Computational singular perturbation analysis of brain lactate metabolism

Progress in The Research of Lactate Metabolism Disruption And Astrocyte-Neuron Lactate Shuttle Impairment in Schizophrenia: A Comprehensive Review

Schizophrenia (SCZ) is a complex neuropsychiatric disorder widely recognized for its impaired bioenergy utilization. The astrocyte-neuron lactate shuttle (ANLS) plays a critical role in brain energy supply. Recent studies have revealed abnormal lactate metabolism in SCZ, which is associated with mitochondrial dysfunction, tissue hypoxia, gastric acid retention, oxidative stress, neuroinflammation, abnormal brain iron metabolism, cerebral white matter hypermetabolic activity, and genetic susceptibility. Furthermore, astrocytes, neurons, and glutamate abnormalities are prevalent in SCZ with abnormal lactate metabolism, which are essential components for maintaining ANLS in the brain. Therefore, an in-depth study of the pathophysiological mechanisms of ANLS in SCZ with abnormal lactate metabolism will contribute to a better understanding of the pathogenesis of SCZ and provide new ideas and approaches for the diagnosis and treatment of SCZ.

Lactate's behavioral switch in the brain: An in-silico model

Emerging evidence emphasizes lactate's involvement in both physiological processes (energy metabolism, memory, etc.) and disease (traumatic brain injury, epilepsy, etc.). Furthermore, the usefulness of mathematical modeling in deciphering underlying dynamics of the brain to investigate lactate roles and mechanisms of action has been well established. Here, we analyze a novel mathematical model of brain lactate exchanges between four compartments: neurons, astrocytes, capillaries, and extracellular space. A system of four ordinary differential equations is proposed to explain interactions between these compartments. We first optimize and analyze the model's parameters under normal, resting state conditions, and then use it to simulate changes linked to elevated arterial lactate. Our results show that even though increased arterial lactate results in increased uptake by astrocytes and release to the extracellular space, it cannot strongly recover the initial drop in neuronal lactate concentration. Also, we show that the direction of lactate transport between the compartments is influenced by the maximum astrocyte production rate and the transport rate between astrocytes and extracellular space.

Mechanistic multiscale modelling of energy metabolism in human astrocytes reveals the impact of morphology changes in Alzheimer's Disease

Astrocytes with their specialised morphology are essential for brain homeostasis as metabolic mediators between blood vessels and neurons. In neurodegenerative diseases such as Alzheimer's disease (AD), astrocytes adopt reactive profiles with molecular and morphological changes that could lead to the impairment of their metabolic support and impact disease progression. However, the underlying mechanisms of how the metabolic function of human astrocytes is impaired by their morphological changes in AD are still elusive. To address this challenge, we developed and applied a metabolic multiscale modelling approach integrating the dynamics of metabolic energy pathways and physiological astrocyte morphologies acquired in human AD and age-matched control brain samples. The results demonstrate that the complex cell shape and intracellular organisation of energetic pathways determine the metabolic profile and support capacity of astrocytes in health and AD conditions. Thus, our mechanistic approach indicates the importance of spatial orchestration in metabolism and allows for the identification of protective mechanisms against disease-associated metabolic impairments.

Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism

We present "on the fly" algorithmic criteria for the accuracy and stability (non-stiffness) of reduced models constructed with the quasi-steady state and partial equilibrium approximations. The criteria comprise those introduced in Goussis (Combust Theor Model 16:869-926, 2012) that addressed the case where each fast time scale is due to one reaction and a new one that addresses the case where a fast time scale is due to more than one reactions. The development of these criteria is based on the ability to approximate accurately the fast and slow subspaces of the tangent space. Their validity is assessed on the basis of the Michaelis-Menten reaction mechanism, for which extensive literature is available regarding the validity of the existing various reduced models. The criteria predict correctly the regions in both the parameter and phase spaces where each of these models is valid. The findings are supported by numerical computations at indicative points in the parameter space. Due to their algorithmic character, these criteria can be readily employed for the reduction of large and complex mathematical models.

A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift

OBJECTIVE

The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the perturbation parameter, and the term with negative shift causes interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically. We have treated the problem by proposing a numerical scheme using the implicit Euler method in the temporal direction and a fitted tension spline method in the spatial direction with uniform meshes.

RESULT

Stability and uniform error estimates are investigated for the developed numerical scheme. The theoretical finding is demonstrated by numerical examples. It is obtained that the developed numerical scheme is uniformly convergent of order one in time and order two in space.

Algorithmic multiscale analysis for the FcRn mediated regulation of antibody PK in human

A demonstration is provided on how algorithmic asymptotic analysis of multi-scale pharmacokinetics (PK) systems can provide (1) system level understanding and (2) predictions on the response of the model when parameters vary. Being algorithmic, this type of analysis is not hindered by the size or complexity of the model and requires no input from the investigator. The algorithm identifies the constraints that are generated by the fast part of the model and the components of the slow part of the model that drive the system within these constraints. The demonstration is based on a typical monoclonal antibody PK model. It is shown that the findings produced by the traditional methodologies, which require significant input by the investigator, can be produced algorithmically and more accurately. Moreover, additional insights are provided by the algorithm, which cannot be obtained by the traditional methodologies; notably, the dual influence of certain reactions depending on whether their fast or slow component dominates. The analysis reveals that the importance of physiological processes in determining the systemic exposure of monoclonal antibodies (mAb) varies with time. The analysis also confirms that the rate of mAb uptake by the cells, the binding affinity of mAb to neonatal Fc receptor (FcRn), and the intracellular degradation rate of mAb are the most sensitive parameters in determining systemic exposure of mAbs. The algorithmic framework for analysis introduced and the resulting novel insights can be used to engineer antibodies with desired PK properties.

Algorithmic asymptotic analysis: Extending the arsenal of cancer immunology modeling

The recent advances in cancer immunotherapy boosted the development of tumor-immune system models, with the aim to indicate more efficient treatments. Physical understanding is however difficult to be acquired, due to the complexity and the multi-scale dynamics of these models. In this work, the dynamics of a fundamental model formulating the interactions of tumor cells with natural killer cells, CD8⁺ T cells and circulating lymphocytes is examined. It is first shown that the long-term evolution of the system towards high-tumor or tumor-free equilibria is determined by the dynamics of an initial explosive stage of tumor progression. Focusing on this stage, the algorithmic Computational Singular Perturbation methodology is employed to identify the underlying mechanisms confining the system's evolution and the governing slow dynamics along them. These insights are preserved along different tumor-immune system and patient-dependent realizations. On top of these identifications, a novel reduced model is algorithmically constructed, which accurately predicts the dynamics of the system during the explosive stage and includes half of the parameters of the detailed model. The present analysis demonstrates the potential of algorithmic asymptotic analysis for acquiring physical understanding and for simplifying the complexity of cancer immunology models. Along with the current techniques on the field, this analysis can provide guidelines for more effective treatment development.