude, which is a prerequisite of self-organized criticality. We also show how different factors, such as polymer length, effective bond length, and relaxation time, affect the end-to-end distribution's survival probability. This model's use may be expanded to solve problems like electronic relaxation in solution, reaction diffusion systems, and so on .
Alzheimer's is a brain disorder encountered generally by aged people where in alpha, beta tangles called plaques form in the brain resulting in disruption of neuronal signals. This condition results in memory loss, confusion, loss of thinking ability and can result in death in later stage. Alzheimer's and other forms of dementia are now becoming a very serious concern since they are affecting around on-third of the population, if we talk about United States especially. Mathematical modelling of these life threatening diseases is being done more frequently and on a serious note because that gives us an idea about how severe the problem has become (stage of the disease), what are the factors and how they take part in the progression of the disease and the most important, how we can manipulate these parameters involved so as to get the desired results and then if required how to implement the solution in real world.
4. M. Ganguly and A. Chakraborty, Effect of different architecture of sink function beyond Dirac delta sink model in looping kinetics of a long polymer molecule in solution, Mol. Phys. 2020. (submitted)
- Brief: We propose a very simple one dimensional analytically solvable model for understanding the problem of long chain polymer end relaxation in solution. This problem is modeled by a monomer diffusing under the influence of parabolic potential in presence of a sink of ultra-short width. The diffusive motion is described by the Smoluchowski equation and shape of the sink is represented by 1) Truncated Gaussian, 2) Truncated exponential and 3) ultra-short rectangular function at arbitrary position. Rate constants are found to be sensitive to the shape of the sink function, even though the width of the sink is too small. This model is of considerable importance as a realistic model in comparison with the point sink model for understanding the problem of polymer looping in solution.
5. M. Ganguly and A. Chakraborty, Dynamics of semiflexible polymer end-to-end distribution and barrierless chemical reactions using Fractional diffusion equation. An exact analytical model. ,Physica Scripta, 2021 (under review)
- Brief : We propose a model for understanding the dynamics of looping of a long chain semi-flexible polymer in solution. Semi-flexible nature of polymer is modeled by using fractional diffusion motion of the end-to-end distance. In the continuum limit, the problem has been modeled mathematically using a modified Smoluchowski equation with a point sink to account for the slower dynamics of the chain in the solvent. We try to see how the Riemann–Liouville derivative slows the dynamics of the process influences the looping dynamics of the system.
- Brief : We provide a general analytical model to understand the dynamics of non-uniform Bicoid morphogen gradient which leads to patterning in the fruit fly, Drosophila Melanogaster. The model links both diffusion and degradation by using a Smoluchowski-like equation alongside a localized sink and a degradation term. We use Green's function in the absence of a sink.The morphogen concentration shows Arrhenius decay as the distance increases from the source of production. We extrapolate the sink function for more general cases of narrow gaussian and narrow exponential and try to find the behavior of decay of morphogen in presence of various sink strengths.
PUBLISHED
2020
- Opening of a weak link of a closed looped polymer immersed in solution. Analytical modelling using a delta function sink, Phys. Scr. , 96, 015003 (2020) (link)
- Interpreting the looping rates of a polymer molecule in solution: Exact solution using a simple analytical method, Chem. Phys. Lett., 749, 137370, (2020) (link)
- The two-state reversible kinetics of a long polymer molecule in solution with a delocalized coupling term. An exact analytical model, Phys. Scr, 95 , 115006 (2020) (link)
- 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 (2019) 122509. (link)
- Exploring the role of relaxation time, bond length and length of the polymer chain in the kinetics of end-to-end looping of a long polymer chain. An exact analytically solvable model, M. Ganguly & A. Chakraborty, Chem. Phys. Lett. , 733 (2019) 136673. (link)
- Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delta function sink model, M. Ganguly & A. Chakraborty, Physica A , 484 (2017) 163 . (link)
Google Scholar: https://scholar.google.co.in/citations?user=gnPz4mkAAAAJ&hl=en&oi=ao