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Spatial Monte Carlo model of integrin clustering
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Nanoscale integrin cluster dynamics controls cellular mechanosensing via FAKY397 phosphorylation

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We developed a multistep process of integrin clustering. In our model, single integrin has two states, i.e., inactive state where integrin has a low affinity with ligands, which are assumed to be uniformly distributed in our simulation domain, and active state where integrin has a high affinity with ligands. The configuration transition of integrin from the inactive state to the active state is the prerequisite for integrin clustering. The molecular mechanisms underlying the lateral clustering of integrins remain controversial. The integrin clustering submodel applied in this work was based on three clustering mechanisms: ITD-mediated clustering, PI(4,5)P2-mediated clustering, and integrin cross-talk–mediated clustering. We note that many other mechanisms have been proposed, and the rationale for focusing on these three is described in the Supplementary Materials. We then built a coarse-grained model to simulate the integrin clustering process based on the multistep processes as described above.

We modeled the integrin clustering via a spatial Monte Carlo algorithm. All reactions including integrin activation and inactivation, integrin clustering and disassociation, and translational diffusion of integrin on the membrane were modeled on a 2D lattice plane with periodic boundary conditions. The integrin molecules were randomly placed in the lattice domains for the initial configuration. The simulation was implemented by randomly choosing an integrin molecule (an occupied lattice site), and then an event was determined (chemical reactions or translational diffusion) based on the probabilities. An event was chosen by calculating the probability distribution for all possible events$PiM=σiMσtot$(6)where i is the integrin site and M is the event; $σiM$ is the transition rate for M event; and σtot is defined as(7)where σD is the transition probability of translational diffusion, and σR is the transition probability of chemical reactions. All transition probabilities are shown in table S1. After integrin clustering, the clustered integrins (three or more integrin molecules) will stop diffusion. The plasma membrane was modeled as a 2D triangle lattice with each pixel being 15 nm in size. We set the integrin density as 500/μm2. Each integrin is simplified as a circular with a radius of 10 nm.

The dynamical parameters of the α5β1 and αvβ3 integrins were taken from the literature. Four dynamical parameters differ for α5β1 and αvβ3 integrins: (i) the diffusion coefficients of integrins (~0.1 μm2/s for α5β1 integrins and ~0.3 μm2/s for αvβ3 integrins); (ii) the activation rate of αvβ3 integrin is 10-fold higher than that of α5β1 integrin, as deduced from free-energy analysis; (iii) the intrinsic ligand binding affinity of the α5β1 integrin is higher than that of the αvβ3 integrin; and (iv) α5β1 integrins have longer lifetime than αvβ3 integrins, in response to the same bond tension. The two types of integrins with different dynamical parameters were dispersed within simulation regions. Note that, because lateral clustering of integrin remains controversial, we assumed that different integrins had the same lateral clustering affinity.

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