Vishwesh V. Kulkarni

Computational design of nucleic acid feedback control circuits.

The design of synthetic circuits for controlling molecular-scale processes is an important goal of synthetic biology, with potential applications in future in vitro and in vivo biotechnology. In this paper, we present a computational approach for designing feedback control circuits constructed from nucleic acids. Our approach relies on an existing methodology for expressing signal processing and control circuits as biomolecular reactions. We first extend the methodology so that circuits can be expressed using just two classes of reactions: catalysis and annihilation. We then propose implementations of these reactions in three distinct classes of nucleic acid circuits, which rely on DNA strand displacement, DNA enzyme and RNA enzyme mechanisms, respectively. We use these implementations to design a Proportional Integral controller, capable of regulating the output of a system according to a given reference signal, and discuss the trade-offs between the different approaches. As a proof of principle, we implement our methodology as an extension to a DNA strand displacement software tool, thus allowing a broad range of nucleic acid circuits to be designed and analyzed within a common modeling framework.

Stability analysis of the GAL regulatory network in Saccharomyces cerevisiae and Kluyveromyces lactis

BackgroundIn the yeast Saccharomyces cerevisiae, interactions between galactose, Gal3p, Gal80p, and Gal4p determine the transcriptional status of the genes required for the galactose utilization. Increase in the cellular galactose concentration causes the galactose molecules to bind onto Gal3p which, via Gal80p, activates Gal4p, which induces the GAL3 and GAL80 gene transcription. Recently, a linear time-invariant multi-input multi-output (MIMO) model of this GAL regulatory network has been proposed; the inputs being galactose and Gal4p, and the outputs being the active Gal4p and galactose utilization. Unfortunately, this model assumes the cell culture to be homogeneous, although it is not so in practice. We overcome this drawback by including more biochemical reactions, and derive a quadratic ordinary differential equation (ODE) based model.ResultsWe show that the model, referred to above, does not exhibit bistability. We establish sufficiency conditions for the domain of attraction of an equilibrium point of our ODE model for the special case of full-state feedback controller. We observe that the GAL regulatory system of Kluyveromyces lactis exhibits an aberration of monotone nonlinearity and apply the Rantzer multipliers to establish a class of stabilizing controllers for this system.ConclusionFeedback in a GAL regulatory system can be used to enhance the cellular memory. We show that the system can be modeled as a quadratic nonlinear system for which the effect of feedback on the domain of attraction of the equilibrium point can be characterized using linear matrix inequality (LMI) conditions that are easily implementable in software. The benefit of this result is that a mathematically sound approach to the synthesis of full-state and partial-state feedback controllers to regulate the cellular memory is now possible, irrespective of the number of state-variables or parameters of interest.

Adaptive control for rejecting disturbances with time-varying frequencies in tape systems

In this paper, we present two adaptive algorithms for tape systems that account for tape tension ripples. Tape tension ripples are caused by reel eccentricities that produce disturbances with time-varying frequencies. In both designs, the frequency and the magnitude of the disturbance are estimated to synthesize an input signal to cancel the disturbance. In the first design, by adjusting the values of the adaptive parameters that are related to the frequency of the disturbance, the estimated frequency reflects the time-varying nature of the disturbance. The second design extends an existing digital adaptive feed-forward cancellation scheme used in hard disk drives for application to tape tension control problems. For both designs, time-varying sinusoidal disturbance signals are used in simulations to analyze and evaluate the performances of the developed adaptive control methods on a model of a tape system.

An overview of innovations and industrial solutions in protein microarray technology

The complexity involving protein array technology reflects in the fact that instrumentation and data analysis are subject to change depending on the biological question, technical compatibility of instruments and software used in each experiment. Industry has played a pivotal role in establishing standards for future deliberations in sustenance of these technologies in the form of protein array chips, arrayers, scanning devices, and data analysis software. This has enhanced the outreach of protein microarray technology to researchers across the globe. These have encouraged a surge in the adaptation of “nonclassical” approaches such as DNA‐based protein arrays, micro‐contact printing, label‐free protein detection, and algorithms for data analysis. This review provides a unique overview of these industrial solutions available for protein microarray based studies. It aims at assessing the developments in various commercial platforms, thus providing a holistic overview of various modalities, options, and compatibility; summarizing the journey of this powerful high‐throughput technology.

Zames-Falb multipliers for MIMO nonlinearities

Zames and Falb (1968) determined a class of multipliers that preserve positivity of monotone SISO nonlinearities. They conjectured that their results might also hold for incrementally positive, norm-bounded MIMO nonlinearities. In this note, we demonstrate that their conjecture regarding MIMO nonlinearities holds true only if a further restriction is applied. Specifically, we show that it suffices either to restrict the nonlinearity to be the gradient of a convex real-valued function or to restrict the multiplier to be a real-valued function of frequency.

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

ROBUST REJECTION OF PERIODIC AND ALMOST PERIODIC DISTURBANCES

Abstract We present algorithms to exponentially reject periodic and almost periodic disturbances, the motivating application being a rejection of reel eccentricity induced disturbances in tape-drive systems. The prevalent periodic disturbance rejection algorithms rely on a constant gain approximation of the system at a particular frequency. These are inadequate for this application because a tape-drive system has parametric uncertainties and because the disturbance is time-varying. We present a robust extension of an existing technique derived by Bodson et al. and further use quadratic and parameter-dependent Lyapunov functions to synthesize gain-scheduled feedback compensators.

Positivity Preservation Properties of the Rantzer Multipliers

The Rantzer multipliers are known to preserve the positivity of certain aberrations of memoryless monotone positive nonlinearities. We show that if the nonlinearity input is constrained to be positive valued for all time instants, these multipliers are positivity preserving for a larger class of nonlinearities. As a result, it follows that the Rantzer multipliers are useful in reducing the conservatism inherent in the multiplier theoretic stability analysis of feedback systems featuring a larger class of nonlinearities than the one these multipliers were originally intended for, so long as the nonlinearity input is positive-valued for all time instants.

Biomolecular implementation of a quasi sliding mode feedback controller based on DNA strand displacement reactions

A fundamental aim of synthetic biology is to achieve the capability to design and implement robust embedded biomolecular feedback control circuits. An approach to realize this objective is to use abstract chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks. Here, we employ this approach to facilitate the implementation of a class of nonlinear feedback controllers based on sliding mode control theory. We show how a set of two-step irreversible reactions with ultrasensitive response dynamics can provide a biomolecular implementation of a nonlinear quasi sliding mode (QSM) controller. We implement our controller in closed-loop with a prototype of a biological pathway and demonstrate that the nonlinear QSM controller outperforms a traditional linear controller by facilitating faster tracking response dynamics without introducing overshoots in the transient response.

Robust Power Allocation for MIMO Beamforming under Time Varying Channel Conditions

We consider the downlink transmit power allocation problems in multi-user MIMO wireless networks using zeroforcing beamforming. Traditionally such problems are solved by water-filling algorithm under the assumption of perfect channel knowledge. However when channel information is not known a priori or time varying the water-filling solution is shown to be unstable. We use the sliding mode control theory to synthesize the transmit powers so that the target SINR requirements of all users are met. We synthesize the sliding mode controller for the case of zero-forcing beamforming. The synthesis problem is solved under time varying Rayleigh fading channel conditions. Our solutions and simulation results show that our sliding mode controller is stable and delivers better quality of service under practical channel conditions.