3 research outputs found
Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty
Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncertainty and bound the variation in the magnitude of the input-output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers
A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating
An important part of system modeling is determining parameter values,
particularly for biomolecular systems, where direct measurements of individual
parameters are typically hard. While Extended Kalman Filters have been used for
this purpose, the choice of the process noise covariance is generally unclear.
In this chapter, we address this issue for biomolecular systems using a
combination of Monte Carlo simulations and experimental data, exploiting the
dependence of the process noise covariance on the states and parameters, as
given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering
technique by updating the process noise covariance at each time step based on
estimates. We compare the performance of this framework with different fixed
values of process noise covariance in biomolecular system models, including an
oscillator model, as well as in experimentally measured data for a negative
transcriptional feedback circuit. We find that the Extended Kalman Filter with
such process noise covariance update is closer to the optimality condition in
the sense that the innovation sequence becomes white and in achieving a balance
between the mean square estimation error and parameter convergence time. The
results of this chapter may help in the use of Extended Kalman Filters for
systems where process noise covariance depends on states and/or parameters.Comment: 23 pages, 9 figure
Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty
Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncertainty and bound the variation in the magnitude of the input-output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers