Computer implemented system for quantifying stability and flexibility relationships in macromolecules

A computerized method of implementing a Distance Constraint Model on a body-bar multigraph representing constraints on a molecular structure to plot a free energy landscape for the molecular structure in a macrostate having known values for solvent entropy, solvent enthalpy and conformational enthalpy, the method comprising:

• using a computer to execute the steps of a topography processor, the steps comprising:
• assigning a rank to each bar in the multigraph to facilitate an ordered placement of bars in a constraint topology reconstruction, wherein said rank is based at least in part on an assigned conformational entropy value;
• grouping all bars that connect each respective pair of vertices and have a same rank into a respective bundle of bars;
• assigning a probability (P) that one of said bars within each bundle is present, wherein P is any real number ranging from 0 to 1;
• calculating a capacity of a first bundle of bars to remove at least a partial degree of freedom within the multigraph by adding the values of P for each bar in the first bundle;
• and
• reconstructing the body-bar multigraph via the topography processor through recursive addition of bundles of bars to remove degrees of freedom, wherein degrees of freedom may be represented by any real number;
• calculating a molecular partition function with the known values for solvent entropy, solvent enthalpy and conformational enthalpy and with a lowest upper bound estimate for conformational entropy,
• wherein the lowest upper bound estimate for conformational entropy comprises conformational entropy contributions of independent constraints within the multigraph that are ranked with respectively lowest conformational entropy value as calculated for at least one primary order parameter, at least one constraint topology, at least one proximity configuration, and at least one template structure.

A computerized method of plotting a free energy landscape for a molecular structure in a macrostate having known values for solvent entropy, solvent enthalpy and conformational enthalpy, the method comprising:

• using a computer to execute the steps of a topography processor, the steps comprising:
• assigning a rank to each bar in the multigraph to facilitate an ordered placement of bars in a constraint topology reconstruction, wherein said rank is based on an assigned conformational entropy value;
• grouping all bars that connect each respective pair of vertices and have the same rank into a respective bundle of bars;
• assigning a probability (P) that one of said bars within each bundle is present, wherein P is any real number ranging from 0 to 1;
• calculating a capacity of a first bundle of bars to remove at least a partial degree of freedom within the multigraph by adding the values of P for each bar in the first bundle;
• and
• reconstructing the body-bar multigraph via the topography processor through recursive addition of bundles of bars to remove degrees of freedom, wherein degrees of freedom may be represented by any real number;
• calculating a molecular partition function with the known values for solvent entropy, solvent enthalpy and conformational enthalpy and with a lowest upper bound estimate for conformational entropy, wherein the lowest upper bound estimate for conformational entropy comprises conformational entropy contributions of independent constraints within the multigraph as calculated for at least one node in the molecular structure;
• displaying a graph on a computer of the free energy landscape of the molecular structure by plotting the molecular partition function calculation for at least one node in the molecular structure.

A computerized method implementing a Distance Constraint Model on a body-bar multigraph representing constraints on a molecular structure, the method comprising:

• using a computer to execute the steps of a topography processor, the steps comprising:
• assigning a rank to each bar in the multigraph to facilitate an ordered placement of bars in a constraint topology reconstruction, wherein said rank is based on an assigned conformational entropy value;
• grouping all bars that connect each respective pair of vertices and have a same rank into a respective bundle of bars;
• reconstructing the body-bar multigraph via the topography processor through recursive addition of bundles of bars to remove degrees of freedom,
• calculating a molecular partition function with the known values for solvent entropy, solvent enthalpy and conformational enthalpy and with a lowest upper bound estimate for molecular conformational entropy, wherein the lowest upper bound estimate for molecular conformational entropy comprises conformational entropy contributions of independent constraints covering the degrees of freedom within the multigraph, and
• wherein said lowest upper bound estimate is calculated by:
• assigning a probability (Q) and calculating a component conformational entropy for said each bar, wherein probability (Q) is a probability ranging from 0 to 1 that said each bar is an independent constraint on a degree of freedom within the molecular structure;
• calculating, in an iterative loop, respective probabilities (Pb) that said bars in each bundle of bars are present, and further in the iterative loop, using one of said respective probabilities (Pb) to calculate an updated probability (Qb), and further in the iterative loop, recalculating said component conformational entropy for said updated probability (Qb);
• converging said component conformational entropy values for each bar toward a node conformational entropy value for at least one node in the multigraph for the molecular structure;
• and identifying a lowest upper bound estimate of molecular conformational entropy for said node.