You can calculate (or even look up in published data) the solubility parameter (either Hildebrand or Hansen) for your solute simply by MD and compare with that of water (just pure states simulation). But as water has hydrogen donor/acceptor sites, a more sophisticated indication of solubility would be interaction parameter (Flory-Huggins equivalent for regular solutions) and for this you need simulation of both pure and mixture systems. Also as others mentioned hydration free energy (free energy of mixing) is a good measure of solubility also (other thermodynamic information can be extracted this way too). For calculation of hydration free energy you need to do thermodynamic integration (GROMACS is good at this) or Umbrella sampling. These slightly complicated. But far from this, you should be concern about force field and partial charges that you are planning to use. Result is highly sensitive to these parameters. I personally suggest GROMOS 53a force field as it has been parametrized to capture experimental hydration free energy of large set of organic materials. Also if you have access to Gaussian, you can calculate the hydration free energy using first principle calculation couple with born implicit solvent model . This works fine for fairly small solutes (conformational sampling problem). If your solute is large (it undergoes conformational changes like several torsion angles which can rotate) especial cares should be taken to sample all possible conformations.

If your give more information about your solute and what you need solubility for, I probably can help more.

Regards

Calculating free energy of solvation may be useful. Using different solvents (polar and nonpolar), you can even calculate partition coefficients.

Yes, you can use the 'Widom (test particle) insertion method' [http://en.wikipedia.org/wiki/Widom_insertion_method] to calculate the solubility like in that paper by Hossein Eslami and Florian Mueller-Plathe [http://guruz.hu/~dezo/Citations/Papers_that_cite_me/Eslami_MM_inpress.pdf].

Hydration free energy, as others here suggested, can be used to qualitatively judge the solubility. However, beware that air-water partition coefficient (i.e. Henry's law constant) is not the same as solubility. For example, Henry's law constant is indirectly determined from vapor pressure and solubility of the molecule.

The following reference may be useful

http://static.msi.umn.edu/rreports/2006/54.pdf

It is a review of several methods used to calculate the solubility of a solute in a solvent expressed in terms of the infinite-dilution limit, where the free energy of hydration is calculated as mentioned here.

You can calculate (or even look up in published data) the solubility parameter (either Hildebrand or Hansen) for your solute simply by MD and compare with that of water (just pure states simulation). But as water has hydrogen donor/acceptor sites, a more sophisticated indication of solubility would be interaction parameter (Flory-Huggins equivalent for regular solutions) and for this you need simulation of both pure and mixture systems. Also as others mentioned hydration free energy (free energy of mixing) is a good measure of solubility also (other thermodynamic information can be extracted this way too). For calculation of hydration free energy you need to do thermodynamic integration (GROMACS is good at this) or Umbrella sampling. These slightly complicated. But far from this, you should be concern about force field and partial charges that you are planning to use. Result is highly sensitive to these parameters. I personally suggest GROMOS 53a force field as it has been parametrized to capture experimental hydration free energy of large set of organic materials. Also if you have access to Gaussian, you can calculate the hydration free energy using first principle calculation couple with born implicit solvent model . This works fine for fairly small solutes (conformational sampling problem). If your solute is large (it undergoes conformational changes like several torsion angles which can rotate) especial cares should be taken to sample all possible conformations.

If your give more information about your solute and what you need solubility for, I probably can help more.

Regards

Yes, you can compute the solubility using Molecular Dynamics. It is probably easier to use Monte Carlo Simulation. Nevertheless if the solubility of the molecule in water is small, and assuming that you know an approppriate model to represent the interactions between water and solute molecules, you can combine water simulation (perhaps using isothermal-isobaric ensemble) with a Widom-like test particle method (either sampling insertion of the molecules into the system or converting water molecules into solute molecules). If the solute molecules are not large compared to water molecules this scheme can work. Some careful thermodynamic analysis is required to relate the simulation results with the thermodynamic definition of solubility.

Using Monte Carlo simulation you can always use a type of semi-grand canonical

ensemble using the variables: pressure, temperature, number of water molecules, and chemical potential of the solute molecules (p,T,N_w,\mu_s); or if the insertions are difficult (p,T,N,\mu_s-\mu_w); where N is the total number of molecules (water + solute) in the system.

A few additions to the above comments:

1) MD with water (by itself or as a solvent) is not easy. Be very careful of every parameter. But it can be done.

2) Step sizes for MD simulation of water need to be less than 1 fs. Calculations even fail with 0.5 fs, though I've achieved stability with 0.5 fs. The step size needs to be 1/10 th of the vibration speed of the molecule. Water molecules vibrate very fast. The consequence of this is that speed of simulations are slower, or you get a short trajectory.

3) I'd strongly discourage use of Hansen Solubility Parameters (HSP) for water. HSP is comprised of three components, dispersion, polar, and hydrogen bonding. The hydrogen bonding of water is so strong compared to other species that results rarely shed any light, let alone give a sense of direction. Infact, one of the conditions at the time of deriving HSP is that this method does not work with highly hydrogen bonded species.

4) Not every Forcefield is able to handle water i.e., not every FF has an explicit term to handle the hydrogen bonding (some FFs like treat hydrogen bonding implicitly in the van der Waals and electrostatic terms). Please check each term of the Forcefield equation. Based on a paper I read from Phillip Choi (University of Alberta), I know that Drieding Forcefield defines hydrogen bonding explicitly.

5) Bottom line -- see point #1 and happy reading and simulating. :))

A.Laaksonen, A.Lyubartsev and F. Mocci "MDynaMix studies of solvation, solubility and permeability" in: " Molecular Dynamics - Studies of Synthetic and Biological Macromolecules, Lichang Wang (Ed.), ISBN: 978-953-51-0444-5, InTech, DOI: 10.5772/35955.