Life sciences through mathematical models

Identifying feasible steady state solutions of a brain energy metabolism model is an inverse problem that allows infinitely many solutions. The characterization of the non-uniqueness, or the uncertainty quantification of the flux balance analysis, is tantamount to identifying the degrees of freedom of the solution. The degrees of freedom of multi-compartment mathematical models for energy metabolism of a neuron-astrocyte complex may offer a key to understand the different ways in which the energetic needs of the brain are met. In this paper we study the uncertainty in the solution, using techniques of linear algebra to identify the degrees of freedom in a lumped model, and Markov chain Monte Carlo methods in its extension to a spatially distributed case. The interpretation of the degrees of freedom in metabolic terms, more specifically, glucose and oxygen partitioning, is then leveraged to derive constraints on the free parameters to guarantee that the model is energetically feasible. We demonstrate how the model can be used to estimate the stoichiometric energy needs of the cells as well as the household energy based on the measured oxidative cerebral metabolic rate of glucose and glutamate cycling. Moreover, our analysis shows that in the lumped model the net direction of lactate dehydrogenase (LDH) in the cells can be deduced from the glucose partitioning between the compartments. The extension of the lumped model to a spatially distributed multi-compartment setting that includes diffusion fluxes from capillary to tissue increases the number of degrees of freedom, requiring the use of statistical sampling techniques. The analysis of the distributed model reveals that some of the conclusions valid for the spatially lumped model, e.g., concerning the LDH activity and glucose partitioning, may no longer hold.

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Uncertainty quantification in flux balance analysis of spatially lumped and distributed models of neuron–astrocyte metabolism

Calvetti

Cheng

Somersalo

2016

J. Math. Biol.

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Beyond the Model Limit: Parameter Inference Across Scales

Callahan¹,

Calvetti²,

Somersalo³

2017

SIAM/ASA J. Uncertainty Quantification

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Brain energetics, mitochondria, and traumatic brain injury

Benaroya

2020

Reviews in the Neurosciences

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We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain’s high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria – the organelle responsible for almost all the energy production in the cell – and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.

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Life sciences through mathematical models

Cited by 5 publications

References 23 publications

Uncertainty quantification in flux balance analysis of spatially lumped and distributed models of neuron–astrocyte metabolism

Uncertainty quantification in flux balance analysis of spatially lumped and distributed models of neuron–astrocyte metabolism

Beyond the Model Limit: Parameter Inference Across Scales

Brain energetics, mitochondria, and traumatic brain injury

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