Christian Cuba Samaniego

Molecular Titration Promotes Oscillations and Bistability in Minimal Network Models with Monomeric Regulators

Molecular titration is emerging as an important biochemical interaction mechanism within synthetic devices built with nucleic acids and the CRISPR/Cas system. We show that molecular titration in the context of feedback circuits is a suitable mechanism to enhance the emergence of oscillations and bistable behaviors. We consider biomolecular modules that can be inhibited or activated by input monomeric regulators; the regulators compete with constitutive titrating species to determine the activity of their target. By tuning the titration rate and the concentration of titrating species, it is possible to modulate the delay and convergence speed of the transient response, and the steepness and dead zone of the stationary response of the modules. These phenomena favor the occurrence of oscillations when modules are interconnected to create a negative feedback loop; bistability is favored in a positive feedback interconnection. Numerical simulations are supported by mathematical analysis showing that the capacity of the closed loop systems to exhibit oscillations or bistability is structural.

Design of a molecular clock with RNA-mediated regulation

We design a new negative feedback molecular oscillator and study its properties analytically and numerically. This oscillator is composed of two synthetic genes interconnected through their RNA outputs. Regulation of the genes activity is achieved by controlling the activity of the enzymes rather than the activity of the promoters. We show that a simple model of this system has the potential to oscillate for appropriate choices of the parameters. Our design can be built experimentally using RNA aptamers.

Stability analysis of an artificial biomolecular oscillator with non-cooperative regulatory interactions

ABSTRACT Oscillators are essential to fuel autonomous behaviours in molecular systems. Artificial oscillators built with programmable biological molecules such as DNA and RNA are generally easy to build and tune, and can serve as timers for biological computation and regulation. We describe a new artificial nucleic acid biochemical reaction network, and we demonstrate its capacity to exhibit oscillatory solutions. This network can be built in vitro using nucleic acids and three bacteriophage enzymes, and has the potential to be implemented in cells. Numerical simulations suggest that oscillations occur in a realistic range of reaction rates and concentrations.

Design and analysis of a synthetic aptamer-based oscillator

We consider a realistic experimental implementation of a negative feedback molecular oscillator built with RNA aptamers proposed in our previous work [1]. This oscillator is composed of two synthetic genes interconnected through their RNA outputs. Regulation of transcription is achieved by controlling the activity of the enzymes rather than the activity of the promoters. We investigate the properties of the systems model analytically, checking if it has the appropriate structure to be an oscillator. Our analysis reveals that it is necessary to include an additional self-activation loop in the system to obtain a model with the structure of a candidate oscillator. We finally study this candidate oscillator with numerical simulations by randomly varying its parameters.

Dynamic Control of Aptamer–Ligand Activity Using Strand Displacement Reactions

Nucleic acid aptamers are an expandable toolkit of sensors and regulators. To employ aptamer regulators within nonequilibrium molecular networks, the aptamer-ligand interactions should be tunable over time, so that functions within a given system can be activated or suppressed on demand. This is accomplished through complementary sequences to aptamers, which achieve programmable aptamer-ligand dissociation by displacing the aptamer from the ligand. We demonstrate the effectiveness of our simple approach on light-up aptamers as well as on aptamers inhibiting viral RNA polymerases, dynamically controlling the functionality of the aptamer-ligand complex. Mathematical models allow us to obtain estimates for the aptamer displacement kinetics. Our results suggest that aptamers, paired with their complement, could be used to build dynamic nucleic acid networks with direct control over a variety of aptamer-controllable enzymes and their downstream pathways.

A bistable biomolecular network based on monomeric inhibition reactions

We model an experimentally plausible implementation of a synthetic RNA-based biochemical toggle switch proposed in previous work by the authors. We show that the system structure is suited to exhibit multistationarity for arbitrary choice of the parameters. The network is based on in vitro transcription and nucleic acid strand displacement reactions. It is composed of two distinct RNA polymerases producing mutually inhibiting RNA aptamers. The aptamer inhibitors create an overall positive loop, where regulation is achieved by modulating the activity of the polymerases rather than the promoter activity. Inhibition occurs via stoichiometric binding of RNA monomers to enzymes and is not a cooperative phenomenon; the only nonlinearities in the differential equations are given by second order reaction rates. Enzyme activity is recovered in the presence of DNA strands that displace the aptamers from their target, and mediate their degradation; recovery is also a bimolecular binding process. Numerical analysis shows that the system admits bistability in a wide range of parameters.

Aggregates of Monotonic Step Response Systems: A Structural Classification

Complex dynamical networks can often be analyzed as the interconnection of subsystems: This allows us to considerably simplify the model and better understand the global behavior. Some biological networks can be conveniently analyzed as aggregates of monotone subsystems. Yet, monotonicity is a strong requirement; it relies on the knowledge of the state representation and imposes a severe restriction on the Jacobian (which must be a Metzler matrix). Systems with a monotonic step response (MSR), which include input–output monotone systems as a special case, are a broader class and still have interesting features. The property of having a monotonically increasing step response (or, equivalently, in the linear case, a positive impulse response) can be evinced from experimental data, without an explicit model of the system. We consider networks that can be decomposed as aggregates of MSR subsystems and we provide a structural (parameter-free) classification of oscillatory and multistationary behaviors. The classification is based on the exclusive or concurrent presence of negative and positive cycles in the system aggregate graph, whose nodes are the MSR subsystems. The result is analogous to our earlier classification for aggregates of monotone subsystems. Models of biomolecular networks are discussed to demonstrate the applicability of our classification, which helps build synthetic biomolecular circuits that, by design, are well suited to exhibit the desired dynamics.

Design of a bistable network using the CRISPR/Cas system

The CRISPR/Cas-based genome editing system has provided a powerful tool for control of gene activity within cells. Here, we model an experimentally plausible architecture harnessing the power of CRISPR/Cas to create a biomolecular bistable switch. The designed in vitro circuit is based on mutual repression of two genes together with two other activator genes. The repression is generated by the binding of catalytically dead endonuclease (dCas9) to the target gene mediated by a guide RNA. The activation is accomplished by use of an antiguide RNA partially complementary to the guide RNA. Using mathematical analysis of the model, we show that the proposed scheme is capable of exhibiting bistability. We further discuss ultrasensitivity of the regulatory modules, and their capacity to manage competition for dCas9 and downstream load.

A minimal biomolecular frequency divider

Many cyclic processes such as neuron firing, cardiac functions, and cell division can exhibit integer variations of their period. Period doubling is often triggered by external events, and is an important phenomenon because it can control a change in the time scale of downstream processes. The capacity for period doubling is also relevant in synthetic molecular circuits where slow and fast modules need to be synchronized. In this paper we describe a rationally designed biomolecular reaction network which operates frequency division of its periodic inputs. The core of this device is a bistable circuit, which is toggled between its two stable states by “push” chemical reactions that process the periodic inputs. We thoroughly analyze the behavior of the system deriving an upper bound on the baseline of the inputs it can process, maintaining its output specifications. All the reactions in the system have first or second order rates, and are potentially implementable in vitro using nucleic acids and enzymes. Numerical analysis shows that frequency division is achieved in a range of realistic parameters.