Biology-inspired graph neural network encodes reactome and reveals biochemical reactions of disease

Functional heterogeneity of healthy human tissues complicates interpretation of molecular studies, impeding precision therapeutic target identification and treatment. Considering this, we generated a graph neural network with Reactome-based architecture and trained it using 9,115 samples from Genotype-Tissue Expression (GTEx). Our graph neural network (GNN) achieves adjusted Rand index (ARI) = 0.7909, while a Resnet18 control model achieves ARI = 0.7781, on 370 held-out healthy human tissue samples from The Cancer Genome Atlas (TCGA), despite the Resnet18 using over 600 times the parameters. Our GNN also succeeds in separating 83 healthy skin samples from 95 lesional psoriasis samples, revealing that upregulation of 26S- and NUB1-mediated degradation of NEDD8, UBD, and their conjugates is central to the largest perturbed reaction network component in psoriasis. We show that our results are not discoverable using traditional differential expression and hypergeometric pathway enrichment analyses yet are supported by separate human multi-omics and small-molecule mouse studies, suggesting future molecular disease studies may benefit from similar GNN analytical approaches.

Glycolytic oscillations in a model of a lactic acid bacterium metabolism

Glycolytic oscillations in yeast have been extensively studied. It is still unclear, if these oscillations are caused by the allosteric enzyme phosphofructokinase or the stoichiometry of glycolysis which contains an autocatalysis with respect to ATP. Bacterial glycolysis shows a different stoichiometry, however, also containing a stoichiometric autocatalysis. For Escherichia coli, the regulation of the enzyme phosphofructokinase is also assumed to be a major reason for oscillations to occur. We investigated glycolytic oscillations in a quantitative kinetic model for Streptococcus pyogenes set-up on the basis of experimental data. We found oscillations within physiologically feasible parameter ranges. We investigated the origin of these oscillations and conclude that, again, both the stoichiometry of the system, as well as its allosterically regulated enzymes can give rise to these oscillations. For the analysis we employed established and new optimization methods for finding oscillatory regimes and present these in the context of this study.

Thermodynamic evaluation of energy metabolism in mixed substrate catabolism: modeling studies of stationary and oscillatory states

Thermodynamic and kinetic calculations were performed in a model of mixed substrate metabolism. The model simulates the catabolic breakdown of a first substrate, glucose (S(1)), in the presence of a second substrate, formate (S(2)), which acts as an additional source of free energy. The principal results obtained with different relative rates of uptake of S(2) allow to predict and interpret the following experimental observations: (1) the existence of increased ATP yields by mixed substrate utilization with a maximum ATP yield and optimum input (or molar) ratio for both substrates; (2) a greater assimilation of S(1) which may be interpreted as a decreasing fraction of energy required for assimilation; (3) a decrease in ATP yields due to increasing energy demand for transport; (4) an increased assimilation of the carbon source (S(1)) as a function of increasing inputs of the additional energy source; (5) thermodynamic efficiency (eta) defined as the ratio between the output power of ATP synthesis and the input catabolic power, increases for S(2)/S(1) ratios ranging between 0.08 and 2 while for ratios higher than two a slight decrease of eta was noticed; and (6) the observed maximum in ATP yield for optimum molar ratio of the two substrates corresponds to high eta predicting that higher biomass yields may be obtained through a variable, high, eta by chanelling fluxes through catabolic pathways with different ATP yields. During oscillatory behavior, maxima in fluxes were almost coincident with maxima in forces. Thus, the pattern of dissipation was not so advantageous as in the single substrate model under starvation conditions.

Control analysis of glycolytic oscillations

The principles involved in the control of the frequency of sustained metabolic oscillations are developed in the context of glycolytic oscillations in Saccharomyces cerevisiae. To this purpose, an existing mathematical model that describes the experimentally obtained oscillations was simplified to a core model. Frequency, relative phase, average concentrations and amplitudes of the oscillations were well approximated by writing the two remaining metabolic variables of the core model (representing [ATP] and [hexose]) as harmonic functions of time and by requiring them to fulfill the differential equations. The extent to which an enzyme (-conglomerate) controls the frequency in a sustained oscillation is defined as the log-log derivative of that frequency with respect to enzyme activity. In both the full model and the core model this control of frequency and the control over the average concentrations proved to be distributed over the enzymes. We identified a summation theorem, stating that the sum of such control coefficients over all processes equals unity for frequency and zero for the average concentrations.

An allometric interpretation of the spatio-temporal organization of molecular and cellular processes

Different levels of organization distinguished by characteristics spatial dimensions, Ec, and relaxation times, Tr, of biological processes ranging from electron transport in energy transduction to growth of microbial and plant cells, are shown to be related through a relation that may be interpreted as allometric and characterized by two different slopes. Processes, at levels of organization occurring in spatial dimensions of micrometers and relaxing in the order of minutes, delimit a 'transition point' between the two curves, that we interpret as a limit for the emergence of macroscopic coherence. The characteristic spatial dimension, Ec, and the relaxation time, Tr, contain dynamical information about the processes occurring at a given level of organization. When a steady state of a biological process at a certain level of organization becomes unstable, the system undergoes a transition to another level of organization. To exemplify the appearance of macroscopic order at levels of organization further from the 'transition point' we present in this report various experimental systems involving many levels of organization allometrically related that exhibit different kinds of self-organized behavior, i.e. bi-stability, oscillations, changes in (a)symmetry.