Performance limitations in autocatalytic networks in biology

Autocatalytic networks, where a member can stimulate its own production, can be unstable when not controlled by feedback. Even when such networks are stabilized by regulating control feedbacks, they tend to exhibit non-minimum phase behavior. In this paper, we study the hard limits of the ideal performance of such networks and the hard limit of their minimum output energy. We consider a simplified model of glycolysis as our motivating example. For the glycolysis model, we characterize hard limits on the minimum output energy by analyzing the limiting behavior of the optimal cheap control problem for two different interconnection topologies. We show that some network interconnection topologies result in zero hard limits. Then, we develop necessary tools and concepts to extend our results to a general class of autocatalytic networks

Performance limitations in autocatalytic networks in biology

Autocatalytic networks, where a member can stimulate its own production, can be unstable when not controlled by feedback. Even when such networks are stabilized by regulating control feedbacks, they tend to exhibit non-minimum phase behavior. In this paper, we study the hard limits of the ideal performance of such networks and the hard limit of their minimum output energy. We consider a simplified model of glycolysis as our motivating example. For the glycolysis model, we characterize hard limits on the minimum output energy by analyzing the limiting behavior of the optimal cheap control problem for two different interconnection topologies. We show that some network interconnection topologies result in zero hard limits. Then, we develop necessary tools and concepts to extend our results to a general class of autocatalytic networks

Autocatalytic Biochemical Networks and Their Fundamental Limits

In the present work, we study autocatalytic pathways which contain reactions that need the use of one of their own productions. These pathways are common in biology; one of the simplest and widely studied autocatalytic pathways is Glycolysis. This pathway produces energy by breaking down Glucose. It is shown that this pathway can be simplified as a network of three biochemical reactions. We first revisit some conditions on the underlying structure of the autocatalytic network, which guarantee the existence of fundamental limits on the output energy of such networks. Then we focus on autocatalytic pathways with several biochemical reactions. Our aim is to characterize the zero-dynamics for a class of autocatalytic networks and then study the fundamental limitations of feedback control laws, using their associated zero-dynamics. For this aim, it is shown that the zero-dynamics of autocatalytic networks play an important role in studying the fundamental limits on performance. Zero-dynamics is defined as the dynamics of a system restricted to the control input and initial conditions such that the output of the system remains zero for all future time instances. We characterize the zero-dynamics for a class of unperturbed autocatalytic networks based on the structure of the original network. It is well-known that by knowing the zero-dynamics of a specific class of systems, one can obtain lower bounds on the best achievable performance (L2-norm of the output) for the system. For a specific class of autocatalytic networks, we characterize their zero-dynamics in terms of the state-space matrices of the underlying network. This can be utilized to quantify inherent fundamental limits on performance (the level of disturbance attenuation) for this class of network. In general, one should apply numerical algorithms to obtain such fundamental limits. We explain our method using a simple but illustrative example

A molecular approach to complex adaptive systems

Complex Adaptive Systems (CAS) are dynamical networks of interacting agents which as a whole determine the behavior, adaptivity and cognitive ability of the system. CAS are ubiquitous and occur in a variety of natural and artificial systems (e.g., cells, societies, stock markets). To study CAS, Holland proposed to employ an agent-based system in which Learning Classifier Systems (LCS) were used to determine the agents behavior and adaptivity. We argue that LCS are limited for the study of CAS: the rule-discovery mechanism is pre-specified and may limit the evolvability of CAS. Secondly, LCS distinguish a demarcation between messages and rules, however operations are reflexive in CAS, e.g., in a cell, an agent (a molecule) may both act as a message (substrate) and as a catalyst (rule). To address these issues, we proposed the Molecular Classifier Systems (MCS.b), a string-based Artificial Chemistry based on Holland’s broadcast language. In the MCS.b, no explicit fitness function or rule discovery mechanism is specified, moreover no distinction is made between messages and rules. In the context of the ESIGNET project, we employ the MCS.b to study a subclass of CAS: Cell Signaling Networks (CSNs) which are complex biochemical networks responsible for coordinating cellular activities. As CSNs occur in cells, these networks must replicate themselves prior to cell division. In this paper we present a series of experiments focusing on the self-replication ability of these CAS. Results indicate counter intuitive outcomes as opposed to those inferred from the literature. This work highlights the current deficit of a theoretical framework for the study of Artificial Chemistries

Kinetic Intersections as a Source of Information on Rate Coefficients

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Fundamental Limits and Tradeoffs in Autocatalytic Pathways

This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. Our study has been motivated by a simplified model of a glycolysis pathway. First, the properties of this class of pathways are investigated through a network model, which consists of a chain of enzymatically catalyzed intermediate reactions coupled with an autocatalytic component. We explicitly derive a hard limit on the minimum achievable L₂-gain disturbance attenuation and a hard limit on its minimum required output energy. Then, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production