Cycling of co-substrates, whereby a metabolite is converted among alternate forms via different reactions, is ubiquitous in metabolism. Several cycled co-substrates are well known as energy and electron carriers (e.g. ATP and NAD(P)H), but there are also other metabolites that act as cycled co-substrates in different parts of central metabolism. Here, we develop a mathematical framework to analyse the effect of co-substrate cycling on metabolic flux. In the cases of a single reaction and linear pathways, we find that co-substrate cycling imposes an additional flux limit on a reaction, distinct to the limit imposed by the kinetics of the primary enzyme catalysing that reaction. Using analytical methods, we show that this additional limit is a function of the total pool size and turnover rate of the cycled co-substrate. Expanding from this insight and using simulations, we show that regulation of these two parameters can allow regulation of flux dynamics in branched and coupled pathways. To support these theoretical insights, we analysed existing flux measurements and enzyme levels from the central carbon metabolism and identified several reactions that could be limited by the dynamics of co-substrate cycling. We discuss how the limitations imposed by co-substrate cycling provide experimentally testable hypotheses on specific metabolic phenotypes. We conclude that measuring and controlling co-substrate dynamics is crucial for understanding and engineering metabolic fluxes in cells.

Seizure generation, propagation, and termination occur through spatiotemporal brain networks. In this paper, we demonstrate the significance of large-scale brain interactions in high-frequency (80-200 Hz) for identification of the epileptogenic zone (EZ) and seizure evolution. To incorporate the continuity of neural dynamics, here we have modeled brain connectivity constructed from stereoelectroencephalography (SEEG) data during seizures using multilayer networks. After introducing a new measure of brain connectivity for temporal networks, named multilayer eigenvector centrality (mlEVC), we applied a consensus hierarchical clustering on the developed model to identify the epileptogenic zone (EZ) as a cluster of nodes with distinctive brain connectivity in the ictal period. Our algorithm could successfully predict electrodes inside the resected volume as EZ for 88% of participants, who all were seizure-free for at least 12 months after surgery. Our findings illustrated significant and unique desynchronization between EZ and the rest of the brain in early to mid-seizure. We showed that aging and duration of epilepsy intensify this desynchronization, which can be the outcome of abnormal neuroplasticity. Additionally, we illustrated that seizures evolve with various network topologies, confirming the existence of different epileptogenic networks in each patient. Our findings suggest not only the importance of early intervention in epilepsy but the possible factor which correlates with disease severity. Moreover, by analyzing the propagation patterns of different seizures, we asserted the necessity of collecting sufficient data for identifying the epileptogenic networks.