Discrete-time L1 adaptive controller to regulate in vivo protein expressions

The application of DNA nanotechnology to interface with cellular environment provides tremendous opportunities to expand the synthetic biological circuits. The current application of DNA nanotechnology spans smart therapeutics (Douglas et al, Science 2012), drug delivery (Perrault, Shih, ACS Nano 2014), imaging (Choi et al, ACS Nano 2014), and probes for cell biology (Shaw et al, Nat Methods 2014). The excellent programmability of nucleic-acid-based parts would enlarge the space of complex functionalities realized in synthetic biological circuits. Building on our earlier works on DNA strand displacement circuits to regulate DNA tweezers driven by transcriptional oscillators, we show how discrete-time L1 adaptive controller can be used to deliver drugs in situ in response to cellular condition. For this, we replace the model predictive controller used (Menolascina et al, PLOS CB 2014). Our controller automatically regulates the administration of inducer molecules to the cells by comparing the actual protein expression level in the cell population with the desired expression level. We intend to use in the automated platform of (Menolascina et al, PLOS CB 2014) which is based on a microfluidic device, a time-lapse microscopy apparatus, and a set of motorized syringes, all controlled by a computer. They have tested the platform to force yeast cells to express a desired fixed, or time-varying, amount of a reporter protein over thousands of minutes. Here, the computer automatically switched the type of sugar administered to the cells, its concentration and its duration, according to the control algorithm. Our discrete-time L1 adaptive controller facilitates superior results on controlling expression of any protein, fused to a fluorescent reporter, provided that an external molecule known to (indirectly) affect its promoter activity is available. Conceptually, our controller is also compatible to work with optogenetic systems that allow one to generate desired perturbations in the intracellular concentration of a specific protein in microbial cell culture. As light can be easily added and removed, this enables an easier dynamic control of protein concentration in culture than would be possible with long-lived chemical inducers. Implementation of this closed-loop control scheme is achieved by sampling individual cells from the culture apparatus, imaging and quantifying protein concentration, and adjusting the inducing light appropriately. The culturing apparatus can be operated as a chemostat, allowing one to precisely control microbial growth and providing cell material for downstream assays. Apart from the obvious applications in phenotype regulations, this method of specifically perturbing the concentration of a single protein and measuring the downstream signaling and transcriptional responses will allow experimentalists to make more informative perturbations to better elucidate the kinetics and architecture of biological networks for disease diagnosis and drug delivery

Biologically inspired design of feedback control systems implemented using DNA strand displacement reactions

The use of abstract chemical reaction networks (CRNs) as a modelling and design framework for the implementation of computing and control circuits using enzyme-free, entropy driven DNA strand displacement (DSD) reactions is starting to garner widespread attention in the area of synthetic biology. Previous work in this area has demonstrated the theoretical plausibility of using this approach to design biomolecular feedback control systems based on classical proportional-integral (PI) controllers, which may be constructed from CRNs implementing gain, summation and integrator operators. Here, we propose an alternative design approach that utilises the abstract chemical reactions involved in cellular signalling cycles to implement a biomolecular controller - termed a signalling-cycle (SC) controller. We compare the performance of the PI and SC controllers in closed-loop with a nonlinear second-order chemical process. Our results show that the SC controller outperforms the PI controller in terms of both performance and robustness, and also requires fewer abstract chemical reactions to implement, highlighting its potential usefulness in the construction of biomolecular control circuits

Load Capacity Improvements in Nucleic Acid Based Systems Using Partially Open Feedback Control

Synthetic biology is facilitating novel methods and components to build in vivo and in vitro circuits to better understand and re-engineer biological networks. Recently, Kim and Winfree have synthesized a remarkably elegant network of transcriptional oscillators in vitro using a modular architecture of synthetic gene analogues and a few enzymes that, in turn, could be used to drive a variety of downstream circuits and nanodevices. However, these oscillators are sensitive to initial conditions and downstream load processes. Furthermore, the oscillations are not sustained since the inherently closed design suffers from enzyme deactivation, NTP fuel exhaustion, and waste product build up. In this paper, we show that a partially open architecture in which an ℒ_1 adaptive controller, implemented inside an in silico computer that resides outside the wet-lab apparatus, can ensure sustained tunable oscillations in two specific designs of the Kim–Winfree oscillator networks. We consider two broad cases of operation: (1) the oscillator network operating in isolation and (2) the oscillator network driving a DNA tweezer subject to a variable load. In both scenarios, our simulation results show a significant improvement in the tunability and robustness of these oscillator networks. Our approach can be easily adopted to improve the loading capacity of a wide range of synthetic biological devices

Improved computation of natural logarithm using chemical reaction networks

Recent researches have focused on nucleic acids as a substrate for designing biomolecular circuits for in situ monitoring and control. A common approach is to express them by a set of idealised abstract chemical reaction networks (ACRNs). Here, we present new results on how abstract chemical reactions, viz., catalysis, annihilation and degradation, can be used to implement circuit that accurately computes logarithm function using the method of Cubic Arithmetic-Geometric Mean (AGM)

Load capacity improvements in transcriptional systems using discrete-time L1-adaptive control

DNA-based circuits relying on predictable thermodynamics and kinetics of DNA strand interactions impart flexibility in synthesizing synthetic biological constructs and in coupling these circuits to in vivo processes [1, 2, 6, 7]. Here, we focus on the synthetic Kim-Winfree oscillator network, illustrated in Fig. 1(i), which is a simple but effective coupled oscillator system in which two DNA switches SW1 and SW2 are coupled through activator and inhibitor blocks realized by RNA signals and auxiliary DNA species (see [3]). A typical experimental realization is closed in the sense that once the operation starts, we do not either add any chemicals, especially NTP fuel, externally into the wet-lab apparatus or remove any chemicals, especially waste products, from the apparatus. Within the closed system, the oscillations are bound to die out sooner or later diminishing NTP fuel eventually stops supporting the production of RNA signals and accumulating waste products clog down the toeholds and, as a result, adversely affect the signal propagation. Furthermore, the oxidation effects and the pH variations tend to deactivate the enzymes. Loading poses an additional challenge since it increases the order and the uncertainty of the system indeed, these oscillators have recently been used in [8] to drive conformational changes of a DNA nanomechanical device called DNA tweezers. We show how L1-adaptive control can be used to mitigate these effects

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

Integrated predictive genome-scale models to improve the metabolic re-engineering efficiency

One of the most common applications of metabolic circuits is to produce a desired chemical in a chassis organism, such as the Escherichia coli (E. coli), by importing heterologous genes encoding for the enzymes that participate in the biosynthetic pathway. Recently, an automated pipeline named RetroPath was developed to synthesise embedded metabolic circuits [1]. These circuits are to be embedded in E. coli for a wide range of applications such as regulating biomass productions, sensing specifc molecules, processing specific molecules, and releasing specific molecules. In this paper, we improve the efficiency of RetroPath via quadratic programming

Metabolic networks in a porcine model of trauma and hemorrhagic shock demonstrate different control mechanism with carbohydrate pre-feed

Background: Treatment with oral carbohydrate prior to trauma and hemorrhage confers a survival benefit in small animal models. The impact of fed states on survival in traumatically injured humans is unknown. This work uses regulatory networks to examine the effect of carbohydrate pre-feeding on metabolic response to polytrauma and hemorrhagic shock in a clinically-relevant large animal model. Methods: Male Yorkshire pigs were fasted overnight (n = 64). Pre-fed animals (n = 32) received an oral bolus of Karo\textregistered\syrup before sedation. All animals underwent a standardized trauma, hemorrhage, and resuscitation protocol. Serum samples were obtained at set timepoints. Proton NMR was used to identify and quantify serum metabolites. Metabolic regulatory networks were constructed from metabolite concentrations and rates of change in those concentrations to identify controlled nodes and controlling nodes of the network. Results: Oral carbohydrate pre-treatment was not associated with survival benefit. Six metabolites were identified as controlled nodes in both groups: adenosine, cytidine, glycerol, hypoxanthine, lactate, and uridine. Distinct groups of controlling nodes were associated with controlled nodes; however, the composition of these groups depended on feeding status. Conclusions: A common metabolic output, typically associated with injury and hypoxia, results from trauma and hemorrhagic shock. However, this output is directed by different metabolic inputs depending upon the feeding status of the subject. Nodes of the network that are related to mortality can potentially be manipulated for therapeutic effect; however, these nodes differ depending upon feeding status

Biomolecular implementation of nonlinear system theoretic operators

Synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications, including biomass maximization, nanoscale drug delivery, and many others. In this paper, we present new results on how abstract chemical reactions can be used to implement commonly used system theoretic operators such as the polynomial functions, rational functions and Hill-type nonlinearity. We first describe how idealised versions of multi-molecular reactions, catalysis, annihilation, and degradation can be combined to implement these operators. We then show how such chemical reactions can be implemented using enzyme-free, entropy-driven DNA reactions. Our results are illustrated through three applications: (1) implementation of a Stan-Sepulchre oscillator, (2) the computation of the ratio of two signals, and (3) a PI+antiwindup controller for regulating the output of a static nonlinear plant