Fig 1.
Overview of the CASPULE pipeline.
It has three components – setup (step 1), simulation (step 2) and analysis (step 3). In step 1, we create a sticker spacer polymer chain in a template-based manner, where a pattern of sticker-spacer serves as a building block. Multiple repeats of such blocks create a chain. Red and grey beads represent stickers and spacers, respectively. Once the chains are created, we pack multiple copies inside the simulation box using the Moltemplate and PACKMOL software packages. This creates an initial condition which may contain many copies of multiple chain types. In step 2, we simulate the polymer condensation using the LAMMPS software. In step 3, we analyze various biophysical properties (cluster size distribution, extent of sticker saturation, radial location of stickers inside the condensate etc.) of the system.
Fig 2.
Quantification of clustering dynamics.
(A) Illustration of the two-component sticker-spacer system. Each component consists of 10 stickers (red and cyan beads) and 40 spacers (yellow beads). We only allow heterotypic interactions, that is, red stickers interact with cyan stickers, but red-red or cyan-cyan are not allowed. (B) Stickers engage in specific interactions (Es). A complementary sticker (red and cyan) pair can form a reversible bond within a cutoff radius, Rcut. Once bonded, they cannot engage with another sticker that may be present within Rcut. In other words, each sticker has a valency of 1. (C) All beads (except bonded stickers) in the system experience non-specific interactions (Ens), modelled by Lennard-Jones (LJ) potential. One bead can interact with multiple beads, permitted by volume exclusions. A bead diameter (σ) is set by the minimum distance between two bead centers. (D) Snapshots of a multi-chain system undergoing clustering as a function of time. A total of 400 chains (200 chains each type) are placed uniformly inside a cubic box (length = 800Å). Sticker-sticker (Es = 6kT) interactions drive inter-chain crosslinking and weaker spacer-spacer (Ens = 0.3kT) interactions tune the cluster compaction. (E) Energy time course of the system. Ebond includes all the bonds (permanent and breakable) present in the system. Epair refers to the sum of contact energies coming from the pairwise Lennard-Jones interactions. Eangle is angular energy. Epotential = Ebond + Epair + Eangle. Energy unit is kcal/mol. (F) Time course of radius of gyration (Rgsystem) and sticker saturation. Inset shows the zoomed in version of the first half. The red dashed line indicates the time needed to equilibrate the system’s Rg, while the blue dashed line indicates the time needed by the stickers to reach to a steady saturation level. In (E,F), data is averaged over 5 stochastic runs. Solid line is mean, shaded area is standard deviation.
Fig 3.
Test of detailed balance for specific interactions.
(A) Thermodynamic criteria of detailed balance for a two-sticker (orange and green) specific interaction scheme. and
are stationary probabilities of finding the system in unbound (U) and bound (B) state, respectively.
and
are transition rates from bound to unbound, and vice versa.
is equilibrium constant that varies exponentially with the depth of the energy well (Es). (B) Simulation setup consisting of two stickers. The expediate the diffusion driven search process, a pseudo-one-dimensional box (with periodic boundaries) is considered where both stickers can switch between bonded and unbonded states. (C) A representative time course of bonding dynamics (1 is bonded and 0 is unbonded). At two successive frames (t and t’), the system (s) can display one of the four possibilities;
(D) Scaling behavior of equilibrium quantities with specific interaction strength, Es. Two sides of vertical axis show two different quantities (color coded). The black dashed line is the linear fit. A linear regression with R² = 0.99 and a p-value of 2 × 10 ⁻ ⁵ indicates an excellent linear fit.
Fig 4.
Quantification of the phase transition boundary.
(A) Illustration of phase transition by titrating specific energy (Es). The cluster dissolves at Es lower than a critical value. Above the critical level of Es, cluster is stable. (B) Average cluster occupancy (ACO) normalized by the total number of chains in the system. See main text for definition. (C) Fraction of bonded sticker or sticker saturation. (D) Inter-sticker dissociation events. The shaded area indicates a region after the phase transition.
Fig 5.
Scaling of execution time with system size.
(A) Three representative clusters with different chain counts () that are simulated with higher number of CPUs (
) in parallel. (B) Execution time (reported in seconds, log10 scale) as a function of the system size.