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 MDANSE Workflow.

Analysis: Structure

This section contains the following plugins:

Area Per Molecule

The area per molecule (APM) analysis in molecular dynamics (MD) assesses the surface area occupied by each molecule within a given system. This tool plays a crucial role in comprehending molecular arrangement and interactions. Users can specify the molecule they wish to analyze. The APM analysis provides valuable insights into how molecules are distributed and interact with one another. This analysis is particularly vital in the study of complex structures like cell membranes. It aids in understanding membrane functionality and its response to various conditions, shedding light on essential biological processes. By utilizing APM analysis in MDANSE, researchers can gain a deeper understanding of molecular systems and their behavior, ultimately contributing to advancements in fields like biophysics and structural biology.

Coordination Number

In chemistry, the coordination number (CN) is the total number of neighbors of a central atom in a molecule or ion. CN plays a vital role in the analysis of complex molecular systems in simulations, serving several key purposes:

  • Packing Effects: CN reveals how atoms are densely packed around central groups. This helps identify stable configurations, phase transitions, and aggregation patterns.

  • Molecular Interactions: It quantifies atom coordination, indicating attractive or repulsive forces. High CN values suggest strong interactions like bonds, while lower CN values imply weaker or repulsive forces.

  • Tracking Structural Changes: CN analysis tracks how atomic coordination evolves over time. This is essential for studying dynamic processes and structural transformations in simulations.

  • Detailed Molecular Organization: CN provides quantitative measures of atom arrangements, aiding in the identification of specific patterns like solvation shells or coordination spheres.

In MDANSE the CN is defined as

(133)\[ \mathrm{CN}_{\alpha\beta}(r) = c_{\beta} \int\limits_{0}^{\infty}\mathrm{d}r \, 4 \pi r^2 \rho g_{\alpha\beta}(r)\]

where \(g_{\alpha\beta}(r)\) is the partial pair distribution function, see Section Pair Distribution Function for details.

Eccentricity

Eccentricity analysis in MDANSE quantifies how spherical a system is and can be used to observe how the geometry of the system changes over time. The eccentricity of a selection of atom is calculated using the equation

(134)\[ \mathrm{ecc} = \frac{\sqrt{\lambda_{3}^2 - \lambda_{1}^2}}{\lambda_{3}}\]

where \(\lambda_{1}\) and \(\lambda_{3}\) are its smallest and largest principal moments of inertia. A spherically symmetric selection of atoms will have an eccentricity approaching 0 and an aspherical selection of atoms will have a eccentricity approaching 1.

Molecular Trace

Molecular trace in MDANSE pertains to a calculation or property related to the analysis of molecular structures within the context of neutron scattering experiments or molecular dynamics simulations. The β€œresolution” parameter in this context determines the level of detail with which molecular structures are represented or analyzed. A higher resolution results in a more detailed representation of molecular behavior, allowing for the tracking of specific molecular entities within simulations. Conversely, a lower resolution simplifies the analysis for computational efficiency, providing a broader overview of molecular behavior. The Molecular Trace calculation is a valuable tool for investigating the movement and behavior of molecular components in complex systems.

In the context of molecular trace analysis, molecular structures are often represented and analyzed in terms of grid points, where each point corresponds to a specific location within the molecular system. The resolution parameter controls the spacing and granularity of these grid points, influencing the detail of the analysis.

Pair Distribution Function

The pair distribution function (PDF) is an example of a pair correlation function, which describes how, on average, the atoms in a system are packed around each other. This proves to be a particularly effective way of describing the average structure of disordered molecular systems such as liquids. Also in systems like liquids, where there is continual movement of the atoms and a single snapshot of the system shows only the instantaneous disorder, it is extremely useful to be able to deal with the average structure.

The PDF is useful in other ways. For example, it is something that can be deduced experimentally from x-ray or neutron diffraction studies, thus providing a direct comparison between experiment and simulation. It can also be used in conjunction with the interatomic pair potential function to calculate the internal energy of the system, usually quite accurately.

Mathematically, the PDF can be computed using the following formula:

(135)\[g(\mathbf{r}) = \sum_{\alpha}\sum_{\beta \geq \alpha} W_{\alpha\beta} g_{\alpha\beta}(\mathbf{r}), \qquad g_{\alpha\beta}(\mathbf{r}) = \frac{1}{Nc_{\alpha}c_{\beta}}\frac{1}{\rho} \frac{\mathrm{d} N_{\alpha\beta}(\mathbf{r})}{ \mathrm{d} \mathbf{r}}\]

where \(g_{\alpha\beta}(\mathbf{r})\) is the partial PDF for \(\alpha\) and \(\beta\) atom-types, \(N(\mathbf{r})\) is the average number of particles in the volume \(\mathrm{d} \mathbf{r}\) at the position \(\mathbf{r}\) between the atom-types \(\alpha\) and \(\beta\) and \(\rho\) is the density of the system.

For isotropic system we can define the PDF as a function of distance

(136)\[g(r) = \sum_{\alpha}\sum_{\beta \geq \alpha} W_{\alpha\beta} g_{\alpha\beta}(r), \qquad g_{\alpha\beta}(r) = \frac{1}{Nc_{\alpha}c_{\beta}} \frac{1}{\rho} \frac{1}{4 \pi r^2} \frac{\mathrm{d} N(r)}{ \mathrm{d} r}\]

where \(N(r)\) is the average number of particles in the volume \(4 \pi r^2 \mathrm{d} r\) at a distance \(r\) between the atom-types \(\alpha\) and \(\beta\).

From the computation of PDF, two related quantities are also calculated; the radial distribution function (RDF) and the total correlation function (TCF)

(137)\[\mathrm{RDF}{(r) = 4}\pi r^{2}\rho g(r), \qquad \mathrm{TCF}{(r) = 4}\pi r\rho\left[ {g{(r) - 1}} \right].\]

All these quantities are initially calculated as intramolecular and intermolecular parts for each pair of atoms, which are then added to create the total PDF/RDF/TCF for each pair of atoms, as well as the total intramolecular and total intermolecular values. Please note, however, that in the case of TCF, the below set of equations have been chosen, which will return results that differ from those of nMOLDYN

(138)\[{\mathrm{TCF}_{\mathrm{intra}}{(r) = 4}\pi r\rho g_{\mathrm{intra}}(r),}\]
(139)\[{\mathrm{TCF}_{\mathrm{inter}}{(r) = 4}\pi r\rho\left[ {g_{\mathrm{inter}}{(r) - 1}} \right],}\]
(140)\[{\mathrm{TCF}_{\mathrm{tot}}{(r) = 4}\pi r\rho\left[ {g_{\mathrm{tot}}{(r) - 1}} \right].}\]

Radius of Gyration

Radius of gyration (ROG) is calculated as a root (atomic mass weighted) mean square distance of the components of a system relative to either its centre of mass or a given axis of rotation. The ROG serves as a quantitative measure which can be used to characterize the spatial distribution of a system such as a molecule or a cluster of atoms. In MDANSE, ROG is calculated relative to the systems centre of mass. It can be defined as

(141)\[ \mathrm{ROG}(t) = \sqrt{ \frac{\sum_{j}m_{j} \vert \mathbf{r}_{j}(t) - \mathbf{r}_{\mathrm{COM}}(t) \vert^{2}}{\sum_{j} m_{j}} }\]

where \(m_j\) is the mass and \(\mathbf{r}_{j}(t)\) are the positions of the atom \(j\), \(\mathbf{r}_{\mathrm{COM}}(t)\) is the centre of mass of the system and \(t\) is the time of the simulation. ROG can be used to describe the overall spread of the molecule and as such is a good measure for the molecule compactness. For example, it can be useful when monitoring folding process of a protein.

Solvent Accessible Surface

The solvent accessible surface calculation involves defining the surface accessibility of molecules or atoms by creating a mesh of points. The number of points is determined by the field discussed, influencing the level of detail in the surface representation. Essentially, a higher density of points leads to a finer-grained representation, capturing smaller surface features and intricacies.

Probe Radius: Measured in nanometers, the probe radius is a crucial parameter influencing the precision of the calculation. Smaller probe radii provide a more detailed and assessment of the molecular surface area, often resulting in a larger reported surface area due to increased sensitivity to surface features.

Voronoi

In MDANSE, Voronoi analysis plays a pivotal role in characterizing the spatial distribution and organization of particles or atoms within a molecular dynamics simulation. This analysis entails the division of the simulation box into Voronoi cells, with each cell centered around a particle. Voronoi cells provide essential insights into the local environment and packing of particles, allowing researchers to understand the arrangement and interactions of molecules in detail. Within MDANSE, the β€œapply periodic_boundary_condition” parameter is available to ensure accurate analysis, particularly for systems extending beyond the simulation box. This capability enables users to uncover valuable details about molecular structures and dynamics.