local helical parameters interpretation question

[cllawson]

My question is how to interpret 3DNA output for local base-pair helical parameters, since they are given in terms of a base-pair step, unlike the output of other programs.  I understand that the minimum local environment needed to define the local parameters is the base-pair step, but I am still a bit confused.

Local base-pair helical parameters
    step       X-disp    Y-disp   h-Rise     Incl.       Tip   h-Twist
   1 CG/CG     -1.27     -0.65      3.09     14.77      5.57     33.94

Are the values listed above defining parameters for the 1st base-pair relative to the 2nd, or the 2nd base-pair relative to the 1st, or is there a different explanation?

thanks,

Cathy Lawson

[xiangjun]

It is not a surprise to me that the local helical parameters as given in 3DNA could be a bit confusing. I have answered this question several times over the years, mostly before the forum was set up. Excerpted below is one I just dug out:

[1] To refer the orientation and position of one base-pair (bp) relative to
    the other, 6 parameters (3 rotations and 3 translations) are required.
    One set of such parameters is (Shift, Slide, Rise, Tilt, Roll and
    Twist), and the other set is (X-displacement, Y-displacement, Helical
    Rise, Inclination, Tip and Helical Twist).

    Obviously these two sets should be completely reversible/dependent: from
    any one set you can get the other, rigorously. You can verify this point
    using "step_hel", a utility program in 3DNA. Graphically this is best
    illustrated by the Calladine-Drew A to B transition model by introducing
    uniform Roll and Slide values at each dinucleotide step. You could see
    these images in 3DNA website, Examples/Calladine_Drew/ directory in 3DNA
    distribution and 3DNA user's manual. The key point is that by
    introducing Roll, you also get Inclination, and with Slide, you get
    X-displacement.

    The "rebuild" program in 3DNA can construct a DNA structure using either
    set of these parameters. Examples of such input files (e.g.,
    "bp_step.par" and "bp_helical.par") can be generated by
    "analyze". Please have a look of the Examples/Analyze_Rebuild directory.

[2] The define a local helical axis, we need two base-pair reference
    frames (i and i + 1). 3DNA finds the single-helical axis (which is
    actually dx times dy) that brings i to coincide with i + 1 by a Helical
    Twist angle. The position which this helix passes through is defined by
    Chasles' theorem as detailed in Figures 12 & 13 of Backcok et al.
    (J. Mol. Biol. 1994, 237, pp 125-156). The calculation of
    X-displacement, Y-displacement, Tip and Inclination is then exactly as
    described in SCHNAaP (J. Mol. Biol. 273, 668-680, i.e., 3DNA calculates
    a set of local helical parameters instead of linear global ones as given
    in SCHNAaP and NewHelix/FreeHelix.)

    To make the above point clear, let's use A1-A2-A3 triplet as an example.
    First, A1-A2 define a local helical axis and a set of local base-pair
    helical parameters are calculated. In 3DNA, these parameters are defined
    in a symmetric manner that bp A1:T1 and bp A2:T2 have exactly the same
    values except for a sign reversal for Y-displacement and Tip.
    Similarly, step A2-A3 define another set of local base-pair helical
    parameters. Thus bp A2:T2 has two sets of helical parameters associated
    with it depending on its context, i.e., either with bp A1:T1 or with bp
    A3:T3. Moreover, the local helical rise and helical twist are directly
    related to a dinucleotide step. These are the reasons that "Local
    base-pair helical parameters" as given in 3DNA refer to base-pair steps.

Please also refer to another post in this forum on "h-twist vs. twist" and the link therein.

HTH,

Xiang-Jun

[cllawson]

Thanks Xiang-Jun for posting this helpful information.

If I understand correctly now what you wrote above,  the x-displacement value for b.p. step A1-A2 applies to both A1-T1 and A2-T2  (they both have the same x-displacement relative to the local helical axis defined by A1-T1 and A2-T2), and the x-displacement value for b.p. step A2-A3 applies to both A2-T2 and A3-T3 (local helical axis defined by A2-T2 and A3-T3).   Base pair A2-T2 then has two different x-displacement values associated with it, depending on whether the local context includes A1-T1 or A3-T3.

Is this a correct interpretation?

[xiangjun]

That's correct.

As a side note, the helical axes in Figure 4 of 3DNA 2003 NAR paper is actually 11 - 1 = 10 fragments which are perfectly aligned in the regular structures.

HTH,

Xiang-Jun