Hydrodynamics Simulation

Simulating the motion of arbitrarily shaped protein molecules.

Ionic current measurements through nanopores can be an effective tool to analyze individual proteins. So far, the shape of non-spherical proteins moving through nanopores has been modelled as ellipsoids, either prolate or oblate. To provide a more realistic description of the protein shape, we modelled anisotropic protein shapes as a cluster of unequally-sized and charged spheres. We rigorously solved Stokes equations of motion coupled to Laplace equation to compute the hydrodynamic and electrophoretic tensors of these clusters from multiple spheres, which made it possible to treat the cluster as one single rigid body. Once computed, these tensors can be used to simulate the dynamics and corresponding current blockage inside the nanopore caused by rotational and translational motion of the cluster. While the computational time of the cluster’s tensors is strongly dependent on the number of beads in the cluster, the simulation of the cluster motion and current blockage is independent of it.

To provide a realistic bead model for different proteins, we started from a downloaded Protein Data Bank (PDB) file, which contains the coordinates of all atoms in a protein. While starting from one bead per atom, we performed a progressive coarse-graining, thus reducing the number of beads used to describe the structure of the protein, to obtain the minimum level of description necessary to capture the behavior of the protein using the previously discussed model. The minimal model is obtained when the addition of beads to the model will not substantially change the simulated motion and corresponding current blockage of the cluster. The use of coarse-grained protein models makes it possible to carry out the simulations with a standard computer. We anticipate that this model will be an enabling tool to correlate experimental nanopores results from protein translocations with simulations in order to recover structural information of proteins.

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