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1. ABSTRACT

In this work, we have developed a general AMBER force field (GAFF) for rational drug design. GAFF is compatible with the AMBER force field and it has parameters for almost all the organic molecules made of C, N, O, H, S, P, F, Cl, Br and I. As a complete force field, GAFF is suitable for study of a great number of molecules (such as database searching) in an automatic fashion.

2. INTRODUCTION

Molecular mechanics are the key component in the armamentarium used by computational chemists for rational drug design and many other tasks. Force fields are the cornerstone of molecular mechanics. A successful force field in drug design should work well both for the biological molecules and the organic molecules. AMBER force fields have a good reputation for the study of proteins and nucleic acids. However, the fact that AMBER only has limited parameters for organic molecules prevents it from being widely used in drug design. Therefore, it is necessary to develop a general AMBER force field that works for most pharmaceutical molecules. It should also be as compatible as possible with the traditional AMBER force fields. Our objective is to develop a general, complete, and compatible force field for rational drug design.

3. FUNCTION FORM

Similar to the other AMBER force fields, the GAFF also applies the following simple harmonic functional form:


Here, req and qeq are equilibrium structural parameters; Kr, Kq, Vn are force constants; n is multiplicity and gamma is phase angle for torsional angle parameters. Details will be given below on how these parameters were derived.

4. ATOM TYPE DEFINATION
Compared to traditional AMBER force field, atom types in GAFF are more general and cover most of the organic chemical space.Table I lists the basic (a) and special (b) atom types in GAFF.

Table I (a). Basic Atom Types in GAFF

Atom type  Description  Atom type  Description 
c 
c1 
c2 
c3 
ca 		 sp2 C in C=O, C=S 
sp1 C 
sp2 C, aliphatic 
sp3 C 
sp2 C, aromatic 		 o 
oh 
os 
 
 		 sp2 O in C=O, COO- 
sp3 O in hydroxyl group 
sp3 O in ether and ester 
 
 
n 
n1 
n2 

n3 
n4 
na 
nh 

no 

 sp2 N in amide 
sp1 N 
sp2 N with 2 subst. 
readl double bond 
sp3 N with 3 subst. 
sp3 N with 4 subst. 
sp2 N with 3 subst 
amine N connected 
to the aromatic rings 
N in nitro group 		 s2 
sh 
ss 
s4 
s6 		 sp2 S (p=S, C=S etc) 
sp3 S in thiol group 
sp3 S in -SR and SS 
hypervalent S, 3 subst. 
hypervalent S, 4 subst. 
hc 
ha 
hn 
ho 
hs 
hp 		 H on aliphatic C 
H on aromatic C 
H on N 
H on O 
H on S 
H on P 
f 
cl 
br 
i 		 any F 
any Cl 
any Br 
any I 		 p2 
p3 
p4 
p5 		 sp2 P (C=P etc) 
sp3 P, 3 subst. 
hypervalent P, 3 subst. 
hypervalent P, 4 subst. 


Table I (b). Special Atom Types in GAFF

Atom type  Description  Atom type  Description 
h1 
h2 
h3 
h4 
h5 
 
 		 H on aliphatic C with 1 EW group;
H on aliphatic C with 2 EW group;
H on aliphatic C with 3 EW group;
H on aromatic C with 4 EW group;
H on aromatic C with 5 EW group;
 
  		cc(cd) 
ce(cf) 
cp(cq) 
cu 
cv 
cx 
cy 		 inner sp2 C in conj. ring systems 
inner sp2 C in conj. chain systems 
bridge aromatic C  
sp2 C in three-memberred rings  
sp2 C in four-memberred rings  
sp3 C in three-memberred rings  
sp3 C in four-memberred rings  
n 
nb 
nc(nd) 
sx 
sy  		aromatic nitrogen 
inner sp2 N in conj. ring systems 
inner sp2 N in conj. chain systems 
conj. S, 3 subst.  
conj. S, 4 subst.   		pb 
pc(pd) 
pe(pf) 
px 
py 		 aromatic phosphorus  
inner sp2 P in conj. ring systems 
inner sp2 P in conj. chain systems 
conj. P, 3 subst.  
conj. P, 4 subst.  
EW: electron-withdraw group


5. CHARGE APPROACH

The charge method used in GAFF is HF/6-31G* RESP charge. However, AM1-BCC, which was parameterized to reproduce the HF/6-31G* RESP charges can be applied in case of large amount of calculations, such as database searching. The van der Waals parameters of GAFF are as same as those used by the traditional AMBER force field.

6. BOND LENGTH PARAMETERIZATION

There are several resources to derive the reference bond length req, including the statistic mean values of bond lengths from X-ray and neutron diffraction as well as high level ab initio calculations (MP2/6-31G* ). Force constants were derived using the following empirical function forms:

Here, m and Kij were determined using bond length parameters in traditional AMBER force field. As a compromise, the parameter m in the above equation is set to 4.0. Fitting details are shown in Figure 1-3. The parameters are listed in Table II.


Figure 1

Figure 2

Figure 3
 

Table II. Bond length parameterization

 
i j rij Kij i j rij Kij
H H 0.738 4.661 H C 1.090 6.217
H N 1.010 6.057 H O 0.96 5.794
H F 0.920 5.600 H Cl 1.280 6.937
H Br 1.410 7.301 H I 1.600 7.802
H P 1.410 7.257 H S 1.340 7.018
C C 1.526 7.643 C N 1.470 7.504
C O 1.440 7.347 C F 1.370 7.227
C Cl 1.800 8.241 C Br 1.940 8.478
C I 2.160 8.859 C P 1.830 8.237
C S 1.820 8.117 N N 1.441 7.634
N O 1.420 7.526 N F 1.420 7.475
N Cl 1.750 8.266 N Br 1.930 8.593
N I 2.120 8.963 N P 1.720 8.212
N S 1.690 8.073 O O 1.460 7.561
O F 1.410 7.375 O Cl 1.700 8.097
O Br 1.790 8.276 O I 2.110 8.854
O P 1.640 7.957 O S 1.650 7.922
F F 1.406 7.358 F Cl 1.648 7.947
F P 1.500 7.592 F S 1.580 7.733
Cl Cl 2.031 8.648 Cl I 2.550 9.309
Cl P 2.040 8.656 Cl S 2.030 8.619
Br Br 2.337 9.012 Br I 2.671 9.380
Br P 2.240 8.729 Br S 2.210 8.728
I I 2.836 9.511 I P 2.490 9.058
I S 2.560 9.161 P P 2.324 8.805
P S 2.120 8.465 S S 2.038 8.316

7. BOND ANGFGLE PARAMETERIZATION

The following list the source of reference bond angles:
  • Cambridge Structure Database (CSD)
  • ab initio (MP2/6-31G*)
  • empirical rules for q (A-B-C)


    • q(A-B-C) = 0.5 [q (A-B-A)+ q (C-B-C)]


The force constant Kqwas also estimated using an empirical function as the following. The parameters are listed in Table III.


Table III. Parameters of bond angle force constant calculations

  
Element C Z
H 0.0 0.784
C 1.339 1.183
N 1.300 1.212
O 1.249 1.219
F 0.000 1.166
Cl 0.000 1.272
Br 0.000 1.378
I 0.000 1.398
P 0.906 1.620
S 1.448 1.280

8. TORSIONAL ANGLE PARAMETERIZATION
The following is the strategy to develop torsional angle parameters.
  • Perform torsional angle scanning to get the rotational profile at MP4/6-311G(d,p)// MP2/6-31G* level
  • Apply PARMSCAN to find the best torsional angle parameters to reproduce the rotational profile
Totally, 200 general torsional angle parameters were developed in GAFF, which gave an average unsigned error of 0.5 kcal/mol to MP4/6-311G(d,p) energies.

Figure 4. An example: rotation profiles of X-c-c-X

9. TEST CASES

  • 9.a How well does GAFF predict the molecular structures?


    • Table IV Comparison of GAFF and other force fields in reproducing geometries of 75 crystallographic structures
     
      GAFF MMFF94 DREIDING TRIPOS 5.2 CHARMm
    RMS of Atomic Displacement (Å) 0.34 0.47 0.24 0.25 0.44
    RMS of Bond Length Deviation (Å) 0.027 0.021 0.035 0.025 ~
    RMS of Bond Angle Deviation (°) 2.2 2.0 3.22 2.5 ~

     
  • 9.b How well does GAFF predict the inter-molecular energies?


    • Table V How well does GAFF perform in calculating the inter-molecular energies
    of 22 base pairs. All the comparison are made to the MP2/6-311G* energies.
     
      GAFF/BCC GAFF/RESP PARM99/RESP
    RMS of Atomic Displacements (Å) 0.56 0.49 0.19
    RMS of DE Compared to ab initio (kcal/mol) 2.50 0.67 0.77

     
  • 9.c How well does GAFF predict the intra-molecular energies?


    • Table VI Performances of widely used force field in reproducing the relative
    energies for 55 compounds. Comparison are made to the experiment.
     
      GAFF/BCC AMBER (parm99) MMFF MM3 CHARMm
    Unsigned Average Error (kcal/mol) 0.51 0.28 0.43 0.52 0.57
    RMS Deviation (kcal/mol) 0.69 0.40 0.54 0.75 0.76

    10. SUMMARY

    In this work, we have developed a general AMBER force field. We hope it is an ideal molecular mechanical tool in rational drug design. We have finished a total of 2000 MP2/6-31G* optimizations and 1260 MP4/6-311G(d,p) single point calculations. From the three test cases, encouraging results were achieved. It is notable that in the third test case, GAFF has comparable performance to those of CHARMm and MM3, although GAFF applies very general force field parameters and crude charge approach.

    Compared to other widely used fields, GAFF has the following distinguishing features. First of all, it is a complete force field, which means all the parameters are available, no parameter-missing happens to GAFF; secondly, this force field is very general and it covers almost all the organic chemical spaces; finally, GAFF is compatible to the AMBER force field. We believe that the combination of GAFF with traditional AMBER will offer a useful molecular mechanical tool for rational drug design, especially for things like binding free energy calculations.

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