Membrane Multi-Phase Solvation Model
The study of the interaction between biological membranes and drugs or small molecules has an impact on many fields of science and technology. Despite great efforts to theoretically describe such systems, we are far from having a practical model we can use to understand their molecular mechanisms. There are two general approaches one can take. Implicit models are fast, but lack accuracy in the results . Explicit models tend to be more accurate, but can be very expensive .
MMPSM is a compromise between the two. The multi-phase solvation model takes into account the different changes in dielectric properties when going from an aqueous environment (ε=80), passing through the polar head groups of the phospholipids (ε=8), into the hydrophobic interior of the membrane (ε=2), without sacrificing atomic detail. MMPSM is a method that allows studying the membrane-drug interaction from a robust thermodynamic standpoint. One can estimate the solvation and transfer free energy of a small molecule into different solvents, mimicking the pass of the drug through the membrane. The partition coefficient, or logP, can be directly derived.
Phospholipid molecules are characterised by having two regions with distinct electrostatic properties. The polar head group is hydrophilic, the tails are hydrophobic. Because of such composition and structure, they tend to aggregate into bilayers in the presence of water. This arrangement creates two different environments (three if we count the water). These phases are depicted in the diagram as red (water), green (polar), and blue (hydrophobic). Biomolecules will behave differently depending in wich of these phases they are immersed. Moreover, biomolecules have a preference to be in one or the other. For example, a polar molecule, e.g. water, will find it difficult to penetrate the membrane because of the hydrophobic core produced by the phospholipid tails.
In the MMPSM approximation, we do not use an explicit membrane. We represent the different phases found in the membrane with solvents with similar electrostatic properties, without sacrificing atomic detail. Hence, we use the Hexadecane molecule to mimic the interior of the membrane (blue), and the Acetyl-methyl-phosphate (AMP) molecule to mimic the polar region (red). Another coarser description of the membrane can be made if we consider only one phase distinct from the water solution. In this case, we can use the Octanol molecule as the solvent. We call these two strategies M2 (three-phase) and M1 (two-phase), respectively.
In the MMPSM framework, one estimates the solvation free energy, ∆Gsolv, of a solute (drug or small molecule) in different solvents through the Thermodynamic Integration method. Once the ∆Gsolv is known for solvent A and for solvent B, we can estimate the transfer free energy, ∆Gtransf, of moving the solute from one solvent to the other. Depending on the sign and value of ∆Gtransf, the process will be energetically favorable (can happen spontaneously) or not. In general, the partition coefficient, or partition constant, is a parameter that indicates the hydro- or lipophilicity of a molecule, i.e., it indicates the preference of the solute for either a polar or organic solvent. Knowing the transfer free energy value, the partition coefficient can be computed according to the relation, ∆Gtransf = -2.303 RT log P, where R is the gas constant, and T the absolute temperature. Read about the distinction between solvation and solubility .
First you need to build the solute-solvent system. This involves creating a computational box with the solute and then fill it up with the solvent molecules. Download the following files, they contain an equilibrated system of pure solvent:
|M1||Octanol||[ GRO ]|
|M2||AMP||[ GRO ]|
|M2||Hexadecane||[ GRO ]|
Insert the solute in the solvent box; delete the necessary solvent molecules to create a cavity big enough to allocate the solute. You will have a new computational box; solute_solvent.gro. You could also use Gromacs' solvate:
If the solvent is water, we suggest to use the default Simple Point Charge (SPC) model, as provided at the Gromacs distribution, for consistency reasons.
> gmx solvate -cp my_solute.pdb -cs MMPSM/Config/solvent.gro -p MMPSM/FF/topol.top -o MMPSM/Config/solute_solvent.gro
You also need to download the Gromos United Atom force field parameters in order to calculate the intra- and inter-molecular solute-solvent interactions:
|M1||Octanol (OTL)||[ ITP ]|
|M2||AMP (_K8C)||[ ITP ]|
|M2||Hexadecane (_MVT)||[ ITP ]|
For the purpose of testing and validation, we also include the force field parameters of another important organic solvent, Dimethyl sulfoxide (DMSO), and two biologically relevant membrane solutes, Cholesterol and Ergosterol.
>MMPSM /Config -octanol.gro -AMP.gro -hexadecane.gro -water.gro -dmso.gro /FF -octanol.itp -AMP.itp -hexadecane.itp -dmso.itp -cholesterol.itp -ergosterol.itp -topol.top /MD -min.mdp -nvt.mdp -npt.mdp -md.mdp
Edit the file >MMPSM/FF/topol.top and change the name of the solute and solvent, the name of the system, and the number of molecules accordingly. This might not be needed if you used Gromacs' solvate.
Generate a binary run input file (TPR) to minimize, NVT-NPT equilibrate the system, and start the production run of the molecular dynamics simulation, using the corresponding molecular dynamics parameter file (MDP):
> gmx grompp -f MMPSM/MD/min.mdp -c MMPSM/Config/solute_solvent.gro -p MMPSM/FF/topol.top -o MMPSM/MD/em.tpr > gmx mdrun -v -deffnm em > > gmx grompp -f MMPSM/MD/nvt.mdp -c MMPSM/MD/em.gro -p MMPSM/FF/topol.top -o MMPSM/MD/nvt.tpr > gmx mdrun -v -deffnm nvt > > gmx grompp -f MMPSM/MD/npt.mdp -c MMPSM/MD/nvt.gro -p MMPSM/FF/topol.top -o MMPSM/MD/npt.tpr > gmx mdrun -v -deffnm npt > > gmx grompp -f MMPSM/MD/md.mdp -c MMPSM/MD/npt.gro -p MMPSM/FF/topol.top -o MMPSM/MD/md.tpr > gmx mdrun -v -deffnm md >
The solvation free energy, ∆Gsolv, is the work required to transfer a molecule (solute) from vacuo into a solution (solvent). The logic followed to estimate the free energy cost to transfer a solute from solvent A to solvent B, ∆GtransfAB, is similar, however, one of the solvents is taken instead of vacuo. In other words, ∆GtransfAB = ∆GsolvB - ∆GsolvA
It is possible to calculate the difference in free energy between two related states using a coupling parameter, λ, in the Hamiltonian of the system. This leads to the Thermodynamic Integration formulation, in which we evaluate the ensemble average n-times, where n is the number of chosen λ values, by performing a set of independent simulations, one for each of the λ values. At the end, an integral running from the first state to the second state is numerically calculated. The technical details of this procedure can be found on an excellent tutorial by Justin A. Lemkul.
We applied MMPSM to the study of the mechanism of action of one of the most important antimycotic drugs used therapeutically worldwide today; Amphotericin B (AmB). The results proved to advance our understanding of a long-standing controversy. Details can be found in this publication [REF].
MMPSM correctly predicts the behaviour of Cholesterol, main component of the membrane of mammals. The same methodology can be used to study the interaction of the biological membrane with other type of small molecules (drugs, hormones, anaesthetics, peptides, etc.).
Because of the intrinsic approximations of the molecular force fields used in the simulations, this approach is currently limited to give a qualitative rather than quantitative view of the systems studied. We will keep this page updated as further methodological developments are made and improved force fields are available.
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