# MC DNA Help - Analysis Stiffness

## Stiffness

### Method

**Elastic force constants** associated with **helical deformation** at the base **pair step level** were determined by inversion of the covariance matrix in helical space, which yields **stiffness** matrices whose diagonal elements provide the stiffness constants associated with pure **rotational** (** twist, roll and tilt**) and

**translational**(

**) deformations within the given step.**

*rise, shift and slide*$$ \Xi_h = k_BTC_h^{-1} = \left[\begin{matrix} k_{twist} & k_{t - r} & k_{t - l} & k_{t - i} & k_{t - s} & k_{t - d} \\ k_{t - r} & k_{roll} & k_{r - l} & k_{r - i} & k_{r - s} & k_{r - d} \\ k_{t - l} & k_{r - l} & k_{tilt} & k_{l - i} & k_{l - s} & k_{l - d} \\ k_{t - i} & k_{r - i} & k_{l - i} & k_{rise} & k_{i - s} & k_{i - d} \\ k_{t - s} & k_{r - s} & k_{l - s} & k_{i - s} & k_{shift} & k_{s - d} \\ k_{t - d} & k_{r - d} & k_{l - d} & k_{i - d} & k_{s - d} & k_{slide} \\ \end{matrix}\right] $$

### Results

**Stiffness** analyses are shown in a set of line plots. The **parameter value** (or average value + standard deviation in case of structure ensemble) is represented with a yellow point-line (y-axis) for each of the base pair steps along the input sequence (x-axis).

#### Shift

**Shift stiffness value** (for structure) or **average value together with its associated standard deviation** (for ensembles) is shown for each of the base pair steps in the sequence in a yellow point-line. Y-axis: **Shift stiffness** value in **Kcal/mol * Angstroms ^{2}**, X-axis: Sequence base pair steps.

#### Slide

**Slide stiffness value** (for structure) or **average value together with its associated standard deviation** (for ensembles) is shown for each of the base pair steps in the sequence in a yellow point-line. Y-axis: **Slide stiffness** value in **Kcal/mol * Angstroms ^{2}**, X-axis: Sequence base pair steps.

#### Rise

**Rise stiffness value** (for structure) or **average value together with its associated standard deviation** (for ensembles) is shown for each of the base pair steps in the sequence in a yellow point-line. Y-axis: **Rise stiffness** value in **Kcal/mol * Angstroms ^{2}**, X-axis: Sequence base pair steps.

#### Tilt

**Tilt stiffness value** (for structure) or **average value together with its associated standard deviation** (for ensembles) is shown for each of the base pair steps in the sequence in a yellow point-line. Y-axis: **Tilt stiffness** value in **Kcal/mol * degrees ^{2}**, X-axis: Sequence base pair steps.

#### Roll

**Roll stiffness value** (for structure) or **average value together with its associated standard deviation** (for ensembles) is shown for each of the base pair steps in the sequence in a yellow point-line. Y-axis: **Roll stiffness** value in **Kcal/mol * degrees ^{2}**, X-axis: Sequence base pair steps.

#### Twist

**Twist stiffness value** (for structure) or **average value together with its associated standard deviation** (for ensembles) is shown for each of the base pair steps in the sequence in a yellow point-line. Y-axis: **Twist stiffness** value in **Kcal/mol * degrees ^{2}**, X-axis: Sequence base pair steps.