Particle simulation approach for subcellular dynamics and interactions of biological molecules

Abstract

Background: Spatio-temporal dynamics within cells can now be visualized at appropriate resolution, due to the advances in molecular imaging technologies. Even single-particle tracking (SPT) and single fluorophore video imaging (SFVI) are now being applied to observation of molecular-level dynamics. However, little is known concerning how molecular-level dynamics affect properties at the cellular level.

Results: We propose an algorithm designed for three-dimensional simulation of the reaction-diffusion dynamics of molecules, based on a particle model. Chemical reactions proceed through the interactions of particles in space, with activation energies determining the rates of these chemical reactions at each interaction. This energy-based model can include the cellular membrane, membranes of other organelles, and cytoskeleton. The simulation algorithm was tested for a reversible enzyme reaction model and its validity was confirmed. Snapshot images taken from simulated molecular interactions on the cell-surface revealed clustering domains (size approximately 0.2 microm) associated with rafts. Sample trajectories of raft constructs exhibited "hop diffusion". These domains corralled the diffusive motion of membrane proteins.

Conclusion: These findings demonstrate that our approach is promising for modelling the localization properties of biological phenomena.

Figure 1

The binding process. (A) The movement trial drives S upward. Here the bond variables of S and T are empty (symbols {φ}). (B) Before the movement, S is checked to determine whether it may bind with T, by searching among the complex candidates. (C) If the table has a combination of single S and single T (S-T) simultaneously, a uniform random number ξ (0 ≤ ξ < 1) and the transition probability p₁ are compared. (D) When ξ <p₁, the movement is accepted.

Figure 2

An interaction without binding. (A) U already occupies the bond variable of T due to the binding of T and U. (B) The process of searching for TS among the candidates. (C) Particle T returns {U}, with discarding of the ST complex.

Figure 3

The unbinding process. Particle S is driven downward by the random walk trial. The TS complex (A) splits into the S and T particles (B).

Figure 4

The modification process. The TS complex (A) is converted to TV (B).

Figure 5

S+E->SE particle simulation. Trajectories of particles S and E bind together with p₂ = 0, taken at every 1.6 × 10²τ from t = 0 to 1.6 × 10⁴τ. The unit of length is 1 μm, based on the scale conversion of (b) in Table I. Red: particle of S species; Green: particle of E species.

Figure 6

Comparison of particle simulation and ODE results. The average of [P] plotted with time (sec) for Monte Carlo (particle) simulations (open symbols) and the corresponding rate equations (line curves). The activation energies and their corresponding kinetic parameters are listed in Table 2: (a) and (c) in Table 2 for (A), while (b) and (d) in Table 2 for (B). The total concentration of E is [E]₀ = 0.1 μM. The initial distribution is random with equal probability for all the sites in the 3D space, with use of 16 samples.

Figure 7

Simulation of cell-surface clustering. A snapshot image taken at t = 2.2 sec. The length scale of each side is in μm. Molecular species: (+) cholesterol, (×) glycosphingolipids, (●) T-cell receptor, and (▲) LAT adaptor protein.

Figure 8

Simulation of cell-surface clustering: Particle trajectories. (A) TCR, (B) LAT, (C) cholesterol, and (D) glycosphingolipid, for t = 0.4–2.3 sec.