758 research outputs found
Shaping Pulses to Control Bistable Biological Systems
In this paper we study how to shape temporal pulses to switch a bistable
system between its stable steady states. Our motivation for pulse-based control
comes from applications in synthetic biology, where it is generally difficult
to implement real-time feedback control systems due to technical limitations in
sensors and actuators. We show that for monotone bistable systems, the
estimation of the set of all pulses that switch the system reduces to the
computation of one non-increasing curve. We provide an efficient algorithm to
compute this curve and illustrate the results with a genetic bistable system
commonly used in synthetic biology. We also extend these results to models with
parametric uncertainty and provide a number of examples and counterexamples
that demonstrate the power and limitations of the current theory. In order to
show the full potential of the framework, we consider the problem of inducing
oscillations in a monotone biochemical system using a combination of temporal
pulses and event-based control. Our results provide an insight into the
dynamics of bistable systems under external inputs and open up numerous
directions for future investigation.Comment: 14 pages, contains material from the paper in Proc Amer Control Conf
2015, (pp. 3138-3143) and "Shaping pulses to control bistable systems
analysis, computation and counterexamples", which is due to appear in
Automatic
Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator
In this paper, we further develop a recently proposed control method to
switch a bistable system between its steady states using temporal pulses. The
motivation for using pulses comes from biomedical and biological applications
(e.g. synthetic biology), where it is generally difficult to build feedback
control systems due to technical limitations in sensing and actuation. The
original framework was derived for monotone systems and all the extensions
relied on monotone systems theory. In contrast, we introduce the concept of
switching function which is related to eigenfunctions of the so-called Koopman
operator subject to a fixed control pulse. Using the level sets of the
switching function we can (i) compute the set of all pulses that drive the
system toward the steady state in a synchronous way and (ii) estimate the time
needed by the flow to reach an epsilon neighborhood of the target steady state.
Additionally, we show that for monotone systems the switching function is also
monotone in some sense, a property that can yield efficient algorithms to
compute it. This observation recovers and further extends the results of the
original framework, which we illustrate on numerical examples inspired by
biological applications.Comment: 7 page
Geometric Properties of Isostables and Basins of Attraction of Monotone Systems
In this paper, we study geometric properties of basins of attraction of
monotone systems. Our results are based on a combination of monotone systems
theory and spectral operator theory. We exploit the framework of the Koopman
operator, which provides a linear infinite-dimensional description of nonlinear
dynamical systems and spectral operator-theoretic notions such as eigenvalues
and eigenfunctions. The sublevel sets of the dominant eigenfunction form a
family of nested forward-invariant sets and the basin of attraction is the
largest of these sets. The boundaries of these sets, called isostables, allow
studying temporal properties of the system. Our first observation is that the
dominant eigenfunction is increasing in every variable in the case of monotone
systems. This is a strong geometric property which simplifies the computation
of isostables. We also show how variations in basins of attraction can be
bounded under parametric uncertainty in the vector field of monotone systems.
Finally, we study the properties of the parameter set for which a monotone
system is multistable. Our results are illustrated on several systems of two to
four dimensions.Comment: 12 pages, to appear in IEEE Transaction on Automatic Contro
An Optimal Control Formulation of Pulse-Based Control Using Koopman Operator
In many applications, and in systems/synthetic biology, in particular, it is
desirable to compute control policies that force the trajectory of a bistable
system from one equilibrium (the initial point) to another equilibrium (the
target point), or in other words to solve the switching problem. It was
recently shown that, for monotone bistable systems, this problem admits
easy-to-implement open-loop solutions in terms of temporal pulses (i.e., step
functions of fixed length and fixed magnitude). In this paper, we develop this
idea further and formulate a problem of convergence to an equilibrium from an
arbitrary initial point. We show that this problem can be solved using a static
optimization problem in the case of monotone systems. Changing the initial
point to an arbitrary state allows to build closed-loop, event-based or
open-loop policies for the switching/convergence problems. In our derivations
we exploit the Koopman operator, which offers a linear infinite-dimensional
representation of an autonomous nonlinear system. One of the main advantages of
using the Koopman operator is the powerful computational tools developed for
this framework. Besides the presence of numerical solutions, the
switching/convergence problem can also serve as a building block for solving
more complicated control problems and can potentially be applied to
non-monotone systems. We illustrate this argument on the problem of
synchronizing cardiac cells by defibrillation. Potentially, our approach can be
extended to problems with different parametrizations of control signals since
the only fundamental limitation is the finite time application of the control
signal.Comment: corrected typo
Effects of cell cycle noise on excitable gene circuits
We assess the impact of cell cycle noise on gene circuit dynamics. For
bistable genetic switches and excitable circuits, we find that transitions
between metastable states most likely occur just after cell division and that
this concentration effect intensifies in the presence of transcriptional delay.
We explain this concentration effect with a 3-states stochastic model. For
genetic oscillators, we quantify the temporal correlations between daughter
cells induced by cell division. Temporal correlations must be captured properly
in order to accurately quantify noise sources within gene networks.Comment: 15 pages, 8 figure
Evaluation of bistable systems versus matched filters in detecting bipolar pulse signals
This paper presents a thorough evaluation of a bistable system versus a
matched filter in detecting bipolar pulse signals. The detectability of the
bistable system can be optimized by adding noise, i.e. the stochastic resonance
(SR) phenomenon. This SR effect is also demonstrated by approximate statistical
detection theory of the bistable system and corresponding numerical
simulations. Furthermore, the performance comparison results between the
bistable system and the matched filter show that (a) the bistable system is
more robust than the matched filter in detecting signals with disturbed pulse
rates, and (b) the bistable system approaches the performance of the matched
filter in detecting unknown arrival times of received signals, with an
especially better computational efficiency. These significant results verify
the potential applicability of the bistable system in signal detection field.Comment: 15 pages, 9 figures, MikTex v2.
Bursting through interconnection of excitable circuits
We outline the methodology for designing a bursting
circuit with robustness and control properties reminiscent of
those encountered in biological bursting neurons. We propose
that this design question is tractable when addressed through the
interconnection theory of two excitable circuits, realized solely
with first-order filters and sigmoidal I-V elements. The circuit
can be designed and controlled by shaping its I-V curves in the
relevant timescales, giving a novel and intuitive methodology for
implementing single neuron behaviors in hardware.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n.670645
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