Silva JR, Pan H, Wu D, Nekouzadeh A, Decker KF, Cui J, Baker NA, Sept D, Rudy Y. A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential. Proc Natl Acad Sci USA, 106, 11102-6, 2009.
Ion-channel function is determined by its gating movement. Yet, molecular dynamics and electrophysiological simulations were never combined to link molecular structure to function. We performed multiscale molecular dynamics and continuum electrostatics calculations to simulate a cardiac K+ channel (IKs) gating and its alteration by mutations that cause arrhythmias and sudden death. An all-atom model of the IKs α-subunit KCNQ1, based on the recent Kv1.2 structure, is used to calculate electrostatic energies during gating. Simulations are compared with experiments where varying degrees of positive charge—added via point mutation—progressively reduce current. Whole-cell simulations show that mutations cause action potential and ECG QT interval prolongation, consistent with clinical phenotypes. This framework allows integration of multiscale observations to study the molecular basis of excitation and its alteration by disease.
Cheng Y, Suen JK, Zhang D, Bond SD, Zhang Y, Song Y, Baker NA, Bajaj CL, Holst MJ, McCammon JA. Finite element analysis of the time-dependent Smoluchowski equation for acetylcholinesterase reaction rate calculations. Biophys J, 92, 3397-406, 2007.
This article describes the numerical solution of the time-dependent Smoluchowski equation to study diffusion in biomolecular systems. Specifically, finite element methods have been developed to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to the mouse acetylcholinesterase monomer and several tetramers. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different time steps. Calculated rates show very good agreement with experimental and the- oretical steady-state studies. Furthermore, these finite element methods require significantly fewer computational resources than existing particle-based Brownian dynamics methods and are robust for complicated geometries. The key finding of biological importance is that the rate accelerations of the monomeric and tetrameric mAChE that result from electrostatic steering are preserved under the non-steady- state conditions that are expected to occur in physiological circumstances.
Zhang D, Suen J, Zhang Y, Song Y, Radic Z, Taylor P, Holst MJ, Bajaj C, Baker NA, McCammon JA. Tetrameric mouse acetylcholinesterase: continuum diffusion rate calculations by solving the steady-state Smoluchowski equation using finite element methods. Biophys J, 88, 1659-1666, 2005.
The tetramer is the most important form for acetylcholinesterase in physiological conditions, i.e., in the neuromuscular junction and the nervous system. It is important to study the diffusion of acetylcholine to the active sites of the tetrameric enzyme to understand the overall signal transduction process in these cellular components. Crystallographic studies revealed two different forms of tetramers, suggesting a flexible tetramer model for acetylcholinesterase. Using a recently developed finite element solver for the steady-state Smoluchowski equation, we have calculated the reaction rate for three mouse acetylcholinesterase tetramers using these two crystal structures and an intermediate structure as templates. Our results show that the reaction rates differ for different individual active sites in the compact tetramer crystal structure, and the rates are similar for different individual active sites in the other crystal structure and the intermediate structure. In the limit of zero salt, the reaction rates per active site for the tetramers are the same as that for the monomer, whereas at higher ionic strength, the rates per active site for the tetramers are ~67%-75% of the rate for the monomer. By analyzing the effect of electrostatic forces on ACh diffusion, we find that electrostatic forces play an even more important role for the tetramers than for the monomer. This study also shows that the finite element solver is well suited for solving the diffusion problem within complicated geometries.
Song Y, Zhang Y, Bajaj C, Baker NA. Continuum diffusion reaction rate calculations of wild type and mutant mouse acetylcholinesterase: adaptive finite element analysis. Biophys J, 87, 1558-66, 2004.
As described previously, continuum models, such as the Smoluchowski equation, offer a scalable framework for studying diffusion in biomolecular systems. This work presents new developments in the efficient solution of the continuum diffusion equation. Specifically, we present methods for adaptively refining finite element solutions of the Smoluchowski equation based on a posteriori error estimates. We also describe new, molecular-surface-based models, for diffusional reaction boundary criteria and compare results obtained from these models with the traditional spherical criteria. The new methods are validated by comparison of the calculated reaction rates with experimental values for wild-type and mutant forms of mouse acetylcholinesterase. The results show good agreement with experiment and help to define optimal reactive boundary conditions.
Song Y, Zhang Y, Shen T, Bajaj CL, McCammon JA, Baker NA. Finite element solution of the steady-state Smoluchowksi equation for rate constant calculations. Biophys J, 86, 2017-29, 2004.
This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.
Tai K, Bond SD, MacMillan HR, Baker NA, Holst MJ, McCammon JA. Finite element simulations of acetylcholine diffusion in neuromuscular junctions. Biophys J, 84, 2234-41, 2003.
A robust infrastructure for solving time-dependent diffusion using the finite element package FEtk has been developed to simulate synaptic transmission in a neuromuscular junction with realistic postsynaptic folds. Simplified rectilinear synapse models serve as benchmarks in initial numerical studies of how variations in geometry and kinetics relate to endplate currents associated with fast-twitch, slow-twitch, and dystrophic muscles. The flexibility and scalability of FEtk affords increasingly realistic and complex models that can be formed in concert with expanding experimental understanding from electron microscopy. Ultimately, such models may provide useful insight on the functional implications of controlled changes in processes, suggesting therapies for neuromuscular diseases.
Baker N, Tai K, Henchman R, Sept D, Elcock A, Holst M, McCammon JA. Mathematics and molecular neurobiology. Computational Methods for Macromolecules: Challenges and Applications. Gan HH, Schlick T, eds., 2002.
Malany S, Baker N, Verweyst M, Medhekar R, Quinn DM, Velan B, Kronman C, Shafferman A. Theoretical and experimental investigations of electrostatic effects on acetylcholinesterase catalysis and inhibition. Chem-Biol Interact, 120, 99-110, 1999.
The role of electrostatics in the function of acetylcholinesterase (AChE) has been investigated by both theoretical and experimental approaches. Second-order rate constants (kE = k(cat)/Km) for acetylthiocholine (ATCh) turnover have been measured as a function of ionic strength of the reaction medium for wild-type and mutant AChEs. Also, binding and dissociation rate constants have been measured as a function of ionic strength for the respective charged and neutral transition state analog inhibitors m-(N,N,N-trimethylammonio)trifluoroacetophenone (TMTFA) and m-(t-butyl)trifluoroacetophenone (TBTFA). Linear free-energy correlations between catalytic rate constants and inhibition constants indicate that kE for ATCh turnover is rate limited by terminal binding events. Comparison of binding rate constants for TMTFA and TBTFA attests to the sizable electrostatic discrimination of AChE. Free energy profiles for cationic ligand release from the active sites of wild-type and mutant AChEs have been calculated via a model that utilizes the structure of T. californica AChE, a spherical ligand, and energy terms that account for electrostatic and van der Waals interactions and chemical potential. These calculations indicate that EA and EI complexes are not bound with respect to electrostatic interactions, which obviates the need for a ‘back door’ for cationic ligand release. Moreover, the computed energy barriers for ligand release give linear free-energy correlations with log(kE) for substrate turnover, which supports the general correctness of the computational model.
Baker NA, McCammon JA. Non-Boltzmann rate distributions in stochastically gated reactions. J Phys Chem B, 103, 615-617, 1999.
Recently, a new mechanism for reaction selectivity, arising from conformational gating of the reactions, has been reported in the acetylcholinesterase system. Fluctuations in the enzyme are thought to greatly slow the access of molecules larger than the normal substrate to the active-site region. By assuming the gate fluctuations occur as a Brownian process in a harmonic well, it is possible to approximate the reaction rates for various limiting cases of substrate size. However, it is not possible to simplify the rates into a ratio which is equivalent to the Boltzmann distribution of states for the gate fluctuations.
Silva JR, Pan H, Wu D, Nekouzadeh A, Decker KF, Cui J, Baker NA, Sept D, Rudy Y. A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential. Proc Natl Acad Sci USA, 106, 11102-6, 2009.
