Is quantum mechanics necessary for predicting binding free energy?
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1 Supporting Information Is quantum mechanics necessary for predicting binding free energy? Ting Zhou, Danzhi Huang and Amedeo Caflisch* Department of Biochemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland Contents of Supporting Information 1 Robustness upon choice of minimization protocol Three-parameter LIECE and QMLIECE models 3 QMLIECE vs. simple models (WNV PR) 3.1 Histogram of ΔGbind values 3. Statistical tests 4 Thermodynamic cycle used in (QM)LIECE to calculate the binding free energy in solution S1
2 1 Robustness upon choice of minimization protocol Protocol Nonbond Minimization Leave-one-out cv q ID parameter ID QMLIECE a LIECE Nonbond ID CHARMM nonbond-specification b 1 NBONDS NBXMOD 5 GROUP SWITCH CDIE VDW VSWI EXTEND GRAD QUAD CUTNB 180 WMIN 1.5 EPS 1.0 NBONDS NBXMOD 5 ATOM SWITCH VATOM VSWITCHED CUTNB 15.0 CTONNB 11 CTOFNB 14 EPS 1.0 E14FAC 0.5 WMIN 1.5 CDIE NBONDS NBXMOD 5 ATOM SWITCH VATOM VSWITCHED CUTNB EPS 1.0 E14FAC 0.5 WMIN 1.5 CDIE NBONDS ATOM FSHIFT CDIE VDW VSHIFT CUTNB 180 WMIN EPS 1.0 NBONDS ATOM FSWITCH CDIE VDW VSHIFT CUTNB 180 WMIN EPS 1.0 S
3 Minimization parameter ID CHARMM minimization commands c cons harm force 0 sele (type C*) end mini sd nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 cons harm force sele (type C*) end mini abnr nstep 00 cons harm force 1 sele (type C*) end cons harm force 0 sele (protein and (type C*) or (type O*) or (type N*)) end mini sd nstep 00 cons harm force 10 sele (protein and (type C*) or (type O*) or (type N*)) end mini abnr nstep 00 cons harm force 8 sele (protein and (type C*) or (type O*) or (type N*)) end mini abnr nstep 00 cons harm force 6 sele (protein and (type C*) or (type O*) or (type N*)) end mini abnr nstep 00 cons harm force 4 sele (protein and (type C*) or (type O*) or (type N*)) end mini abnr nstep 00 cons harm force sele (protein and (type C*) or (type O*) or (type N*)) end mini abnr nstep 00 cons harm force 1 sele (protein and (type C*) or (type O*) or (type N*)) end cons harm force 0 sele (type C*) end mini sd nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 cons harm force sele (type C*) end mini abnr nstep 00 cons harm force 1.1 sele (type C*) end cons harm force 0 sele (type C*) end mini sd nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 cons harm force sele (type C*) end mini abnr nstep 00 cons harm force 1. sele (type C*) end cons harm force 0 sele (type C*) end mini sd nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 mini abnr nstep 00 cons harm force sele (type C*) end mini abnr nstep 00 cons harm force 1.3 sele (type C*) end Table 1. Influence of minimization protocol on fitting results for 44 peptidic inhibitors of WNV PR. a These leave-one-out q of QMLIECE were calculated using semiempirical Hamiltonian PM3. We finally chose RM1 Hamiltonian because we found that RM1 is more sophisticated than PM3, and could attain higher fitting qualities. b The explanation of charmm nonbond-specification can be found at c The explanation of charmm minimization commands can be found at S3
4 Three parameter LIECE and QMLIECE models α β ΔG tr,rot,bond Leave-one-out cross-valid rms error (kcal mol 1 ) (kcal mol 1 ) WNV PR (44 peptidic inhibitors) αδe vdw +βδg QM_elesol +ΔG tr,rot,bond Standard deviation ±0.031 ±0.005 ±1.3 αδe vdw +βδg MM_elesol +ΔG tr,rot,bond a Standard deviation ±0.09 ±0.008 ±1.6 q CDK (73 non peptidic inhibitors) αδe vdw +βδg QM_elesol +ΔG tr,rot a Standard deviation ±0.06 ±0.03 ±0.6 αδe vdw +βδg MM_elesol +ΔG tr,rot Standard deviation ±0.01 ±0.00 ±0.6 Table. Three-parameter LIECE and QMLIECE models. a Parameters with leave-one-out standard deviation larger than the average value are statistically not significant and are given in italics. S4
5 3 QMLIECE vs. simple models (WNV PR) 3.1 Histogram of ΔG bind values The 44 inhibitors can be separated according to number of positively charged groups as in the histograms enclosed. By inspection of the histograms one could speculate that the activity is related simply to the number of charges except for the compounds with q= (and q=1 which are only two) which seem shifted to less negative values. Conut q=0(n=5) q=1(n=) q=(n=3) q=3(n=14) Exp. ΔG of binding (kcal/mol) 3. Statistical tests In response to an anonymous reviewer we compare the probability of chance correlation of QMLIECE and simple models derived using the total charge. The QMLIECE model is the two-parameter model as in Equation (1) in the main text. The LIECE and binary (LB) is a three-parameter model ΔG = ΔG Q bind MM_elesol where ΔG MM_elesol is the electrostatic contribution of binding free energy calculated by force field method, and Q is a binary descriptor described below.. The binary descriptor (BD) is a five-parameter model ΔG bind =1.141Q Q Q-0.350Q where Q n is a binary descriptor, equals to one for ligands with charge of n and zero for all others. S5
6 These statistical tests evaluate the predictive power of QMLIECE and two simple models. For each of the three models a total of models are generated by random guessing of the binding affinities (see main text for details). The rationale behind this statistical test is that the significance of the model is low if there is a significant correlation between descriptors and randomized values of ΔG bind. In other words, the S6
7 distance between the actual model (cross) and random models (dots) is an indicator of predictive power, i.e., lack of chance correlation. Note that the QMLIECE performs better in this test than LB, and much better than BD. This behavior is consistent with the decreasing physical soundness and increasing amount of fitting parameters in going from QMLIECE to LB and BD. The horizontal line at q =0.4 and the vertical line at R=0.6 are drawn to better compare the plots. 4 Thermodynamic cycle used in (QM)LIECE to calculate the binding free energy in solution ΔG = ΔG + ΔG -ΔG -ΔG vacuo solvation solvation solvation elesol prot/lig prot/lig prot lig S7
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