Molecular Modeling of the Intracellular Environment

The inside of cells is highly crowded with bio-macromolecules, such as proteins, DNA, RNA. This environment is quite different from the conditions in a test tube that we usually use for analysis of biomolecular functions, where the macromolecular concentration is ~100 times less than inside cells. This crowding significantly alters motions (kinetics) and stability (thermodynamics) of those molecules. Therefore, modeling of the intracellular environment is an important first step towards whole cell simulation.

Recently, we simulated a virtual cytoplasmic system of E. coli to elucidate the nature of motions of macromolecules inside cells by using a Brownian dynamics method. Our simulation study showed that hydrodynamic interactions play an important role in macromolecular motions in cells: Hydrodynamic interactions greatly reduce the diffusion coefficient and create collective motions at cellular concentrations.

Reference: T. Ando and J. Skolnick. Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion. Proc Natl Acad Science 2010, 107:18457-18462.

Our work is featured in "American Scientis" (vol. 99, No. 1).

Simulation systems of a virtual cytoplasmic system of E. coli
molecular_system.png sphere_system.png
(Left) Molecular-shaped system. Box size is 100 nm x 100 nm x 100 nm. This system contains, ribosome, RNA polymerase, some members of glycolytic enzymes, tRNA, GFP and so on. Macromolecular concentration reaches at 300 mg/ml. (Right) Equivalent sphere system. In this model, each molecule is represented by a sphere with its Stokes radius.

Movies of our simulations

A Molecular_steric.gif B Sphere_steric.gif C Sphere_HI.gif D Sphere_nonspe.gif

(A) Molecular-shaped system with steric repulsions (25 microsecond to 30 microsecond). (B) Equivalent-sphere system with steric repulsions (25 microsecond to 30 microsecond). (C) Equivalent-sphere system with hydrodynamic interactions (10 microsecond to 15 microsecond). (D) Equivalent-sphere system with non-specific attractive interactions (45 microsecond to 50 microsecond).
When we consider only repulsive interactions between macromolecules, motions (diffusion) of GFP protein (drawn in green) are much faster than experimental results. On the other hand, when hydrodynamic interactions are incorporated into simulation, the diffusion constant of GFP is in good agreement with experiment. If we introduce non-specific attractive interactions to reproduce experimental diffusivity of GFP molecule, large molecules stick together.

What is "hydrodynamic interactions"?
Particles immersed in a fluid perturb the solvent flow as they move, and motions of other particles are affected by this perturbation. This effect is termed hydrodynamic interactions. The interactions can give rise to collective motions between particles. The following Movie is a very good example that show how the hydrodynamic interactions affect motions of particles in a fluid. The simulation conditions are described in the paper, "Dynamic simulation of hydrodynamically interacting particles" by L. Durlofsky, J. F. Brady and G. Bossis (J. Fluid Mech. (1987) 180:21-49). In a simulation of the inside of cells, we also observed significant collective dynamics between macromolecules in time and space at cellular concentrations.

3particles_noHI.gif 3particles_HI.gif
Sedimentation of three identical spheres without (Left) and with (right) hydrodynamic interactions.