Title of Invention

Analysis of biomolecular solvation sites by the 3D-RISM theory.

Technical Field

This invention is an algorithm and software for investigating solvation sites in biomolecules. It is relevant to the fields of experimental refinement and pharmaceutical design.

Background Art Solvent plays several critical roles in the function of biomolecules. In particular, microscopic effects of solvent such as hydrogen bonding and binding affinity augmentation by the "solvent-displacement effect" are necessary for critical analysis of ligand binding. Minute knowledge of such effects is necessary for reliable prediction, explanation and design of molecular systems. Thus it is no wonder increasing attention is paid by the pharmaceutical- design community to solvent molecules inside active site of protein.

Experimental methodologies for analyzing atomistic water behavior can be extremely useful but are often hindered by limited spatial resolution. Theoretically, sophisticated analysis of water based on simulation has been development for over a decade. In 1998, Lazaridis derived inhomogeneous fluid theory in two landmark papers. ¹ ' ² Several years later, Young et al developed a solvation site based approach, commonly called "Watermap,"[PTLl-3] to the forefront by applying Lazaridis' theory towards identification of displaceable water sites to enhance ligand binding. ³ ' ⁴ Similarly, recent work by Nguyen et al uses, rather, a grid-based application of Lazaridis' theory. ⁵

Although the "explicit-solvent" simulations, on which this analysis is based, enable incredible precision, the sampling problem limits reliable analysis to smaller systems depending on the available computational budget. Even for extremely expensive simulations though, it is questionable whether sufficient sampling of water and ions has occurred in buried regions of the solute where the solvent exchange rate is very slow. ^6'9 Citation List

Patent Literature

PTLl: USP 7,970,581

PTL2: USP 7,970,580

PTL3: USP 7,756,674

Non Patent Literature

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Summary of Invention

The invention is an algorithm and related software to analyze the local thermodynamics and structural properties of solvation sites in biomolecules using the 3D-RISM theory. The invention produces reliable spatial and thermodynamic properties of solvation sites readily usable for pharmaceutical design.

Technical Problem

In order to perform rational drug design, much information is needed about the interactions that affect drug binding. One important factor is the role of solvent sites in the active site. These sites are impossible to characterize experimentally. Conventional techniques such as implicit solvation are fundamentally useless with this regard. Postprocessing of explicit solvent simulations may be useful if it weren't for the fact that these simulations are severely hindered by the computational time to sample solvent. [PTL 1-3] Consequently such techniques are either extremely time consuming or simply unreliable. Thus there is no reliable, efficient method for performing analysis of solvation sites, severely limiting pharmeceutical design potential.

Solution to Problem

This invention utilizes a methodology, 3D-RISM, which quickly obtains reliable, converged solvent structural data for biomolecules, then postprocesses the data in order to clearly characterize solvation sites. The resulting information, including site locations, orientations, and thermodynamic properties can be directly used in pharmaceutical design efforts such as virtual screening pharmacaphore modeling.

Advantageous Effects of Invention

This invention will allow much faster analysis of biomolecular sites in various solvent conditions. The analysis will be a boon for pharmeceutical design efforts. The invention showed systematic agreement with high-resolution experimental data and with simulation-based water analysis techniques. Our calculations on HIV-1 protease took just under 11 minutes total on an 8-core workstation. This method can directly take into account cosolvent and ionic effects on solvent structure and thermodynamics, which cannot be realized by more conventional methods such as the continuum solvent models and molecular simulation. Thus we assert that our method is both extremely practical and reasonably accurate method for solvation-site analysis.

Brief Description of Drawings

Figure 1. shows a flowchart of the main aspects in the context of expected use of this invention.

Description of Embodiments The invention is embodied as a computer program written in Python. The program performs file search, reading, analysis and writing.

DETAILED DESCRIPTION

This invention circumvents the solvent sampling problem by using the three-dimensional reference interaction site model (3D-RISM) theory. ^10,11 3D-RISM attains complete atomistic sampling of solvent, including ions, by utilizing an integral approach. 3D-RISM has been successful in locating water in proteins compared to experiment ^12"15 and simulation, ¹⁶ ion locations and pathways, hydration free energies, fragment poses, ^" and drug poses, as well as many more applications less relevant to this work. With current implementations, the equilibrium solvent distribution of a biologically relevant system can be calculated in minutes to hours.

3D-RISM first utilizes RISM calculations to find the susceptibility function of the solvent based on specified atomic interaction potentials and mixture concentrations. The solvent susceptibility is then utilized in the 3D-RJSM equations, including the atomic solvent-solute interaction potential. The 3D-RISM equations coupled with an appropriate closure relation are iterated until self-consistency resulting in the 3D solvent distribution function g(r), the total correlation function h(r), the direct correlation c(r), as well as other distributions and properties.

To characterize solvation sites, the location of the site must first be identified. We find the sites using the maximum probability in: P( ^T )n, — P( ^T )n-i * (1 - Θ(|Γ - r™"* - R\)) ^ Here, P( ^T )o = oi?( ^r )c, _n is the iteration number, and R is a present exclusion radius (here lA). This algorithm is iterated until a cutoff is reached, here we cutoff at a number of solvent molecules placed. The resulting discrete distribution represents high occupancy sites whose properties may be of interest in solvation site analysis. The embodiment employs the

Successive Orthogonal Images (SOI) approach, ⁶ which produces more uniform coverage of rotational space. A uniform distribution is obtained by 1) creating a uniform distribution of points on the unit sphere, V ¹ , 2) For each point on the sphere create a set of uniform vectors, V ² , also within the unit sphere which are orthogonal to the vector pointing from the center to that point, 3) trivially determine an orthogonal vector to the two previous vectors, 4) determine the rotation, M, expressed in Euler angles corresponding to the three orthogonal vectors based on an arbitrary reference geometry. The resulting set rotations exists within SO(3) and represents a uniform set of rotations. For efficiency in computation we find the optimal angular difference, o, and sizes of \V ^l I and l^ ² l for a fixed number of rotations. Equation 3.1 in reference 28 shows that i^ ² l = 4 /α ² and Ι^Ί = 2TT/G thus we set ^a = (8n ² /N _rot ) Vhere N _T ot = I V ² \ ^■ |V ^X |. We take the solvent atom closest to the center of geometry (Oxygen for water) as a fixed, "anchor" for rotations. For each position of an anchor, the rotational probability distribution function can be described as:

= Z~ ^l g ₁ (r _anchor + Γ ₇ , _Ω )

^■ yesites (2) Here ^Γ ,ω is the relative position of the solvent-site Ί given rotation ω from some arbitrary original geometry and Z is the partition function. The solvation-site is defined as the 6D conformational space available by moving the anchor atom within a 1.0 A radius sphere centered on the originally identified location, r _n . The highest likelihood pose lies at the maximum of P(w\ ^r ) where l ^r - ^T n \≤ R.

The implementation characterizes "solvation sites" using integrations over the solvation site volume, Vn. The excess chemical potential or solvation free energy is evaluated simply using the total and direct correlation functions for many 3D-RISM closures including the KH- closure which we use here. ^11,27

Δμ™ = Pok _B T∑f _v [i ( r)) ² e (- r)) - ) ~ ^ 'tew]

For the partial molar volume, the adapted Kirkwood-Buff equations toward 3D-RISM

CALCULATION DETAILS

System geometries tested for this implementation were taken from the PDB: HIV-1 protease (2ZYE). ³⁰ Protein interaction parameters were taken from the ff99SB parameter set. ³¹ KNI-272 was parameterized using Gaussian 09 ³² using HF 6-31G* basis set and GAFF parameters ³³ using antechamber ³ with RED IV ³⁵ parameterization. Protonation states were taken from available deuterium data from the experimental structure. Alanine Dipeptide structure and all parameters were prepared using tLEaP. Pure water at 55.5 M using modified SPC parameters. ³⁶ 3D-RISM calculations were run using the AmberTools rism3d.snglpnt.MPI module. ³⁶ ' ³⁷ All calculations were performed on an HP Z 100 8-core Intel 3.2 GHz Xeon workstation. The 3D-RISM calculation on HIV-1 protease and Alanine Dipeptide using the KH closure took 6.5 minutes and 39 seconds respectively. Postprocessing was performed using a Python script, which took 4.3 minutes to run in serial.

RESULTS

The embodiment was tested by comparing experimental waters to their nearest predicted solvation site and compared the RMSD between the pair of poses with—TS. Linear fits give r - -0.47 and r = -0.67 for -TS _tra ns and -TS _rot respectively. The strongest correlation was with the total contribution of entropy to the free energy, -TS _rot where r = -0.76.

-TStrans had a r =-0.48 against distance between experimental and predicted oxygens. The experimental B-factor also had a correlation of r - 0.46 with the 0-0 distance.

The data suggest that there is a reasonable correlation between "structural predictability" and entropy.

Next, quantitative comparisons of thermodynamic quantities to those obtained by simulation-based analysis were obtained. In 2003, Li and Lazaridis ³⁸ studied an isolated water bound between the flaps and the inhibitor KNI-272 bound from of HIV- 1 protease using structure 1HPX ³⁹ and the simulation-based approach. In Table 1, their data is compared to the results of this implementation. For this water, the estimates for solvation free energy agreed to less than 1 kcal/mol. The entropic contribution was underpredicted by 1-2 kcal/mol. The solvent-solute interaction energy was also under-predicted by about 7 kcal/mol. While the differences may be partly attributed to force field differences and solute structures, other factors are likely due to limitation of methodological errors for generating the initial data (sampling error in simulation and closure error in 3DRISM).

Although Lazaridis' work calculates the total solvation free energy by addition of explicit terms, this implementation calculates only the first order terms in energy and entropy but calculates the solvation free energy directly. The PV term in the free energy for most the sites including the flap water, this term was nearly zero.

The site in the vicinity of KNI-272, the "flap" water, despite its steep entropic penalty, favorably contributes to the solvation free energy. The results included less favorable waters nearby the inhibitor (e.g. water 354 with Δ(7=-4.96 kcal/mol) as well as other sites in the hinge region as high as -0.93, and near the termini as high as +1.65 kcal/mol. Such water sites may be reasonable targets for displacement in drug-design efforts.

Industrial Applicability

This invention can be used by pharmeceutical scientists and molecular design scientists in order to better understand the microscopic solvent effects in their system, enabling intelligent design.