On Parkinson's disease and its mathematical models

Manfred Sneps-Sneppe


The article examines hypotheses for the occurrence of Parkinson's disease (PD). Historically, the dopamine hypothesis was the first and distinctive feature of the pathology of PD is the depletion of dopaminergic cells, and the drug L-DOPA is the only remedy that alleviates the course of the disease. Other hypotheses (insulin resistance, immunotherapy, serotonin) are less studied and require deeper insight into the brain. Insulin resistance has received the fundamental study using the theory of biochemical systems (the mathematical model contains 339 equations), unfortunately, without practical conclusions. The immunotherapy hypothesis in neurological diseases is even more in its infancy. L-DOPA is very effective in the first years of use. However, over time, patients begin to experience dyskinesias, the most troublesome side effect of L-DOPA. Experimental evidence points to serotonin as a promising anti-dyskinetic therapy for PD patients treated with L-DOPA. But when will it be possible to figure this out, bearing in mind that fifteen serotonin receptors have already been identified? In our opinion, the newest hypothesis – a disorder of fat metabolism most closely reflects the essence of Parkinson's disease, but the hypothesis is in the initial state of research. Adipose tissue is an endocrine organ that synthesizes many biologically active substances – adipocytokines, which affect insulin resistance (IR), glucose and lipid metabolism, and inflammation. Their study is complicated because some members of the adipocytokine family reduce IR, while others increase it. In conclusion, we note that the etiology of neurodegeneration in Parkinson's disease remains unclear.

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Bakshi, S., Chelliah, V., Chen, C. and van der Graaf, P.H. (2019) Mathematical biology models of Parkinson's disease. CPT: pharmacometrics & systems pharmacology, 8(2), pp.77-86.

Bharathi, P., Nagabhushan, P. and Rao, K.J. (2008) A mathematical approach to understanding the kinetics of α-synuclein aggregation: Relevance to Parkinson's disease. Computers in Biology and Medicine, 38(10), pp.1084-1093.

Qi, Z., Miller, G.W. and Voit, E.O. (2012) Mathematical models of dopamine metabolism in Parkinson’s disease. Systems biology of Parkinson's disease, P. Wellstead and M. Cloutier (eds.), pp.151-171.

Viviana A. Ruiz-Pozo, et al. (2023) The Molecular Mechanisms of the Relationship between Insulin Resistance and Parkinson’s Disease Pathogenesis. Nutrients. 15(16): 3585.

Savageau M.A. (1969) Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J. Theor. Biol. 25. pp. 365-369.

Matthews D.R., Hosker J.P., Rudenski A.S., Naylor B.A., Treacher D.F., Turner R.C. (1985) Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man. Diabetologia. 28(7): 412-419.

Braatz E.M., Coleman R.A. (2015) A mathematical model of insulin resistance in Parkinson’s disease. Computational Biology and Chemistry, Vol 56, Pages 84-97.

Al-Tuwairqi S.M. and Badrah A.A. (2023) Modeling the dynamics of innate and adaptive immune response to Parkinson’s disease with immunotherapy. AIMS Mathematics, 8(1), pp.1800-1832.

Pinna A., Parekh P., Morelli M. (2023) Serotonin 5-HT1A receptors and their interactions with adenosine A2A receptors in Parkinson's disease and dyskinesia. Neuropharmacology, Vol 226, 109411.

Pasquini J., et al. (2018) Progression of tremor in early stages of Parkinson’s disease: a clinical and neuroimaging study. Brain, 141: 811–21.

DiGiovanni, G., Esposito, E., DiMatteo, V. (2010). Role of serotonin in central dopamine dysfunction. CNS neuroscience & therapeutics, 16(3), 179-194.

DiMatteo, et al. (2008) Serotonin modulation of the basal ganglia circuitry: therapeutic implication for Parkinson’s disease and other motor disorders. Progress in Brain Research. G. DiGiovanni, V. Di Matteo & E. Esposito (Eds.), Vol. 172, pp 423-463.

Carta M., et al. (2008) Serotonin–dopamine interaction in the induction and maintenance of L-DOPA-induced dyskinesias. DiGiovanni G., et al. Serotonin–dopamine interaction: electrophysiological evidence. Progress in brain research, 172: 465-478.

Caligiore D., et al. (2021) Increasing Serotonin to Reduce Parkinsonian Tremor. Front. Syst. Neurosci. 15, p.682990.

Ugolev A. M. Pishhevarenie i ego prisposobitel'naja jevoljucija. M., 1961

Parfenov A.I., Chernin V.V., Bondarenko V.M., Rybal'chenko O.V. (2014) Simbiontnoe pishhevarenie v svete teorii A.M. Ugoleva o pishhevaritel'no-transportnom konvejere. RMZh; 15: 1088.

Ugolev A. M. Teorija adekvatnogo pitanija i trofologija. Sankt-Peterburg: Nauka, 1991.

Gershon, M.D. (1981) The enteric nervous system. Annual review of neuroscience, 4(1), pp.227-272.

Yin-Xia Chao, et al. (2020) Gut–Brain Axis: Potential Factors Involved in the Pathogenesis of Parkinson's Disease. Front Neurol. 27; 11: 625446.

Bloomingdale, P., et al. (2022). Hallmarks of neurodegenerative disease: A systems pharmacology perspective. CPT: Pharmacometrics & Systems Pharmacology, 11(11), 1399-1429.

Toledo, A.R.L., Monroy, G.R., Salazar, F.E., Lee, J.Y., Jain, S., Yadav, H. and Borlongan, C.V. (2022) Gut-brain axis as a pathological and therapeutic target for neurodegenerative disorders. International Journal of Molecular Sciences, 23(3), p.1184.

Ruiz-Pozo V.A., et al. (2023) The Molecular Mechanisms of the Relationship between Insulin Resistance and Parkinson's Disease Pathogenesis. Nutrients. 15(16):3585. doi: 10.3390/nu15163585.

Alfonsetti, M., Castelli, V., d’Angelo, M. (2022). Are we what we eat? Impact of diet on the gut-brain axis in Parkinson’s disease. Nutrients, 14(2), 380.

Yemula, N., Dietrich, C., Dostal, V., & Hornberger, M. (2021). Parkinson’s disease and the gut: symptoms, nutrition, and microbiota. Journal of Parkinson's Disease, 11(4), 1491-1505.

Ofuji, Hanae, et al. (2023) A Mathematical Modeling and Treatment Analysis of Dynamic Glucose Metabolism with Brain-based Regulatory Mechanism. IFAC-PapersOnLine. 56.2 3630-3635.

Regensburger, M., Chaudhry, S.R., Yasin, H., Zhao, Y., Stadlbauer, A., Buchfelder, M. and Kinfe, T. (2023) Emerging roles of leptin in Parkinson’s disease: chronic inflammation, neuroprotection, and more? Brain, Behavior, and Immunity, 107, pp.53-61.

Markova, T. N., Mishhenko, K., Petina, V. (2022) Adipocitokiny: sovremennyj vzgljad na definiciju, klassifikaciju i rol' v organizme. Problemy jendokrinologii. Tom 68, # 1.

Lerner, A.; Neidhöfer, S.; Matthias, T. (2017) The Gut Microbiome Feelings of the Brain: A Perspective for Non-Microbiologists. Microorganisms, 5, 66.


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