## Wednesday, December 2, 2009

### The Blog has moved

to another location. The blog feed is now merged with the Quantum Pharmaceuticals official site http://q-pharm.com. See you there!

## Monday, August 31, 2009

### The nature of phospholipid membranes repulsion at nm-distances

Why hydrophobic membranes repel at small distances? We apply recently developed phenomenological theory of polar liquids to calculate the repulsive pressure between two hydrophilic membranes at nm-distances. We find that the repulsion does show up in the model and the solution to the problem fits the published experimental data well both qualitatively and quantitatively. Moreover, we find that the repulsion is practically independent on temperature, and thus put some extra weight in favor of the so called hydration over entropic hypothesis for the membranes interactions explanation. The calculation is a good “proof of concept” example a continuous water model application to non-trivial interactions on nm-size bodies in water arising from long-range correlations between the water molecules.

More details can be found here:

arXiv:0908.0632 [pdf, other]

More details can be found here:

arXiv:0908.0632 [pdf, other]

The nature of phospholipid membranes repulsion at nm-distances

Labels:
polar liquid,
solvation energy,
water

## Saturday, June 20, 2009

### hERG binding correlates with LogP?

Here is a very good analysis from human ERG blockers article:

The plot below (created usingVortex)shows pIC50 calculated from the literature IC50 data versus calculated logP determined usingalogPS, the colour coding shows the overall general tend of increasing hERG activity as logP increases, it also highlights the reduced liability seen with acids (green) and zwitterions (red).

Whilst the majority of data is derived from radioligand binding experiments (using either Dofetilide or MK-499), there is a substantial amount of data from patch clamp experiments, I collated enough data now (covering 4 orders of magnitude) to give an idea of how the assays compare. As you can see there is a reasonable correlation between the assays, but there are one or two outliers. Which is more predictive of in vivo activity is an excellent question that I don’t have the data to answer yet.

I still need to increase the size of the data-set, and if anyone can direct me to any publicly available data, or to publications that contain data i'd much appreciate it.

Worth reading, Medicinal Chemistry of hERG Optimizations: Highlights and Hang-Ups, Jamieson, Journal of Medicinal Chemistry, 2006, 5029

The plot below (created usingVortex)shows pIC50 calculated from the literature IC50 data versus calculated logP determined usingalogPS, the colour coding shows the overall general tend of increasing hERG activity as logP increases, it also highlights the reduced liability seen with acids (green) and zwitterions (red).

Whilst the majority of data is derived from radioligand binding experiments (using either Dofetilide or MK-499), there is a substantial amount of data from patch clamp experiments, I collated enough data now (covering 4 orders of magnitude) to give an idea of how the assays compare. As you can see there is a reasonable correlation between the assays, but there are one or two outliers. Which is more predictive of in vivo activity is an excellent question that I don’t have the data to answer yet.

I still need to increase the size of the data-set, and if anyone can direct me to any publicly available data, or to publications that contain data i'd much appreciate it.

Worth reading, Medicinal Chemistry of hERG Optimizations: Highlights and Hang-Ups, Jamieson, Journal of Medicinal Chemistry, 2006, 5029

## Monday, April 6, 2009

### Molecular polarization on a polar liquid interface: the structure of a water surface

The orientations of water molecules within the liquid depend on interplay of long-range dipole-dipole interaction and short range hydrogen-bonding interactions. At room temperature water is in paraelectric (disordered) phase and thus average dipole moment of any large enough fraction of the liquid vanishes.

This observation is not necessarily true at the liquid boundary. Since no molecules "like" to point at a hydrophobic interface direction (this would imply many uncompensated hydrogen bonds), most of the molecules orient along the liquid surface, the boundary between the liquid and a hydrophobic may become polarized (become essentially ferroelectric). Practically this amounts to a formation of stable network of hydrogen bonds on the interface.

The solution corresponding to such polarized boundary can be obtained in the very latest "incarnation" of the QUANTUM water model (See the attached figures). The first one demonstrates the density of the liquid starting from the gas phase on the left (model liquid density 0.3) and to the liquid phase (model density 1). The transition between the two phases is similar to that in classical model of van der Waals liquid.

The second graph corresponds to the polarization density (mean dipole moment of a liquid volume). Comparing the two graphs we see that the interface is indeed polarized and the polarization decays quickly into the bulk both of the gas and the liquid phase and, as the detailed calculation shows, contributes to the surface tension coefficient considerably.

In short we observe that depending on the ordering state of the water layer next to a molecular surface the effective surface tension may be different by a large number. Another observation suggests that the water density depletion next to a fully hydrophobic (and thus ordering) surface can be large (up to 30-50%)

This observation is not necessarily true at the liquid boundary. Since no molecules "like" to point at a hydrophobic interface direction (this would imply many uncompensated hydrogen bonds), most of the molecules orient along the liquid surface, the boundary between the liquid and a hydrophobic may become polarized (become essentially ferroelectric). Practically this amounts to a formation of stable network of hydrogen bonds on the interface.

The solution corresponding to such polarized boundary can be obtained in the very latest "incarnation" of the QUANTUM water model (See the attached figures). The first one demonstrates the density of the liquid starting from the gas phase on the left (model liquid density 0.3) and to the liquid phase (model density 1). The transition between the two phases is similar to that in classical model of van der Waals liquid.

The second graph corresponds to the polarization density (mean dipole moment of a liquid volume). Comparing the two graphs we see that the interface is indeed polarized and the polarization decays quickly into the bulk both of the gas and the liquid phase and, as the detailed calculation shows, contributes to the surface tension coefficient considerably.

In short we observe that depending on the ordering state of the water layer next to a molecular surface the effective surface tension may be different by a large number. Another observation suggests that the water density depletion next to a fully hydrophobic (and thus ordering) surface can be large (up to 30-50%)

## Wednesday, March 11, 2009

### New Quantum Water Model helps find stable ss DNA conformation in solution

ss DNA Molecular dynamics trajectory using the latest Quantum force field helps to find a perfectly stable conformation of the biomolecule in solution. The outcome of the simulation is very reasonable, given the fact that ss DNA (such as telomers) tend indeed to form such loops (see the Figure on the right). The Figure shows the structure of a DNA quadruplex formed by telomere repeats. The conformation of the DNA backbone diverges significantly from the typical helical structure

## Friday, January 23, 2009

### Solvation energy of a large atom cluster: continuous solvation energy test - II

As it has been already stated here, binding energy calculation of a small molecule to a large protein poses a difficult problem: a method for molecular electrostatic energy calculation should work well both for the protein ligand complex, the protein and the ligand at infinite separation. The protein and the complex are large molecules, whereas the ligand is, by definition, small.

Not every computational approach for the solvation energy calculation is fit for the job though. To elucidate the nature of the problems at hand we performed the following model calculation:

- we prepared a spherical "protein" of a large (but realistic) radius

- we placed a single-atom ligand with a charge at a given distance from the "protein" center (see the Figure)

- we calculated the solvation energy of the system as a function of the ligand distance both when the protein is neutral and charged (in the latter case the protein charge is opposite to that of the "ligand")

We used four different methods for the electrostatic contribution to the solvation energy calculation: Poisson equation solver (in its surface electrostatic incarnation, blue) QUANTUM MGB (cyan) and the two "classic" GB methods, based on the Coulomb approximation: HCT (magenta) and AGBNP (yellow).

The first Figure, corresponding to an overall electrically neutral cluster, shows absolute deficiency of HCT approach deep enough inside the "protein". The problem is caused by unrealistic assumptions with regard to the overlap integrals calculations is occurs pretty frequently in realistic proteins. AGBNP method represents one of the latest GB approaches and is practically free of these difficulties. However, AGBNP is based on Coulomb approximation and thus fails to recover correct behavior of the solvation energy close to the "protein" boundary: AGBNP energy is off by a large number from both QMGB and the exact solution. QMGB and Poisson solutions agree very well everywhere!

The last Figure shows the same calculation for a charged model "protein-ligand" complex. Once again, HCT fails entirely, AGBNP does not work properly at the "protein" boundary and both Poisson solver and QMGB agree very well, though QMGB is about one order of magnitude faster than the Poisson solver!

Practically all this means that QMGB represents a fast and accurate approximation to the Poisson equation solution. QMGB approach does not rely on Coulomb approximation and is shown to work both for small molecules and large molecular clusters involving molecules of very different sizes. Therefore, with QMGB one can find a single transferable set of GB parameters capable of describing large and small molecules on the same footing.

Not every computational approach for the solvation energy calculation is fit for the job though. To elucidate the nature of the problems at hand we performed the following model calculation:

- we prepared a spherical "protein" of a large (but realistic) radius

- we placed a single-atom ligand with a charge at a given distance from the "protein" center (see the Figure)

- we calculated the solvation energy of the system as a function of the ligand distance both when the protein is neutral and charged (in the latter case the protein charge is opposite to that of the "ligand")

We used four different methods for the electrostatic contribution to the solvation energy calculation: Poisson equation solver (in its surface electrostatic incarnation, blue) QUANTUM MGB (cyan) and the two "classic" GB methods, based on the Coulomb approximation: HCT (magenta) and AGBNP (yellow).

The first Figure, corresponding to an overall electrically neutral cluster, shows absolute deficiency of HCT approach deep enough inside the "protein". The problem is caused by unrealistic assumptions with regard to the overlap integrals calculations is occurs pretty frequently in realistic proteins. AGBNP method represents one of the latest GB approaches and is practically free of these difficulties. However, AGBNP is based on Coulomb approximation and thus fails to recover correct behavior of the solvation energy close to the "protein" boundary: AGBNP energy is off by a large number from both QMGB and the exact solution. QMGB and Poisson solutions agree very well everywhere!

The last Figure shows the same calculation for a charged model "protein-ligand" complex. Once again, HCT fails entirely, AGBNP does not work properly at the "protein" boundary and both Poisson solver and QMGB agree very well, though QMGB is about one order of magnitude faster than the Poisson solver!

Practically all this means that QMGB represents a fast and accurate approximation to the Poisson equation solution. QMGB approach does not rely on Coulomb approximation and is shown to work both for small molecules and large molecular clusters involving molecules of very different sizes. Therefore, with QMGB one can find a single transferable set of GB parameters capable of describing large and small molecules on the same footing.

Labels:
Generalized Born,
IC50,
polar liquid,
solvation energy

### Solvation energy of a diatomic molecule: continuous solvation energy test - I

Diatomic molecule is the simplest example of a realistic solvation energy calculation. Indeed, any reasonable solvation energy model gives exact value for a single atom.

Depending on the radii of the atoms involved the solvation energy of a pair may be a very good test of a solvation energy model and transferability of its parameters. In what follows we show the results of our Modified GB (MGB) approach for the test system. The graph below represents the solvation energies for similar and opposite charges pairs.

The upper (blue) solid curve represents the atom pair with opposite charges, whereas the lower (red) curve corresponds to the atoms with similar charges. First of all, the behavior of the two energies is easy to understand. At infinite separation both curves saturate at -0.125 (which is the Born solvation energy of the two charges of 0.5 and bare radii 2.). If the total charge is 0 (the opposite charges case, blue curve), at r=0 we have Es=0 as well. If the total charge is 2x0.5=1 (the red curve), then at r=0 we have Es=-0.25, as it should be for a combined charge within the sphere of radius 2.

Although the asymptotic values are OK, this does not mean the whole curve is fine. To compare our approach with true electrostatic we performed the calculation of the model system solving the Poisson equation as well as by two "classic" GB models (that of HCT and AGNP). The results for a diatomic molecule with zero total charge are represented on the last graph.

The electrostatic part of the solvation energy corresponds to the blue curve of the previous graph and is calculated either by a (surface-electrostatic) Poisson equation solver (blue), QUANTUM's MGB (cyan), AGBNP (yellow) and HCT GB model (yellow). As it is clear from here, all the approaches give very similar results for the "small" molecule and are practically indistinguishable. Indeed, it is well known that practically any sort of GB approximation gives good results for solvation energies of small molecules.

The difference between QMGB method and "classic" GB approaches and its relation to the exact solution becomes more obvious if we consider a charged diatomic molecule (a molecular ion with total charge, say, 1 placed on one of the atoms). The exact (blue) and QMGB (cyan), once again, are both in agreement with each other, whereas both "classic" GB approaches, HCT and AGBNP fail to recover correct asymptotic value at zero inter-atomic separation. The latter difference between GB solutions and the exact value of the solvation energy is not important for small molecules (low atom density) but is extremely important for ligand binding calculations (to be explained).

Depending on the radii of the atoms involved the solvation energy of a pair may be a very good test of a solvation energy model and transferability of its parameters. In what follows we show the results of our Modified GB (MGB) approach for the test system. The graph below represents the solvation energies for similar and opposite charges pairs.

The upper (blue) solid curve represents the atom pair with opposite charges, whereas the lower (red) curve corresponds to the atoms with similar charges. First of all, the behavior of the two energies is easy to understand. At infinite separation both curves saturate at -0.125 (which is the Born solvation energy of the two charges of 0.5 and bare radii 2.). If the total charge is 0 (the opposite charges case, blue curve), at r=0 we have Es=0 as well. If the total charge is 2x0.5=1 (the red curve), then at r=0 we have Es=-0.25, as it should be for a combined charge within the sphere of radius 2.

Although the asymptotic values are OK, this does not mean the whole curve is fine. To compare our approach with true electrostatic we performed the calculation of the model system solving the Poisson equation as well as by two "classic" GB models (that of HCT and AGNP). The results for a diatomic molecule with zero total charge are represented on the last graph.

The electrostatic part of the solvation energy corresponds to the blue curve of the previous graph and is calculated either by a (surface-electrostatic) Poisson equation solver (blue), QUANTUM's MGB (cyan), AGBNP (yellow) and HCT GB model (yellow). As it is clear from here, all the approaches give very similar results for the "small" molecule and are practically indistinguishable. Indeed, it is well known that practically any sort of GB approximation gives good results for solvation energies of small molecules.

The difference between QMGB method and "classic" GB approaches and its relation to the exact solution becomes more obvious if we consider a charged diatomic molecule (a molecular ion with total charge, say, 1 placed on one of the atoms). The exact (blue) and QMGB (cyan), once again, are both in agreement with each other, whereas both "classic" GB approaches, HCT and AGBNP fail to recover correct asymptotic value at zero inter-atomic separation. The latter difference between GB solutions and the exact value of the solvation energy is not important for small molecules (low atom density) but is extremely important for ligand binding calculations (to be explained).

Labels:
Generalized Born,
polar liquid,
solvation energy

Subscribe to:
Posts (Atom)