Abstract
The study of dynamic functions of large-scale biological networks has intensified in recent years. A critical component in developing an understanding of such dynamics involves the study of their hierarchical organization. We investigate the temporal hierarchy in biochemical reaction networks focusing on: (1) the elucidation of the existence of “pools” (i.e., aggregate variables) formed from component concentrations and (2) the determination of their composition and interactions over different time scales. To date the identification of such pools without prior knowledge of their composition has been a challenge. A new approach is developed for the algorithmic identification of pool formation using correlations between elements of the modal matrix that correspond to a pair of concentrations and how such correlations form over the hierarchy of time scales. The analysis elucidates a temporal hierarchy of events that range from chemical equilibration events to the formation of physiologically meaningful pools, culminating in a network-scale (dynamic) structure–(physiological) function relationship. This method is validated on a model of human red blood cell metabolism and further applied to kinetic models of yeast glycolysis and human folate metabolism, enabling the simplification of these models. The understanding of temporal hierarchy and the formation of dynamic aggregates on different time scales is foundational to the study of network dynamics and has relevance in multiple areas ranging from bacterial strain design and metabolic engineering to the understanding of disease processes in humans.
Highlights
The network of interactions that occur between biological components on a range of various spatial and temporal scales confer hierarchical functionality in living cells
Time scale decomposition is a well-established, classical approach to dissecting network dynamics and there is a notable history of analyzing the time scale hierarchy in metabolic networks and matching the events that unfold on each time scale with a physiological function [1,2,3,4,5,6]
A critical aspect toward understanding metabolism is the set of dynamic interactions between metabolites, some of which occur very quickly while others occur more slowly
Summary
The network of interactions that occur between biological components on a range of various spatial and temporal scales confer hierarchical functionality in living cells. There is structure in this dynamic hierarchy of events, in biochemical networks in which the fastest motions generally correspond to the chemical equilibria between metabolites, and the slower motions reflect more physiologically relevant transformations. Appreciation of this observation can result in elucidating structure from the network and simplifying the interactions. In this study we present an in silico analysis method to determine pooling of variables in complex dynamic models of biochemical reaction networks This method is used to study metabolic network models and allows us to identify and analyze pool formation resulting from the underlying stoichiometric, thermodynamic, and kinetic properties
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