Simulating Iron Deficiency in Plant Plastids With a Flexible Physics-Informed Neural Network Approach

Abstract

Flux balance analysis has proven to be a successful approach in metabolic engineering and systems biology to predict intracellular fluxes of large genome-scale networks and the essentiality of genes encoding enzymes and regulatory factors. Flux balance analysis (FBA) relies on a key assumption of a metabolic state being persistent ("steady") over a given time frame. This assumption works well for microbial growth because of the ease with which microbial media can be fixed, biomass can be decomposed, and growth rates can be measured. However, the assumption is far less tenable for the cells and tissues of complex multicellular organisms, particularly if any integrated data is sampled from a heterogeneous collection of developing cells continually interacting between and across tissues. These will likely exhibit transient metabolic states equilibrating over varying timescales, and many FBA studies in complex organisms typically either ignore time as a parameter, or integrate data taken over long timescales (days/weeks). In this work, we adopt and modify a previously published machine learning approach originally developed to hybridize several aspects of a constraint-based approach with machine-learning in order to predict growth. This approach accommodates transient state dynamics, at the cost of tolerating a controlled amount of slack in the steady-state assumption, in order to enable transcript-constrained flux estimation in plant tissues without optimizing a growth objective. For our case study, we reconstruct the metabolism of the plastid of Poplar and Sorghum, integrating data sampled from leaf tissue under varying levels of iron bioavailability. The two species diverge sharply: Sorghum suppresses its photosynthetic electron transport and Calvin cycle abruptly at day 7 and its carbon delivery to biomass collapses to a third of control by day 21, whereas Poplar declines gradually and retains roughly 70%. Normalizing each reaction score to the plastid proteome pool makes the two species comparable and exposes reallocation as the pool contracts, including a split within Sorghums sulfate assimilation that tracks which enzymes carry iron cofactors.