Purpose

This tutorial is designed to illustrate the application of NMFF and the MMTSB Tool Set to the flexible refinement of an atomic level structure of a viral capsid into an electron density map from cryo-EM, electron tomography, etc. In this exercise we will create an electron density map corresponding to the swollen state of STMV (right figure) and refine the atomic coordinates of the native STMV conformation into this density using the normal mode flexible fitting algorithm. Models for the native and "swollen" STMV are shown in the figure on the right and below. We note that STMV has not been characterized in a swollen state, as can be observed for a number of other viral capsids. However, we are using this artificial example because of the small size of the capsid protein and the STMV viral capsid. STMV, or Satellite Tobacco Mosaic Virus is a small T=1 viral capsid. You can learn more about STMV at the ViperDB (VIrus Particle ExploreR DataBase)

To perform the calculations in this tutorial you will need to have the NMFF suite of programs installed. Installation instructions for NMFF can be found here. We will also use parts of the MMTSB Tool Set. Other useful programs include vmd, which is used to visualize the structural and electron density data, however, your favorite structure/density viewing/manipulation program (e.g., O, etc.) can also be used.

Preparing the data

First we need to get the "raw" pdb files for the capsid protein in the native state and construct the entire capsid. To do this we can go to the ViperDB entry for STMV and download the pre-constructed coordinates for the full capsid by clicking on the download full capsid (in the middle panel). This file, called 1a34_full.vdb, will be used to construct the native CA based model we refine into the "swollen" density for STMV. The model structure we will use to build the swollen density from is 1a34_swollen_ca.pdb (Note this is a model constructed by expanding the native conformation along its icosahedral normal modes to yield a conformation approximately 20 Å expanded from the native. It is not a physically realized conformation.) Download these files using the links above.

We now want to extract the CA atoms from the structure 1a34_full.vdb. To do this it's easiest to use the unix command grep. The following unix command will do this (Note , unix> denotes the unix system prompt and the command follows.)

unix>grep CA 1a34_full.vdb > 1a34_i60_ca.pdb

With this command we created the new pdb file named 1a34_i60_ca.pdb. Let's now make the electron density map for the swollen state using the NMFF suite component program pdb2sim_map. This program requires three arguments and takes an optional fourth. To make the electron density map representing 1a34_swollen_ca.pdb at approximately 24 Å resolution with a 2 Å grid spacing, use the command.

unix>pdb2sim_map 1a34_swollen_ca.pdb 12 STMV_swollen_24.xpl 2

Note that the electron density map is written in the X-plor format. Also, see that the 24 Å resolution is achieved by setting the 2nd parameter to 12 (desired resolution/2).

Anticipated output and further analysis

Some snippets of output from running NMFF on this refinement program are as follows:

nmff-em start at 16:20:18
nmff-em parameters
    initial pdb structure                          = ../structure/1a34_i60_ca.pdb
    number of atoms in the pdb file                = 8820
    target em map                                  = ../density/STMV_swollen_24.xpl
    resolution of the cryo-em map                  = 24.0
    cut-off used in ennma                          = 8.0
    lowest frequency mode included                 = 1
    maximum number of mode used for the refinement = 15
    number of iteration loops                      = 300
    virus T number                                 = 1
    maximum displacement allowed at each step (A)  = 1.0
    maximum number of trial of gradient            = 2
    nmff directory                                 = ../../../brooks/src/nmff/em
    nma directory                                  = ../../../brooks/src/nma/rtb
    correlation coefficient output                 = corr_coef.dat
initial cc: 0.849644
begin iteration at 16:20:28
-----------------------------------------------------------------------
begin iteration 0 with the modes 1 - 5 at 16:20:28
open current pdb file: mov0.pdb
start normal mode calculation at 16:20:28
file# mode#
    1    95
    2    24
    3   180
    4    35
    5   135
start gradient calculation at 16:21:00
    calculate gradients for modes 1 - 5
start structure deformation at 16:23:59
    atom with maximum displacement = 7953
    with scale = 206118.815222269, move by            1 A
    mode   amplitude   
         2  -74.1522744
         1  -11.3035764
         3  -10.9114354
         4 -0.00176296514
         5 -0.000842135521
    total rmsd  0.807096505, max displacement        1, at atom   7953
result of iteration: 0, gradient try: 1, cc: 0.876496, saved mov1.pdb
cc increased to 0.876496, previous cc was 0.849644
proceed to next iteration, continue gradient mode
-----------------------------------------------------------------------
-----------------------------------------------------------------------
------------------------DELETED OUTPUT---------------------------------
-----------------------------------------------------------------------
-----------------------------------------------------------------------
-----------------------------------------------------------------------
begin iteration 10 with the modes 1 - 5 at 16:57:32
open current pdb file: mov10.pdb
start normal mode calculation at 16:57:32
file# mode#
    1   174
    2    36
    3   142
    4    27
    5   110
start gradient calculation at 16:58:04
    calculate gradients for modes 1 - 5
start structure deformation at 17:01:02
    atom with maximum displacement = 1632
    with scale = 5198671.31990427, move by            1 A
    mode   amplitude   
         2  -72.7616435
         3   19.4446423
         1  -1.34066975
         4 0.0766861205
         5 0.00383251768
    total rmsd  0.802077389, max displacement        1, at atom   1632
result of iteration: 10, gradient try: 1, cc: 0.993102, saved mov11.pdb
correlation coefficient decreased
move again along the same modes with amplitude divided by 2
    mode   amplitude   
         2  -36.3808218
         3   9.72232116
         1 -0.670334875
         4 0.0383430603
         5 0.00191625884
    total rmsd  0.401038694, max displacement      0.5, at atom   1632
result of iteration: 10, gradient try: 2, cc: 0.993874, saved mov11.pdb
cc increased to 0.993874, previous cc was 0.993767
proceed to next iteration, start newton-raphson
-----------------------------------------------------------------------
begin iteration 44 with the modes 1 - 26 at 12:27:03
too many normal modes (26) are included (> 20); give up

This general information flow goes on for (in this case) 11 iterations. Note that the initial correlation coefficient is about 0.85 and after the last iteration the refinement exits after making an attempt to improve the correlation coefficient further (now at 0.99) with a newton-raphson refinement step.

In the figure below we illustrate the course of the refinement by plotting the (left axis) correlation coefficient between the model computed density and the target electron density STMV_swollen_24.xpl versus refinement step.

In the animation to the right we can see the course of the motion of the 1a34-based model into the density from the swollen state.