This section is dealing with specific types of analysis performed by MDANSE. If you are not sure where these fit into the general workflow of data analysis, please read The MDANSE Workflow.

Analysis Theory: Other

Infrared

Dipole AutoCorrelation Function

Dipole AutoCorrelation Function is valuable for studying molecular vibrations and infrared spectra using dipole auto-correlation. Researchers can gain insights into the vibrational modes and spectral characteristics of molecules, aiding in the identification and analysis of chemical compounds. Infrared spectroscopy is a fundamental technique in chemistry and material science, making this analysis essential for understanding molecular behavior and composition in simulations.

Macromolecules

Refolded Membrane Trajectory

The Macromolecules focuses on the analysis of large molecular structures. Refolded Membrane Trajectory Analysis is instrumental in manipulating and examining complex membrane structures within macromolecules. Understanding and refining macromolecular structures are vital for various applications, including drug design, biomolecular research, and materials science.

Thermodynamics

This section contains the following Plugins:

Density

Density is used in molecular dynamics simulations to calculate and analyze the density of particles within a simulated system. Density refers to the concentration of particles (atoms, molecules, or ions) in a given volume of space. This helps researchers understand how particles are distributed within the simulation box and how their density changes over time. By calculating density profiles or histograms, scientists can gain insights into phase transitions, the formation of clusters, or the behavior of molecules in various regions of the system. Understanding density is crucial for studying phase changes, solvation, and other thermodynamic processes in molecular systems.

Temperature

The temperature is another essential tool in molecular dynamics simulations that allows researchers to monitor and control the temperature of the simulated system. Temperature is a fundamental thermodynamic variable that influences molecular motion and interactions. This plugin provides the means to calculate and adjust the temperature throughout a simulation, ensuring that the system remains at the desired temperature or follows a specific temperature profile. Monitoring temperature fluctuations and deviations from the desired values is crucial for accurately simulating and understanding the thermodynamic behavior of molecules. Controlling temperature is particularly important when studying phase transitions, chemical reactions, and equilibrium properties of molecular systems.

Trajectory

The Plugins within this section are listed below. They are used to adjust the trajectory in some way.

Box Translated Trajectory

A “Box Translated Trajectory” in molecular dynamics simulations refers to a technique where the entire simulation box, representing the space in which molecules interact, is shifted or translated during the simulation. This approach can be useful for correcting periodic boundary condition artifacts, studying different regions of a system, applying unique boundary conditions, or mitigating surface effects. The translation of the simulation box allows researchers to explore specific aspects of molecular behavior and system properties within the computational environment.

Center Of Masses Trajectory

The Center Of Mass Trajectory (COMT) analysis consists in deriving the trajectory of the respective centres of mass of a set of groups of atoms. In order to produce a visualizable trajectory, MDANSE assigns the centres of mass to pseudo-hydrogen atoms whose mass is equal to the mass of their associated group. Thus, the produced trajectory can be reused for other analysis. In that sense, COMT analysis is a practical way to reduce noticeably the dimensionality of a system.

Cropped Trajectory

A “Cropped Trajectory” in molecular dynamics simulations refers to a shortened version of the trajectory data file, focusing on a specific time segment of a simulation. This cropping process is useful for reducing data size, isolating relevant events, improving computational efficiency, and enhancing visualization. It allows researchers to concentrate on the critical dynamics or interactions within a molecular system while excluding unnecessary or transient data.

Global Motion Filtered Trajectory

It is often of interest to separate global motion from internal motion, both for quantitative analysis and for visualization by animated display. Obviously, this can be done under the hypothesis that global and internal motions are decoupled within the length and timescales of the analysis. MDANSE can create Global Motion Filtered Trajectory (GMFT) by filtering out global motions (made of the three translational and rotational degrees of freedom), either on the whole system or on a user-defined subset, by fitting it to a reference structure (usually the first frame of the MD). Global motion filtering uses a straightforward algorithm:

for the first frame, find the linear transformation such that the coordinate origin becomes the centre of mass of the system and its principal axes of inertia are parallel to the three coordinates axes (also called principal axes transformation),
this provides a reference configuration C_ref,
for any other frames f, finds and applies the linear transformation that minimizes the RMS distance between frame f and C_ref.

The result is stored in a new trajectory file that contains only internal motions. This analysis can be useful in case where diffusive motions are not of interest or simply not accessible to the experiment (time resolution, powder analysis … ).

Rigid Body Trajectory

To analyse the dynamics of complex molecular systems it is often desirable to consider the overall motion of molecules or molecular subunits. We will call this motion rigid-body motion in the following. Rigid-body motions are fully determined by the dynamics of the centroid, which may be the centre-of-mass, and the dynamics of the angular coordinates describing the orientation of the rigid body. The angular coordinates are the appropriate variables to compute angular correlation functions of molecular systems in space and time. In most cases, however, these variables are not directly available from MD simulations since MD algorithms typically work in cartesian coordinates. Molecules are either treated as flexible, or, if they are treated as rigid, constraints are taken into account in the framework of cartesian coordinates [Ref23]. In MDANSE, Rigid-Body Trajectory (RBT) can be defined from a MD trajectory by fitting rigid reference structures, defining a (sub)molecule, to the corresponding structure in each time frame of the trajectory. Here ‘fit’ means the optimal superposition of the structures in a least-squares sense. We will describe now how rigid body motions, i.e. global translations and rotations of molecules or subunits of complex molecules, can be extracted from a MD trajectory. A more detailed presentation is given in [Ref24]. We define an optimal rigid-body trajectory in the following way: for each time frame of the trajectory the atomic positions of a rigid reference structure, defined by the three cartesian components of its centroid (e.g. the centre of mass) and three angles, are as close as possible to the atomic positions of the corresponding structure in the MD configuration. Here ‘as close as possible’ means as close as possible in a least-squares sense.

Optimal superposition. We consider a given time frame in which the atomic positions of a (sub)molecule are given by

(131)\[{x_{\alpha},{\alpha = 1}\ldots N}\]

. The corresponding positions in the reference structure are denoted as

(132)\[{x_{\alpha}^{(0)},{\alpha = 1}\ldots N}\]

. For both the given structure and the reference structure we introduce the yet undetermined centroids X and X⁽⁰⁾, respectively, and define the deviation

(133)\[{\Delta_{\alpha}\doteq D(q){\left\lbrack {x_{\alpha}^{(0)} - X^{(0)}} \right\rbrack - \left\lbrack {x_{\alpha} - X} \right\rbrack}.}\]

Here D(q) is a rotation matrix which depends on also yet undetermined angular coordinates which we chose to be quaternion parameters, abbreviated as vector q = (q₀, q₁, q₂, q₃). The quaternion parameters fulfil the normalization condition

(134)\[{q \dot {q = 1}}\]

[Ref25]. The target function to be minimized is now defined as

(135)\[{m{\left( {q;X,X^{(0)}} \right) = {\sum\limits_{\alpha}{\omega_{\alpha}|\Delta|_{\alpha}^{2}}}}.}\]

where \(\omega_{\alpha}\) are atomic weights (see Section ??). The minimization with respect to the centroids is decoupled from the minimization with respect to the quaternion parameters and yields

(136)\[{{X = {\sum\limits_{\alpha}\omega_{\alpha}}}x_{\alpha},}\]

(137)\[{{X^{(0)} = {\sum\limits_{\alpha}\omega_{\alpha}}}x_{\alpha}^{(0)}.}\]

We are now left with a minimization problem for the rotational part which can be written as

(138)\[m{(q) = {\sum\limits_{\alpha}{\omega_{\alpha}\left\lbrack {{D(q)r}_{\alpha}^{(0)} - r_{\alpha}} \right\rbrack^{2}}}\overset{!}{=}\mathit{Min}}.\]

The relative position vectors

(139)\[{{r_{\alpha} = {x_{\alpha} - X}},}\]

(140)\[{r_{\alpha}^{(0)} = {x_{\alpha}^{(0)} - X^{(0)}}}\]

are fixed and the rotation matrix reads [Ref25]

(141)\[\begin{split}D(q) = \begin{matrix} {q_{0}^{2} + q_{1}^{2} - q_{2}^{2} - q_{3}^{2}} & {2\left( {{- q_{0}}{q_{3} + q_{1}}q_{2}} \right)} & {2\left( {q_{0}{q_{2} + q_{1}}q_{3}} \right)} \\ {2\left( {q_{0}{q_{3} + q_{1}}q_{2}} \right)} & {q_{0}^{2} + q_{2}^{2} - q_{1}^{2} - q_{3}^{2}} & {2\left( {{- q_{0}}{q_{1} + q_{2}}q_{3}} \right)} \\ {2\left( {{- q_{0}}{q_{2} + q_{1}}q_{3}} \right)} & {2\left( {q_{0}{q_{1} + q_{2}}q_{3}} \right)} & {q_{0}^{2} + q_{3}^{2} - q_{1}^{2} - q_{2}^{2}} \\ \end{matrix}\end{split}\]

Quaternions and rotations. The rotational minimization problem can be elegantly solved by using quaternion algebra. Quaternions are so-called hypercomplex numbers, having a real unit, 1, and three imaginary units, I, J, and K. Since IJ = K (cyclic), quaternion multiplication is not commutative. A possible matrix representation of an arbitrary quaternion,

(142)\[{{A = a_{0}}\cdot{1 + a_{1}}\cdot{I + a_{2}}\cdot{J + a_{3}}\cdot K,}\]

reads

(143)\[\begin{split}A = \begin{matrix} a_{0} & {- a_{1}} & {- a_{2}} & {- a_{3}} \\ a_{1} & a_{0} & {- a_{3}} & a_{2} \\ a_{2} & a_{3} & a_{0} & {- a_{1}} \\ a_{3} & {- a_{2}} & a_{1} & a_{0} \\ \end{matrix}\end{split}\]

The components \(a_{\upsilon}\) are real numbers. Similarly, as normal complex numbers allow one to represent rotations in a plane, quaternions allow one to represent rotations in space. Consider the quaternion representation of a vector r, which is given by

(144)\[{{R = x}\cdot{I + y}\cdot{J + z}\cdot K,}\]

and perform the operation

(145)\[{{R^{'} = \mathit{QRQ}^{T}},}\]

where Q is a normalised quaternion

(146)\[{\text{|}Q\text{|}^{2}\doteq{{q_{0}^{2} + q_{1}^{2} + q_{2}^{2} + q_{3}^{2}} = \frac{1}{4}}\mathit{tr}\text{\textbackslash\{}Q^{T}Q{\text{\textbackslash\}} = 1.}}\]

The symbol tr stands for ‘trace’. We note that a normalized quaternion is represented by an orthogonal 4 x 4 matrix. R’ may then be written as

(147)\[{{R^{'} = x^{'}}\cdot{I + y^{'}}\cdot{J + z^{'}}\cdot K,}\]

where the components x’, y’, z’, abbreviated as r’, are given by

(148)\[{{r^{'} = D}(q)r.}\]

The matrix D(q) is the rotation matrix defined in 95.

Solution of the minimization problem. In quaternion algebra, the rotational minimization problem may now be phrased as follows:

(149)\[{m{(q) = {{\sum\limits_{\alpha}{{\omega_{\alpha}\text{|}\mathit{QR}}_{\alpha}^{(0)}Q}^{T}} - R_{\alpha}}}{\text{|}^{2}\overset{!}{=}\mathit{Min}}.}\]

Since the matrix Q representing a normalized quaternion is orthogonal this may also be written as

(150)\[{{{m{(q) = {\sum\limits_{\alpha}\omega_{\alpha}}}\text{|}\mathit{QR}}_{\alpha}^{(0)} - R_{\alpha}}Q\text{|}^{2}{.\overset{!}{=}\mathit{Min}}.}\]

This follows from the simple fact that

(151)\[{\text{|}A{\text{|} = \text{|}}\mathit{AQ}\text{|}}\]

, if Q is normalized. Eq. 104 shows that the target function to be minimized can be written as a simple quadratic form in the quaternion parameters [Ref24],

(152)\[{m{(q) = q}\cdot\mathit{Mq},}\]

(153)\[{{M = {\sum\limits_{\alpha}{\omega_{\alpha}M_{\alpha}}}}.}\]

The matrices M_ are positive semi-definite matrices depending on the positions \(r_{\alpha}\) and \(r_{\alpha}^{(0)}\):

|image32|

The rotational fit is now reduced to the problem of finding the minimum of a quadratic form with the constraint that the quaternion to be determined must be normalized. Using the method of Lagrange multipliers to account for the normalization constraint we have

(154)\[{m^{'}{\left( {q,\lambda} \right) = q}\cdot{\mathit{Mq} - \lambda}{\left( {q\cdot{q - 1}} \right)\overset{!}{=}\mathit{Min}}.}\]

This leads immediately to the eigenvalue problem

(155)\[{{\mathit{Mq} = \lambda}q,}\]

(156)\[{q\cdot{q = 1.}}\]

Now any normalized eigenvector q fulfils the relation

(157)\[{{\lambda = q}\cdot\mathit{Mq}\equiv m(q)}\]

. Therefore, the eigenvector belonging to the smallest eigenvalue, λ_min, is the desired solution. At the same time λ_min gives the average error per atom. The result of RBT analysis is stored in a new trajectory file that contains only RBT motions.

Unfolded Trajectory

An “Unfolded Trajectory” in the context of molecular dynamics simulations refers to a trajectory data file that has been processed or analyzed to reveal the unfolding or expansion of molecular structures over time. This term is particularly relevant in the study of biomolecules or polymers, where understanding the dynamic evolution and changes in these structures holds significant importance for scientific applications, including drug design, materials science, and biomolecular research. Unfolding trajectories provide valuable insights into molecular behavior and interactions, contributing to the development of new materials and the design of therapeutic compounds.

Virtual Instruments

McStas Virtual Instrument

McStas enables researchers to create virtual instruments that replicate the behavior of real neutron or X-ray instruments. This capability streamlines the design, optimization, and testing of experiments within a virtual environment before conducting physical experiments. Such simulations help researchers conserve valuable time and resources while simultaneously enhancing the precision and reliability of their experiments. McStas finds widespread application in fields like materials science and condensed matter physics.

Miscellaneous

This section normally contains only one Plugin, which is present for both trajectories and analysis results. However, some other Plugins appear under certain circumstances.

Data info

The “Data Info” function provides an overview of the data stored in the selected HDF (Hierarchical Data Format) file. When used with trajectory files, it displays information such as the location of the trajectory on disk, the number of time steps, the universe (the HDF object), direct cell parameters at the beginning, reciprocal cell parameters at the beginning, a list of molecules, and a list of variables contained within the trajectory. It serves as a helpful tool for understanding the details of the data in the file, which can be vital for further analysis or interpretation.

Animation

The Animation feature enhances the functionality of the Molecular Viewer. When activated, it creates a new bar below the Molecular Viewer interface, allowing users to visually observe the entire molecular dynamics (MD) simulation. This feature provides a visual representation of the simulation’s progress, making it easier for researchers to observe and analyze the dynamic behavior of molecules throughout the simulation. It’s a valuable tool for gaining insights into molecular interactions and motions over time.

Density Superposition

The Density Superposition function is specifically designed for trajectories. It becomes accessible when the Molecular Viewer is active, and a left-click action is performed within it. When activated, it allows users to overlay density information from the trajectory data. This feature can be valuable for comparing the density distributions of different molecular species or analyzing density changes over the course of a simulation, providing insights into molecular arrangements and interactions within the system.

Trajectory Viewer

The Trajectory Viewer is a graphical interface that allows users to visualize and inspect trajectory data from molecular dynamics simulations. It provides a visual representation of the movement and behavior of molecules over time, enabling researchers to gain insights into molecular interactions and dynamics.

My jobs

This section only appears if you have used the Save analysis template button in the main window’s toolbar. It contains all the analyses created this way and allows them to be run.

Plotter

2D/3D Plotter

The “Plotter,” including the “2D/3D Plotter,” is a data visualization tool designed for visualizing and graphically representing data obtained from analysis results. It allows users to create two-dimensional (2D) and three-dimensional (3D) plots and charts, facilitating data analysis and presentation.

User definition

This section contains definitions or selections made for the selected HDF (Hierarchical Data Format) file. These user-defined selections serve a similar purpose to the “User Definition Editor” and help customize interactions with the data within the HDF file.

Viewer

Molecular Viewer

Jobs

The Viewer, specifically the “Molecular Viewer,” is a tool for visualizing molecular structures and simulations. It provides an interactive 3D representation of molecules, allowing users to explore and analyze molecular dynamics. The “Jobs” panel lists ongoing or completed analysis jobs, helping users track the progress of their analyses and providing information on started, completed, or running analyses.

These features and sections enhance the functionality of the software for molecular dynamics simulations, simplifying data visualization, analysis, and management for researchers.