Sampling studies with draining energy

Here is the result of an attempt to reduce hysteresis in the crown ether Na+ <-> K+ perturbation. Since the simulations were run with constant energy (i.e. no temperature scaling), and since in each case where SHAKE was used, the low tolerance used (0.0005) resulted in an energy drain, the temperature dropped from around 250K to 50K over two nanoseconds with SHAKE on hydrogens (runs could be as long as 13 ns). In each case, a brief dynamics run using temperature scaling to keep to the target temperature was performed between 'forward' and 'reverse' perturbations, so this is the only significance of the different target temperatures reported below.

T=300K First, all bonds are held rigid using SHAKE; then just bonds with hydrogens; then the step size in the latter case is reduced from 2fs to 1 fs. In all these cases, a very short run gave minimal hysteresis while longer runs were problematic.

                Free Energies for Na+ <-> K+ for various sampling times
                              (temperature = 300K)

        ------------------ steps: equil/data ---------------------------------
        100/200	       100/500        500/1000       500/5000        500/10000
        ----------------------------------------------------------------------

-- shake=all, step=2fs

1->0    -10.4         -10.9             -9.8           -9.2

0->1    -10.5          -9.2             -8.1           -7.5

mean     10.5 (0.1)    10.1 (1.7)        9.0 (1.7)      8.4 (1.7)
(hyst)

-- shake=H, step=2fs

1->0    -11.1         -10.9            -10.4           -9.3
0->1    -10.8         -10.1             -9.9           -6.8

         11.0 (0.3)    10.5 (0.8)       10.2 (0.5)      8.1 (2.5)

-- shake=H, step=1fs

1->0    -10.4         -10.0            -10.1           -9.4         -9.5
0->1    -10.2          -8.8            -10.0           -7.4         -6.9

         10.3 (0.2)     9.4 (1.2)       10.1 (0.1)      8.4 (2.0)    8.2 (2.6)

Sampling for longer times at lower temperatures Another series of runs was performed to see what it would take to get reasonable answers. Initially, 200,000 steps of sampling were performed per window (20 times the amount in the longest run above), yielding essentially no hysteresis and numbers comparable to those of the shortest runs in the table above. Each run took about 18 hours on an HP 9000/735 (36 hours for forward+reverse). Then the sampling time was reduced for runs that had reasonable hysteresis.

In the first 300K run, it was observed that T drifted down to around 50K during the first two nanoseconds and stayed there. Accordingly, 300K runs were also done with constant temperature.


        -- steps: equil/data --
        100/20000    100/200000     
         ~1.6 hrs      ~18 hrs
        -----------------------

-- shake=H, step=1fs, T=10K

1->0    -10.2         -10.1
0->1    -10.0         -10.0

-- shake=H, step=1fs, T=100K 

1->0    -10.2         -10.1
0->1    -10.1         -10.0

-- shake=H, step=1fs, constant energy (ntt=0), T drifted from 300->50K

1->0    -10.2         -10.1
0->1     -9.8         -10.0

-- shake=H, step=1fs, constant temperature (ntt=1) T=300K

1->0    -10.2          -9.1
0->1     -9.3          -8.7

-- shake=H, step=2fs, constant energy, T=100K

1->0                  -11.8
0->1                   -8.7

Demo by Bill Ross.

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