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Open AccessArticle

Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors

Faculty of Physics, Lomonosov Moscow State University, 1/2 Leninskie gory, 119991 Moscow, Russia
National Medical Research Centеr of Pediatric Hematology, Oncology and Immunology named after Dmitry Rogachev, 1 Samory Mashela St, 117198 Moscow, Russia
Institute for Biochemical Physics (IBCP), Russian Academy of Sciences (RAS), Russian Federation, Kosyigina 4, 119334 Moscow, Russia
Center for Theoretical Problems of Physico-Сhemical Pharmacology, Russian Academy of Sciences, 30 Srednyaya Kalitnikovskaya str., 109029 Moscow, Russia
Faculty of Biological and Medical Physics, Moscow Institute of Physics and Technology, 9 Institutskii per., 141700 Dolgoprudnyi, Russia
Department of Normal Physiology, Sechenov First Moscow State Medical University, 8/2 Trubetskaya St., 119991 Moscow, Russia
Author to whom correspondence should be addressed.
Life 2020, 10(6), 97;
Received: 1 June 2020 / Accepted: 24 June 2020 / Published: 26 June 2020
(This article belongs to the Section Biochemistry, Biophysics and Computational Biology)
The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D. View Full-Text
Keywords: computational modeling; particle aggregation; receptor clustering; Smoluchowski coagulation computational modeling; particle aggregation; receptor clustering; Smoluchowski coagulation
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Garzon Dasgupta, A.K.; Martyanov, A.A.; Filkova, A.A.; Panteleev, M.A.; Sveshnikova, A.N. Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors. Life 2020, 10, 97.

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