Abhishek Dey

Temperature is an important determinant of bacterial growth. While the dependence of bacterial growth on different temperatures has been well studied for many bacterial species, prediction of bacterial growth rate for dynamic temperature changes is relatively unclear. Here, the authors address this issue using a combination of experimental measurements of the growth, at the resolution of 5 min, of Escherichia coli and mathematical models. They measure growth curves at different temperatures and estimate model parameters to predict bacterial growth profiles subject to dynamic temperature changes. They compared these predicted growth profiles for various step‐like temperature changes with experimental measurements using the coefficient of determination and mean square error and based on this comparison, ranked the different growth models, finding that the generalised logistic growth model gave the smallest error. They note that as the maximum specific growth increases the duration of this growth predominantly decreases. These results provide a basis to compute the dependence of the growth rate parameter in biomolecular circuits on dynamic temperatures and may be useful for designing biomolecular circuits that are robust to temperature.

The dynamical behaviour of biomolecular systems changes between either linear or nonlinear in different parameter regimes. Data-driven techniques used for modelling the biomolecular systems either model the biomolecular systems as the linear time-invariant systems in all parameter regimes or use computationally expensive nonlinear modelling structures to represent their behaviour. Furthermore, these modelling techniques require time-consuming experimental design for data acquisition. Therefore, in this paper, firstly, we utilize the broadband multisine signals to acquire the data in one single experiment. Secondly, we use a novel local polynomial approach to estimate nonparametrically the best linear approximation (BLA) of the biomolecular system in the frequency band of interest. Finally, the usefulness of the technique is demonstrated through simulation case-studies for obtaining the BLA for two biomolecular systems.

The period and amplitude of biomolecular oscillators are functionally important properties in multiple contexts. For a biomolecular oscillator, the overall constraints in how tuning of amplitude affects period, and vice versa, are generally unclear. Here, the authors investigate this co‐variation of the period and amplitude in mathematical models of biomolecular oscillators using both simulations and analytical approximations. The authors computed the amplitude–period co‐variation of 11 benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, classifying the various co‐variation patterns such as a simultaneous increase/decrease in period and amplitude. Next, the authors repeated the classification using a power norm‐based amplitude metric, to account for the amplitudes of the many biomolecular species that may be part of the oscillations, finding largely similar trends. Finally, the authors calculate ‘scaling laws’ of period–amplitude co‐variation for a subset of these benchmark oscillators finding that as the approximated period increases, the upper bound of the amplitude increases, or reaches a constant value. Based on these results, the authors discuss the effect of different parameters on the type of period–amplitude co‐variation as well as the difficulty in achieving an oscillation with large amplitude and small period.

Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, the authors adapt and develop the method of describing functions to represent the input–output responses of biomolecular signalling systems. They approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearisation. Furthermore, they develop analytical upper bounds for the computational error estimates. Finally, they use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can add more insight into the local behaviour of these systems than standard linearisation, compute responses to other periodic inputs and to analyse limit cycles.

Developing tools to understand biomolecular systems is important both for the analysis of naturally occurring systems as well as for the design of new ones. However, there is a need to develop new tools suited for analysis of such systems and to adapt existing tools used in other similar contexts. Here, we apply the method of sinusoidal-input describing function for the analysis of such systems using a combination of analytic and computational means. Using this technique, we approximate the input-output response of simple representative biomolecular signaling systems exhibiting different saturating as well as hysteretic input-output maps. We investigate the dependence of this approximation on system parameters. Finally, we estimate the error involved in these approximations finding that they are always better than standard linearization. These results provide system approximations that can help to compute system response to other periodic inputs as well as analysis and design of cell behaviour such as limit cycles and frequency entrainment.

Robust compensation in the continuous domain using high frequency periodic controllers was proposed in [6] and its application to Cart-Inverted Pendulum system was demonstrated in [7]. Again, a method for robust compensation in discrete domain using 2-periodic controllers has been proposed in [11]. In this paper this 2-periodic controller is applied for robust compensation of the Cart-Inverted Pendulum system. The improvements in results (relative to linear-discrete-time-invariant (LDTI) controllers) are compared in simulation with the same obtained in [7].