Volume 86, Issue 4, Pages 2017-2029 (April 2004) Finite Element Solution of the Steady-State Smoluchowski Equation for Rate Constant Calculations  Yuhua Song, Yongjie Zhang, Tongye Shen, Chandrajit L. Bajaj, J. Andrew McCammon, Nathan A. Baker  Biophysical Journal  Volume 86, Issue 4, Pages 2017-2029 (April 2004) DOI: 10.1016/S0006-3495(04)74263-0 Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 1 Schematic of problem domain denoting the various surfaces and volumes described in the text. Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 2 Adaptive tetrahedral meshes for mouse acetylcholinesterase. (Bottom) The molecular surface and outer sphere S0; the active site gorge is shown in greater detail inside the red box. (Middle) Magnification of the red box in the bottom picture. (Top) The tetrahedral mesh of the interval volume between the molecular surface and the outer sphere S0 (cross section). Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 3 Data scaling for the adaptive mesh; surfaces are described in the text. Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 4 Illustration of the discretized problem domain for the spherical test case. (a) Partial domains of the fixed sphere; the outer boundary of the domain is 40 times the radius of the sphere. (b) Subset of the mesh near the fixed sphere surface. Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 5 Geometry of mAChE finite element mesh (left) and its active site gorge (right). Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 6 Reactive surfaces 1–6 of mAChE (bottom to top) from the reactive boundary definition described in the text. The views of these surfaces start from the outside of the protein (bottom) and move to the interior (top) as the surfaces move inside the active site gorge. Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 7 Reaction rates of mAChE calculated with the SMOL FE program with reactive surface 1 (●), calculated from Brownian dynamics with reactive surface 1 (■), and from experimental data (Radic et al., 1997) fit to the Debye-Hückel limiting law (solid line). Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions

Figure 8 Correlation plots for calculations of reaction rate using the SMOL program and using BD with spherical surface reactive boundary definitions. For each method, calculations are made for six reactive surfaces and ionic strength ranges 0.00, 0.05, 0.10, 0.15, 0.3, 0.45, 0.6, and 0.67M. For ● data points, BD results are plotted on the x axis, SMOL results are plotted on the y axis. The solid line is the linear fit of the data, and its slope is 0.84 with a Pearson correlation coefficient of 0.91. Biophysical Journal 2004 86, 2017-2029DOI: (10.1016/S0006-3495(04)74263-0) Copyright © 2004 The Biophysical Society Terms and Conditions