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