Tweaking BP frequencies settings. Following is an attempt to figure this out in order to be able to tweak the BP frequencies setting with some quantitative figures.

Spooky2

April 10, 2017 01:36

DNA is a kind of ladder with steps. The length of the ladder is a measure of the wavelength of the said DNA. This length is known from the number of steps of the ladder. Each step is made of a « base pair », hence the name « Base Pair frequencies ».

The product of the interstep space by the number of steps gives the wavelength of the DNA from which we get the frequency.

Interstep space is known in the literature as the Rise per BP (RBP) and is given in Angström (1Å=1E-10 m).

We can write RBP = c/Ti with RBP in meter or in Angström where:

c = vacuum lightspeed = 299 792 458 m/s ±0.5 m/s close to 3E9 m/s

Ti = frequency in Herz/BP (1 Herz = 1/second) is the BP to Herz factor provided in the Spooky system tab.

In Spooky, BP numbers are provided as integers in the BP database.

In the Spooky system tab, we find Ti = 863808777288135000 Hz which means that
863808777288134500 Hz < Ti < 863808777288135500 Hz
so Ti = 863808777288135000 Hz ± 500 Hz which is close to 8.6E17 Hz

Hence RBP = c/Ti = 0.00000000034698201157 m = 3.4698201157 Å

Nota: for a figure known as X±x, in French language x is the « erreur absolue » (= absolute error) and x/X is the « erreur relative » (=relative error). As I don’t know the English wording, I will translate from French.
Can anyone improve my English?

What is the absolute error on RBP ?
Error on A/B = E(A/B), when A and B are known as A±a and B±b is :

E(A/B) = (A+a)/(B-b) – (A-a)/(B+b) = the biggest ratio minus the smallest.

neglecting a² and b², this gives : E(A/B) = 2*(aB+bA)/B² = ±(aB+bA)/B²

Applying this result with A = c and B = Ti, we get :

E(RBP) = E(c/Ti) = 2*(0.5*8.6E17 + 500*3E9)/74*E34 = 1.16E-8 Å

hence RBP = 3.46982012 ±0.6E-8 Å
and the relative error on RBP = D(RBP) = 0.6E-8/3.46*100 % = 1.7E-7 %

This leaves me perplexed as for the most common DNA shape (=B-DNA), scientific literature gives no better accuracy
then E(RBP) = 0.005 Å hence D(RBP)= 0.005/3.5*100 = 0.14 %, as shown on charts below.

Following are 3 calculations of the BP to Hz factor (Ti) using 3 different values of the Rise per BP (RBP) picked up from the 3 charts at the end of the post

1- Calculation of Ti = BP to Hz factor with Rise per BP = 3.4 Å ± 0.05 Å
If we rely on the coloured chart (Comparison of different forms of DNA, see below), for B-DNA which is the most common kind encountered in biological tissues, RPB = 3.4 Å. No further decimals being provided, it is assumed that the RBP value lies between 3.35 and 3.45, i.e RPB = 3.4 Å ± 0.05 Å.

Hence Ti = c/RBP = 881742523529412000 Hz/BP

What is the absolute error on Ti ?
Recalling that E(A/B) = 2*(aB+bA)/B² = ±(aB+bA)/B²
E(Ti) = E(c/RBP) = 2*(0.5*3.4E-10 + 5E-12*3E9)/11.6E-20
= (3.4E-10 + 3E-2)/1.2E-19 = 2.6E17 Hz/BP = ± 1.3E17 Hz/BP

Thence,
Ti = 8.8E17 Hz ± 1.3E17 Hz or 7.5E17 Hz < Ti < 10.1E17 Hz
with D(Ti) = ±1.3/8.82*100 % = ±14.7 %

For Spooky tweaking, this means that :
→ 8.82E17 Hz/BP should be input in the system tab BP to Hz value with
→ Spectrum% not smaller then 14.7 % and with
→ X=WCM as high as possible (=96).
An additional frequency wobble can be added, the width of which would be 14.7/96 % = 0.15 %
With DT = dwelling time (sec) ; RR = 2 * gating rate = refresh rate (Hz), the step number for the wobble is DT * RR.
Thus, the 2*X teeth frequency comb wobbles on one interteeth space, improving greatly the sweeping.

2 - Calculation of Ti = BP to Hz factor with Rise per BP = 3.32 Å ±0.005Å
In the chart "Average helix parameters...", RBP is given as 3.32 Å. No further decimals being provided, it is assumed
that 3.315 Å< RBP < 3.325 Å.

Ti = c/RBP = 9.02989331325301E+17 Hz/BP

What is the absolute error on Ti ?
Recalling that E(A/B) = 2*(aB+bA)/B² = ±(aB+bA)/B²
E(Ti) = E(c/RBP) = 2*(0.5*3.3E-10 + 5E-13*3E9)/11E-20
= (3.3E-10 + 3E-3)/1.1E-19 = 2.7E16 Hz/BP = ± 0.14E17 Hz/BP

Thence,
Ti = 9.03E17 Hz ± 0.14E17 Hz or 8.89E17 Hz < Ti < 9.17E17 Hz
with D(Ti) = ±0.14/9*100 % = ±1.5 %

For Spooky tweaking, this means that :
→ 9.03E17 Hz/BP should be input in the system tab BP to Hz value with
→ Spectrum% not smaller then 1.5 % and with
→ X=WCM as high as possible (=96).
An additional frequency wobble can be added, the width of which would be 1.5/96 % = 0.016 %
With DT = dwelling time (sec) ; RR = 2 * gating rate = refresh rate (Hz), the step number for the wobble is DT * RR.

3 - Calculation of Ti = BP to Hz factor with Rise per BP = 3.35 Å ± 0.05 Å
With the 3rd chart, for B-DNA which is the most common kind encountered in biological tissues, RBP is given as 3.3 Å < RPB < 3.4 Å, so we can write RPB = 3.35 Å ± 0.05 Å.

Hence Ti = c/RBP = 8.94902859701493E+17 Hz/BP

What is the absolute error on Ti ?
Recalling that E(A/B) = 2*(aB+bA)/B² = ±(aB+bA)/B²
E(Ti) = E(c/RBP) = 2*(0.5*3.35E-10 + 5E-12*3E9)/11.22E-20
= (3.4E-10 + 3E-2)/1.12E-19 = 2.7E17 Hz/BP = ± 1.3E17 Hz/BP

Thence,
Ti = 8.9E17 Hz ± 1.3E17 Hz or 7.6E17 Hz < Ti < 10.2E17 Hz
with D(Ti) = ±1.3/8.9*100 % = ±14.6 %

For Spooky tweaking, this means that :
→ 8.9E17 Hz/BP should be input in the system tab BP to Hz value with
→ Spectrum% not smaller then 14.6 % and with
→ X=WCM as high as possible (=96).
An additional frequency wobble can be added, the width of which would be 14.6/96 % = 0.15 %
With DT = dwelling time (sec) ; RR = 2 * gating rate = refresh rate (Hz), the step number for the wobble is DT * RR.
Thus, the 2*X teeth frequency comb wobbles on one interteeth space, improving greatly the sweeping.

The three calculations in one chart: