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

Abstract

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.

Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics

“…It should be noted that the analysis performed here is limited to the positive values of parameters near the physiologically meaningful values obtained from the experimental data. The mathematical model (Equation (1)), which was shown to be capable of a description of other biological processes such as polymerization and clustering [13], could demonstrate other types of behavior. For the most of the study, only two parameters were varied simultaneously (Figure 4).…”

“…In these models, the computational cost is high (e.g., 72 × 1072 × 10 core-hours for running a typical simulation [10]) even with the amount of described ligand-receptor interactions being reduced. The second subgroup of the mathematical models utilizes the Smoluchowski equation [11] and mass action kinetics [12,13]. Generally, they have similar problems, although on a smaller scale [13].…”

“…The second subgroup of the mathematical models utilizes the Smoluchowski equation [11] and mass action kinetics [12,13]. Generally, they have similar problems, although on a smaller scale [13]. An additional drawback of such modeling lies in the assumption of the system's homogeneity, which is not valid for the thrombus growth setting but could be valid for platelet aggregometry [2].…”

Cellular automaton modelling of platelet aggregation

“…Часто используемой группой подходов являются модели, основанные на законе действующих масс. В частности, модели, основанные на уравнении коагуляциифрагментации Смолуховского [6], [7], [10], [11]. Такие модели позволяют изучать систему в целом, а также отдельные популяции димеров, тримеров и т.п., однако не могут описать эволюцию роста отдельного агрегата.…”

“…Для цитирования: Васильев Г.А. SBPReports 2022 29 сентября; 3 (2) pp [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. …”