Table 1. Important simulation variables and order parameters.

Notation/Terminology	Physical Interpretation	Definition
Ntot	Total number of polymer chains in the system. Ntot = 400 in our simulations.	–
Lclus	Size of the single largest cluster	represented as fraction of Ntot
Sclus	Size of the cluster	represented as fraction of Ntot
Cmono	Concentration of polymer chains in the simulation box	In units of μM
φ	Bulk density of proteins (in their monomeric state) when the individual chains are randomly placed in the simulation box at the start of the simulation.	${\displaystyle \varphi =\frac{N_{tot}}{(4/3)\pi R_G^{3,}}.R_g^{\prime }}$ is the the radius of gyration of proteins when they are randomly positioned in simulation box at the start of the simulation.
φclus	Intra-cluster density of polymer chains.	${\displaystyle {\varphi }_{clus}=\frac{S_{clus}}{(4/3)\pi R_g^{3_{clus}}}.R_g^{clus}}$ is the radius of gyration of the system of proteins within the cluster.
φclus /φ	Normalized intracluster density describing the degree of enrichment of polymer chains within the cluster.	For system-spanning networks, φclus /φ→1. For dense clusters, φclus /φ >> 1.
εns	Interaction strength for isotropic, non-specific interactions between linker regions. εns in LD simulations is a pairwise interaction strength between individual beads In kMC simulations, εns is the net non-specific interaction strength between two lattice particles.	– .
εsp	Strength of attractive interaction between functional domains (specific interactions).	–
φlattice	Bulk density of monomers in the 2D-lattice in kMC simulations. This quantity is analogous to the concentration of monomers on the lattice.	φlattice = Ntot/L2, where L is the size of the 2D square-lattice.
λ	Valency of the polymer chain, that is the number of adhesive functional domains per interacting polymer chain.	–
Κ	Bending stiffness of the linker regions in LD simulations. A higher value of K is used to model stiffer linkers that prefer a more open configuration.	Κ = 2 kcal/mol, in LD simulations with flexible linkers.
η	The viscosity of the medium in LD simulations	η = 10−3Pa.s in LD simulations, unless mentioned otherwise.
kdiff	Diffusion rate of free monomers in the 2D-lattice kMC simulations.	–
kbond	Rate of formation of specific interactions between neighboring particles in 2D-lattice kMC simulations.	–