DNA or Deoxyribonucleic acid like most biomolecules can undergo a conformational change. During a conformational change the molecule shifts from one molecular configuration to another. This property is crucial to many biological processes, such as DNA replication, transcription and DNA repairing.

Coarse-grained models such as a chain of linearly coupled pendulum in a weak non-linear potential have been used to study the conformational behaviour of the molecule (check the video on the left which shows the simulation of the model). Various reduced-order models have also been proposed that explains well the conformational properties of the full model. These reduced-order models are based on an important approximation, i.e. it assumes the higher-order Fourier modes of the full model doesn't interact among themselves and only interact with the zeroth mode. Our work showed that the approximations on which the reduced-order model are based might not hold if the chain length of the coupled oscillatory model is large. Further, our work highlighted two length regimes of the DNA model where the conformational behaviour can be different.

For more details please check the below link:

1. Banerjee, S., Shah, K., & Sen, S. (2020). On the length scale dependence of DNA conformational change under local perturbation. Biosystems, 198, 104228.

2. Banerjee, S., Shah, K., & Sen, S. (2019). Optimal parameters for conformational change in DNA. Multiscale Simulation and Mathematical Modelling of Complex Biological Systems (MSMM). (Poster presentation)

Check these related articles!

1. Mezić, I. (2006). On the dynamics of molecular conformation. Proceedings of the National Academy of Sciences, 103(20), 7542-7547.

2. Du Toit, P., Mezić, I., & Marsden, J. (2009). Coupled oscillator models with no scale separation. Physica D: Nonlinear Phenomena, 238(5), 490-501.

In nature, oscillatory systems can arise due to a temporal organisation of different biomolecular activities. An interesting property of these biomolecular oscillators is that they can exhibit oscillations that are robust to environmental perturbations. An excellent example of this behaviour can be found in individual cyanobacteria. These microbes are known to exhibit oscillatory bioluminescence that is robust to cell division and cellular noise. Standard mathematical models are often used to understand the mechanisms that contribute to the robust behaviour of bio-molecular oscillators. Particularly, such an approach offers a platform to understand the factors (both intrinsic and structural) that contribute to an oscillator's robustness towards perturbations of both types, steady and dynamic.

In our work, we used a standard mathematical model of a bio-molecular oscillator, repressilator, to understand the factors that can make an oscillator robust to dynamic perturbations such as a pulse. The property of interest is that the oscillator should be able to fast reject any pulse perturbation that is applied to it. To test this robustness property, first, we proposed a settling time metric derived using Floquet theory to quantify the transient response of the repressilator model. Second, using this metric, we studied the role of intrinsic and structural parametric variations on the oscillator's transient response. We found that the variations that improve effective delay in the oscillatory circuit also improves the transient response of the circuit.

For more details check the below link:

1. Banerjee, S., & Sen, S. (2020). Robustness of a biomolecular oscillator to pulse perturbations. IET systems biology, 14(3), 127-132.

2. Banerjee, S., Bokka, V., Sen, S. (2018). Attenuation of pulse disturbances in biomolecular oscillators’, IFAC-PapersOnLine, 51, (1), pp. 301–30.

Check these related articles!

1. Stricker, J., Cookson, S., Bennett, M.R., et al. (2008) A fast, robust and tunable synthetic gene oscillator, Nature, 456, (7221), pp. 516–519

2. Klausmeier, C. A. (2008). Floquet theory: a useful tool for understanding nonequilibrium dynamics. Theoretical Ecology, 1(3), 153-161.