Biophysics and Nanoscale Systems
Charge-Transfer EAM Studies of
Kinesin Molecular Motor
Protein Mechanochemistry
Vijay Janardhanam1, Godwin Amo-Kwao1, Steven J. Koch1, Steven M. Valone2, and Susan R. Atlas1
1
UNM Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131; 2Materials Science and Technology
Division, Los Alamos National Laboratory, Los Alamos, NM 87545
E-mail: susie@sapphire.phys.unm.edu
Introduction. The ability to accurately simulate the dynamics and elucidate
the functionality of complex biophysical and biomimetic systems is currently
hampered by the lack of atomistic potentials capable of faithfully
representing reactive interactions and charge transfer among constituent
atomic and molecular species. As a first step toward simulating the catalytic
core of the molecular motor protein kinesin (see figure) for direct
comparison with single-molecule experimental motility data, we are working
to implement a second-generation atomistic charge-transfer embedded
atom (CT-EAM) potential based on the theoretical framework of Valone and
Atlas [1-4], and to test the new potential through structural and dynamical
studies of liquid water [5]. This research has the long-term goal of enabling a
detailed understanding of the molecular mechanism underlying kinesin
catalysis and mechanochemistry (see figure below from laboratory of SJ
Koch, illustrating kinesin gliding motility assay in which motion of the kinesin
microtubule track is visualized). In this project, a close collaboration between
theory and experiment enables an `iterative loop’ in which information about
forces and the effects of changes in the local solvent or charge environment
as measured experimentally are incorporated directly into the potential
refinement process.
The CT-EAM potential corresponds to
the highest rung of a ‘theory-model
hierarchy’ in which progressively
more advanced density functional
theories have direct theoretical
parallels in corresponding force fields
(see figure). The CT-EAM represents
the apex of this hierarchy, and is in
principle capable of describing
correctly bond formation and
breaking, essential characteristics of a
molecular dynamics simulation force
field intended for application to
biophysical systems. It accomplishes
this through a formal extension of the
well-known embedded-atom method
(EAM) originally designed for metallic
systems. The CT-EAM potential
incorporates information not only
about neutral atomic species
embedded in the surrounding manybody (chemical) environment, but
also corresponding ions, up to
appropriate positive and negative
charge states for each atom. The
resulting CT-EAM is essentially an
ensemble average over charge-stateindexed embedding and electrostatic
interaction terms corresponding to
these various states. A key feature of
the potential is the incorporation of
atom-in-molecule charge densities
rather than isolated atom densities in
the description of the embedding
background; this ensures selfconsistency between all components
of the potential, and provides a
refined description of the local
bonding environments of the
interacting atoms.
For the present application to studies of the structures of
water clusters and the simulation of liquid water dynamical
properties, the CT-EAM parameterization is based on a
database of high-quality first-principles electronic structure
calculations performed for key configurational and charge
states of the water monomer and dimer-based clusters, and
component pseudo-atom (atom-in-molecule) electron density
distributions. Structural studies performed with this firstgeneration form of the CT-EAM potential reveal remarkable
agreement with theoretical quantum chemistry (UHF)
predictions for the incremental binding energies of water
clusters up to n=20 (see figure) and correlated predictions (not
shown). The second-generation CT-EAM water potential
under development will incorporate a significantly more
detailed description of the atom-in-molecule charge density
distributions for the charged atomic species comprising the
building blocks of the CT-EAM potential, and will be tested in
simulations of dynamical water properties for comparison
with fixed-charge force fields such as the TIP and SPC models, and fluctuating charge models based on an assumption of quadratic
dependence of the energy on charge, known to fail in the dissociation limit.
References
[1] Density Functional Theory of the Embedded-Atom Method:
Multiscale Dynamical Potentials with Charge Transfer, SR Atlas and
SM Valone, to be submitted; arXiv:cond-mat (2009).
[2] SM Valone and SR Atlas, Phys. Rev. Lett. 97, 256402 (2006).
[3] SM Valone and SR Atlas, Phil. Mag. 86, 2683 (2006).
[4] SM Valone and SR Atlas, J. Chem. Phys. 120, 7262 (2004).
[5] Environment Dependent charge potential for water, arXiv:condmat/0705.0857v1, K Muralidharan, SM Valone, and SR Atlas (2007).
Acknowledgements
This work is supported by the DoD DTRA CB Basic Research Program
under Grant No. HDTRA1-09-1-008; early theoretical development of the CT-EAM and its density functional foundations was supported by NSF
grants CHE-0304710 (SRA/SMV) and DMR-9520371 (SRA). The work of SMV was performed at Los Alamos National Laboratory under the auspices
of the U.S. Department of Energy, under contract No. DE-AC52-06NA25396. We are grateful to the UNM Center for Advanced Research Computing
for providing the computational resources used in this work.