Topological tradeoffs in autocatalytic metabolic pathways

Metabolic pathways in cells convert external food and resources into useful cell components and energy. In many cases the cell employs product inhibition to regulate and control these pathways. We investigate the performance of such regulation and control on certain autocatalytic pathways. Specifically, we examine how well the pathways can maintain the desired output concentrations in the presence of disturbances, such as perturbations in resources, enzyme concentrations and product demand. Using control theoretic tools, we show the effects of the pathway size, the reversibility of the intermediate reactions and the coupling of pathways through the consumption of intermediate metabolites on performance. In addition, we establish some necessary conditions on the existence of fixed points and their stability for such pathways

Topological tradeoffs in autocatalytic metabolic pathways

Metabolic pathways in cells convert external food and resources into useful cell components and energy. In many cases the cell employs product inhibition to regulate and control these pathways. We investigate the performance of such regulation and control on certain autocatalytic pathways. Specifically, we examine how well the pathways can maintain the desired output concentrations in the presence of disturbances, such as perturbations in resources, enzyme concentrations and product demand. Using control theoretic tools, we show the effects of the pathway size, the reversibility of the intermediate reactions and the coupling of pathways through the consumption of intermediate metabolites on performance. In addition, we establish some necessary conditions on the existence of fixed points and their stability for such pathways

The compositional and evolutionary logic of metabolism

Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which layers of that system emerged. Metabolism also serves as the foundation in other hierarchies, at least up to cellular integration including bioenergetics and molecular replication, and trophic ecology. The recapitulation of patterns first seen in metabolism, in these higher levels, suggests metabolism as a source of causation or constraint on many forms of organization in the biosphere. We identify as modules widely reused subsets of chemicals, reactions, or functions, each with a conserved internal structure. At the small molecule substrate level, module boundaries are generally associated with the most complex reaction mechanisms and the most conserved enzymes. Cofactors form a structurally and functionally distinctive control layer over the small-molecule substrate. Complex cofactors are often used at module boundaries of the substrate level, while simpler ones participate in widely used reactions. Cofactor functions thus act as "keys" that incorporate classes of organic reactions within biochemistry. The same modules that organize the compositional diversity of metabolism are argued to have governed long-term evolution. Early evolution of core metabolism, especially carbon-fixation, appears to have required few innovations among a small number of conserved modules, to produce adaptations to simple biogeochemical changes of environment. We demonstrate these features of metabolism at several levels of hierarchy, beginning with the small-molecule substrate and network architecture, continuing with cofactors and key conserved reactions, and culminating in the aggregation of multiple diverse physical and biochemical processes in cells.Comment: 56 pages, 28 figure

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

Analysis and Design of Robust and High-Performance Complex Dynamical Networks

In the first part of this dissertation, we develop some basic principles to investigate performance deterioration of dynamical networks subject to external disturbances. First, we propose a graph-theoretic methodology to relate structural specifications of the coupling graph of a linear consensus network to its performance measure. Moreover, for this class of linear consensus networks, we introduce new insights into the network centrality based not only on the network graph but also on a more structured model of network uncertainties. Then, for the class of generic linear networks, we show that the H_2-norm, as a performance measure, can be tightly bounded from below and above by some spectral functions of state and output matrices of the system. Finally, we study nonlinear autocatalytic networks and exploit their structural properties to characterize their existing hard limits and essential tradeoffs. In the second part, we consider problems of network synthesis for performance enhancement. First, we propose an axiomatic approach for the design and performance analysis of linear consensus networks by introducing a notion of systemic performance measure. We build upon this new notion and investigate a general form of combinatorial problem of growing a linear consensus network via minimizing a given systemic performance measure. Two efficient polynomial-time approximation algorithms are devised to tackle this network synthesis problem. Then, we investigate the optimal design problem of distributed system throttlers. A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. Finally, a framework is developed to produce a sparse approximation of a given large-scale network with guaranteed performance bounds using a nearly-linear time algorithm

Disturbance Propagation in Interconnected Linear Dynamical Networks

We consider performance analysis of interconnected linear dynamical networks subject to external stochastic disturbances. For stable linear networks, we define scalar performance measures by considering weighted H2--norms of the underlying systems, which are defined from the disturbance input to a desired output. It is shown that the performance measure of a general stable linear network can be tightly bounded from above and below using some spectral functions of the state matrix of the network. This result is applied to a class of cyclic linear networks and shown that the performance measure of such networks scales quadratically with the network size. Next, we focus on first-- and second--order linear consensus networks and introduce the notion of Laplacian energy for such networks, which in fact measures the expected steady-state dispersion of the state of the entire network. We develop a graph-theoretic framework in order to relate graph characteristics to the Laplacian energy of the network and show that how the Laplacian energy scales asymptotically with the network size. We quantify several inherent fundamental limits on Laplacian energy in terms of graph diameter, node degrees, and the number of spanning trees, and several other graph specifications. Particularly we characterize several versions of fundamental tradeoffs between Laplacian energy and sparsity measures of a linear consensus network, showing that more sparse networks have higher levels of Laplacian energies. At the end, we show that several existing performance measures in real--world applications, such as total power loss in synchronous power networks and flock energy of a group of autonomous vehicles in a formation, are indeed special forms of Laplacian energies

Hard Limits And Performance Tradeoffs In A Class Of Sequestration Feedback Systems

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems

Contrasting Views of Complexity and Their Implications For Network-Centric Infrastructures

There exists a widely recognized need to better understand and manage complex “systems of systems,” ranging from biology, ecology, and medicine to network-centric technologies. This is motivating the search for universal laws of highly evolved systems and driving demand for new mathematics and methods that are consistent, integrative, and predictive. However, the theoretical frameworks available today are not merely fragmented but sometimes contradictory and incompatible. We argue that complexity arises in highly evolved biological and technological systems primarily to provide mechanisms to create robustness. However, this complexity itself can be a source of new fragility, leading to “robust yet fragile” tradeoffs in system design. We focus on the role of robustness and architecture in networked infrastructures, and we highlight recent advances in the theory of distributed control driven by network technologies. This view of complexity in highly organized technological and biological systems is fundamentally different from the dominant perspective in the mainstream sciences, which downplays function, constraints, and tradeoffs, and tends to minimize the role of organization and design