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

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

Architecture, constraints, and behavior

This paper aims to bridge progress in neuroscience involving sophisticated quantitative analysis of behavior, including the use of robust control, with other relevant conceptual and theoretical frameworks from systems engineering, systems biology, and mathematics. Familiar and accessible case studies are used to illustrate concepts of robustness, organization, and architecture (modularity and protocols) that are central to understanding complex networks. These essential organizational features are hidden during normal function of a system but are fundamental for understanding the nature, design, and function of complex biologic and technologic systems

Modeling Robustness Tradeoffs in Yeast Cell Polarization Induced by Spatial Gradients

Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this work, we investigated the tradeoffs among these performance objectives using a generic model that captures the basic spatial dynamics of polarization in yeast cells, which are small. We varied the positive feedback, cooperativity, and diffusion coefficients in the model to explore the nature of this tradeoff. Increasing the positive feedback gain resulted in better amplification, but also produced multiple steady-states and hysteresis that prevented the tracking of directional changes of the gradient. Feedforward/feedback coincidence detection in the positive feedback loop and multi-stage amplification both improved tracking with only a modest loss of amplification. Surprisingly, we found that introducing lateral surface diffusion increased the robustness of polarization and collapsed the multiple steady-states to a single steady-state at the cost of a reduction in polarization. Finally, in a more mechanistic model of yeast cell polarization, a surface diffusion coefficient between 0.01 and 0.001 µm2/s produced the best polarization performance, and this range is close to the measured value. The model also showed good gradient-sensitivity and dynamic range. This research is significant because it provides an in-depth analysis of the performance tradeoffs that confront biological systems that sense and respond to chemical spatial gradients, proposes strategies for balancing this tradeoff, highlights the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization, and furnishes a framework for future spatial models of yeast cell polarization

Ecosystem biogeochemistry considered as a distributed metabolic network ordered by maximum entropy production

Author Posting. © The Author(s), 2009. This is the author's version of the work. It is posted here by permission of The Royal Society for personal use, not for redistribution. The definitive version was published in Philosophical Transactions of the Royal Society B 365 (2010): 1417-1427, doi:10.1098/rstb.2009.0272.We examine the application of the maximum entropy production principle for describing ecosystem biogeochemistry. Since ecosystems can be functionally stable despite changes in species composition, we utilize a distributed metabolic network for describing biogeochemistry, which synthesizes generic biological structures that catalyze reaction pathways, but is otherwise organism independent. Allocation of biological structure and regulation of biogeochemical reactions is determined via solution of an optimal control problem in which entropy production is maximized. However, because synthesis of biological structures cannot occur if entropy production is maximized instantaneously, we propose that information stored within the metagenome allows biological systems to maximize entropy production when averaged over time. This differs from abiotic systems that maximize entropy production at a point in space-time, which we refer to as the steepest descent pathway. It is the spatiotemporal averaging that allows biological systems to outperform abiotic processes in entropy production, at least in many situations. A simulation of a methanotrophic system is used to demonstrate the approach. We conclude with a brief discussion on the implications of viewing ecosystems as self organizing molecular machines that function to maximize entropy production at the ecosystem level of organization.The work presented here was funded by the PIE-LTER program (NSF OCE-0423565), as well as from NSF CBET-0756562, NSF EF-0928742 and NASA Exobiology and Evolutionary Biology (NNG05GN61G)

Ecosystem properties and principles of living systems as foundation for sustainable agriculture – Critical reviews of environmental assessment tools, key findings and questions from a course process

With increasing demands on limited resources worldwide, there is a growing interest in sustainable patterns of utilisation and production. Ecological agriculture is a response to these concerns. To assess progress and compliance, standard and comprehensive measures of resource requirements, impacts and agro-ecological health are needed. Assessment tools should also be rapid, standardized, userfriendly, meaningful to public policy and applicable to management. Fully considering these requirements confounds the development of integrated methods. Currently, there are many methodologies for monitoring performance, each with its own foundations, assumptions, goals, and outcomes, dependent upon agency agenda or academic orientation. Clearly, a concept of sustainability must address biophysical, ecological, economic, and sociocultural foundations. Assessment indicators and criteria, however, are generally limited, lacking integration, and at times in conflict with one another. A result is that certification criteria, indicators, and assessment methods are not based on a consistent, underlying conceptual framework and often lack a management focus. Ecosystem properties and principles of living systems, including self-organisation, renewal, embeddedness, emergence and commensurate response provide foundation for sustainability assessments and may be appropriate focal points for critical thinking in an evaluation of current methods and standards. A systems framework may also help facilitate a comprehensive approach and promote a context for meaningful discourse. Without holistic accounts, sustainable progress remains an illdefined concept and an elusive goal. Our intent, in the work with this report, was to use systems ecology as a pedagogic basis for learning and discussion to: - Articulate general and common characteristics of living systems. - Identify principles, properties and patterns inherent in natural ecosystems. - Use these findings as foci in a dialogue about attributes of sustainability to: a. develop a model for communicating scientific rationale. b. critically evaluate environmental assessment tools for application in land-use. c. propose appropriate criteria for a comprehensive assessment and expanded definition of ecological land use