Structurally robust biological networks

Background: The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results: In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions: The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters

Genome-Scale in silico Reconstruction of the Reactive Oxygen Species (ROS) Generating Metabolism in Pseudomonas putida KT2440 and Study of the role of ROS in Different Metabolic Processes

The understanding of the genotype-phenotype relationship is a fundamental biological question widely studied, but still not understood in all its dimension. The existence of emergent systems' properties largely complicates the lineality of this relationship making it mandatory for the study of such properties to fully understand the biological systems. The robustness, understood as the porperty that allows the systems to maintain their functions despite external and internal perturbations, is a system-level phenomenom ubiquitously observed in living systems (Blanchini and Franco 2011). Metabolic networks can be affected by variables that have the power of modulating it as a whole and, most likely, of influencing the referred-to molecular mechanisms. Those variables, one of whihch being endogenous ROS generating metabolism, must be included in metabolic in silico models to study this robustness. We decided to model endogenous ROS generation in Pseudomonas putida KT2440 genome-scale model. P. putida is a model microorganism in biotechnology and possesses an extremely versatile metabolism, which makes it the perfect candidate to study complex metabolic processes (Belda et al. 2016). The objective of this project is to go deep in the understanding of endogenous ROS metabolism and to study the role of ROS in different metabolic processes. To do so, we built and validated the ROS generating genome-scale model and used it as a tool for two purposes: (1) to analyse, in silico, the main metabolic mechanisms to prevent the cell from ROS damage and (2) to generate hypothesis about the role of ROS in different metabolic processes that we approached experimentaly. As a result of this investigation, we have came up with (1) the theory that the main cellular mechanisms to fight back endogenous ROS generation are fuelled by NADH, and not by the activation of NADPH generating metabolic pathways, as we find in scientific literature (Mailloux, Lemire, and Appanna 2011). (2) We have also found that ROS plays an important role in different molecular mechanisms involving robustness, as the carbon flux deviation to the accumulation of  polyhydroxyalkanoate; and also influenciate the global metabolic regulator gen crc

Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness

Recent research in both the experimental and mathematical communities has focused on biochemical interaction systems that satisfy an "absolute concentration robustness" (ACR) property. The ACR property was first discovered experimentally when, in a number of different systems, the concentrations of key system components at equilibrium were observed to be robust to the total concentration levels of the system. Followup mathematical work focused on deterministic models of biochemical systems and demonstrated how chemical reaction network theory can be utilized to explain this robustness. Later mathematical work focused on the behavior of this same class of reaction networks, though under the assumption that the dynamics were stochastic. Under the stochastic assumption, it was proven that the system will undergo an extinction event with a probability of one so long as the system is conservative, showing starkly different long-time behavior than in the deterministic setting. Here we consider a general class of stochastic models that intersects with the class of ACR systems studied previously. We consider a specific system scaling over compact time intervals and prove that in a limit of this scaling the distribution of the abundances of the ACR species converges to a certain product-form Poisson distribution whose mean is the ACR value of the deterministic model. This result is in agreement with recent conjectures pertaining to the behavior of ACR networks endowed with stochastic kinetics, and helps to resolve the conflicting theoretical results pertaining to deterministic and stochastic models in this setting

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm's theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis

Stability and Control of Biomolecular Circuits through Structure

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building feedback control through such structures. In this work, we develop the tool of log derivatives to capture structures in how the production and degradation rates of molecules depend on concentrations of reactants. We show that log derivatives could establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through the structures captured. Due to the method's simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations

Tuning Synaptic Connections instead of Weights by Genetic Algorithm in Spiking Policy Network

Learning from the interaction is the primary way biological agents know about the environment and themselves. Modern deep reinforcement learning (DRL) explores a computational approach to learning from interaction and has significantly progressed in solving various tasks. However, the powerful DRL is still far from biological agents in energy efficiency. Although the underlying mechanisms are not fully understood, we believe that the integration of spiking communication between neurons and biologically-plausible synaptic plasticity plays a prominent role. Following this biological intuition, we optimize a spiking policy network (SPN) by a genetic algorithm as an energy-efficient alternative to DRL. Our SPN mimics the sensorimotor neuron pathway of insects and communicates through event-based spikes. Inspired by biological research that the brain forms memories by forming new synaptic connections and rewires these connections based on new experiences, we tune the synaptic connections instead of weights in SPN to solve given tasks. Experimental results on several robotic control tasks show that our method can achieve the performance level of mainstream DRL methods and exhibit significantly higher energy efficiency

Time-scale separation based design of biomolecular feedback controllers (extended version)

Time-scale separation is a powerful property that can be used to simplify control systems design. In this work, we consider the problem of designing biomolecular feedback controllers that provide tracking of slowly varying references and rejection of slowly varying disturbances for nonlinear systems. We propose a design methodology that uses time-scale separation to accommodate physical constraints on the implementation of integral control in cellular systems. The main result of this paper gives sufficient conditions under which controllers designed using our time-scale separation methodology have desired asymptotic performance when the reference and disturbance are constant or slowly varying. Our analysis is based on construction of Lyapunov functions for a class of singularly perturbed systems that are dependent on an additional parameter that perturbs the system regularly. When the exogenous inputs are slowly varying, this approach allows us to bound the system trajectories by a function of the regularly perturbing parameter. This bound decays to zero as the parameter's value increases, while an inner-estimate of the region of attraction stays unchanged as this parameter is varied. These results cannot be derived using standard singular perturbation results. We apply our results to an application demonstrating a physically realizable parameter tuning that controls performance.This work was supported in part by the National Science Foundation through grant NSF-CMMI 1727189

Absolute concentration robustness in power law kinetic systems

Absolute concentration robustness (ACR) is a condition wherein a species in a chemical kinetic system possesses the same value for any positive steady state the network may admit regardless of initial conditions. Thus far, results on ACR center on chemical kinetic systems with deficiency one. In this contribution, we use the idea of dynamic equivalence of chemical reaction networks to derive novel results that guarantee ACR for some classes of power law kinetic systems with deficiency zero. Furthermore, using network decomposition, we identify ACR in higher deficiency networks (i.e. deficiency $\geq$ 2) by considering the presence of a low deficiency subnetwork with ACR. Network decomposition also enabled us to recognize and define a weaker form of concentration robustness than ACR, which we named as `balanced concentration robustness'. Finally, we also discuss and emphasize our view of ACR as a primarily kinetic character rather than a condition that arises from structural sources.Comment: submitted for publication; 26 pages. arXiv admin note: text overlap with arXiv:1908.0449