  Computational molecular modeling and visualization has seen significant
progress in recent years with sev- eral molecular modeling and visualization
software systems in use today. Nevertheless the molecular biology community
lacks techniques and tools for the rigorous analysis, quantification and
visualization of the associated errors in molecular structure and its
associated properties. This paper attempts at filling this vacuum with the
introduction of a systematic statistical framework where each source of
structural uncertainty is modeled as a ran- dom variable (RV) with a known
distribution, and properties of the molecules are defined as dependent RVs. The
framework consists of a theoretical basis, and an empirical implementation
where the uncertainty quantification (UQ) analysis is achieved by using
Chernoff-like bounds. The framework enables additionally the propagation of
input structural data uncertainties, which in the molecular protein world are
described as B-factors, saved with almost all X-ray models deposited in the
Protein Data Bank (PDB). Our statistical framework is also able and has been
applied to quantify and visualize the uncertainties in molecular properties,
namely solvation interfaces and solvation free energy estimates. For each of
these quantities of interest (QOI) of the molecular models we provide several
novel and intuitive visualizations of the input, intermediate, and final
propagated uncertainties. These methods should enable the end user achieve a
more quantitative and visual evaluation of various molecular PDB models for
structural and property correctness, or the lack thereof.
