Models of Solute Aggregation Using Cellular Automata

Kier, Lemont B.; Cheng, Chao‐Kun; Nelson, Jean D.

doi:10.1002/cbdv.200800285

Cited by 6 publications

(8 citation statements)

References 11 publications

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“…Considering relatively low STIM1 counts in platelet it is reasonable to use different type of approach for SOCE modelling. One of this approaches can be lattice-based models [21], where the system is represented by a mesh of cells that have a finite number of states. Each cell evolves according to a specific set of rules that represents temporal evolution of the system.…”

Section: Introductionmentioning

confidence: 99%

STIM1-ORAI1 direct interaction cannot govern store-operated calcium entry (SOCE) in platelets

Dasgupta

2021

SBPR

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Store-operated calcium entry (SOCE) plays an important role in platelet function. It is generally assumed that the mechanism of SOCE relies on the direct interaction of STIM1 and ORAI1 proteins with specific STIM1:ORAI1 stoichiometry. However, in platelets, other pathways may take place. Here we aim to investigate the mechanisms of SOCE in platelets. We developed a lattice-based mathematical model that represented STIM1-ORAI1 interactions and applied it to both HEK cells, where SOCE mechanism is well established, and platelets. The model was able to describe STIM1-ORAI1 behavior in HEK cells successfully. We used the same parameters for protein interaction and applied them to platelets. As a result, we demonstrated that the number of STIM1 proteins on ER membrane could not assure the needed stoichiometry to proper SOCE in platelets.

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Section: Introductionmentioning

confidence: 99%

STIM1-ORAI1 direct interaction cannot govern store-operated calcium entry (SOCE) in platelets

Dasgupta

2021

SBPR

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“…Several mathematical models of the process of aggregation have been proposed [22][23][24][25][26][27][28]. One of the commonly used approaches is the cellular automata models [24], where the system is represented by a mesh of cells that have a finite number of states. Each cell evolves, according to a specific set of rules that represent the temporal evolution of the system.…”

Section: Introductionmentioning

confidence: 99%

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

Dasgupta

Martyanov

Filkova

et al. 2020

Life

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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.

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“…The use of stochastic CA‐based models, which will be employed in this article, is already reported in literature 19, 35–39. Kier et al19 developed a CA‐based model to describe the interaction between two H 2 O molecules employing a stochastic CA.…”

Section: Introductionmentioning

confidence: 99%

“…Their CA‐based model is used to model a.o. the solid‐liquid interface,38 the bulk structure of water37 and solute diffusion through water,39 the latter also being modeled by Chopard and Droz 35, 36…”

Section: Introductionmentioning

confidence: 99%

Design and parameterization of a stochastic cellular automaton describing a chemical reaction

Weeën

Baetens

2011

J Comput Chem

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Although most of the work concerned with reaction kinetics concentrates on empirical findings, stochastic models, and differential equations, a growing number of researchers is exploring other methods to elucidate reaction kinetics. In this work, the parameterization of an utter discrete spatio-temporal model, more specifically, a cellular automaton (CA), describing the reaction of HCl with CaCO(3) , is suggested. Furthermore, a system of partial differential equations (PDE), deduced from a set of CA rules, is implemented to compare both modeling paradigms. In this article, the experimental setup to acquire time series of data is explained, a stochastic CA-based model and a continuous PDE-based model capable of describing the reaction are proposed, the models are parameterized using the experimental data and, finally, the relationship between a discrete time step of the CA-based model and the physical time is studied. Essentially, the parameterization of both models can be traced back to the quest for a solution of the inverse problem in which a (set of) rule(s), respectively a system of PDE, is deduced starting from the observed data. It is demonstrated that the proposed CA- and PDE-based models are capable of describing the considered chemical reaction with a high accuracy, which is confirmed by a root mean squared error between the simulated and observed data of 0.388 and 0.869 g CO(2) , respectively. Further, it is shown that an exponential or linear relationship can be used to link the physical time to a discrete time step of the CA-based model.

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Models of Solute Aggregation Using Cellular Automata

Cited by 6 publications

References 11 publications

STIM1-ORAI1 direct interaction cannot govern store-operated calcium entry (SOCE) in platelets

STIM1-ORAI1 direct interaction cannot govern store-operated calcium entry (SOCE) in platelets

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

Design and parameterization of a stochastic cellular automaton describing a chemical reaction

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