The thermodynamic constraints which best reflect the conditions of many experiments and industrial processing correspond to fixed chemical potentials, pressure and temperature where particle number can fluctuate (from a statistical perspective this is known as the “Grand Canonical Ensemble”), rather than fixed particle number, pressure and temperature, yet most simulation methods in the condensed phase enforce the latter. For instance, many activated processes of relevance to the chemical and pharmaceutical industries occur at constant concentration, e.g. crystallization usually happens at constant supersaturation (Liu et al. 2018, Perego et al. 2015); catalysis usually involves porous materials, where, if diffusion is fast compared to reaction, the appropriate ensemble is the grand canonical. Chemical reactions in solution usually happen at a given concentration of reactants, and many biological processes, to be understood properly, need to be modeled at constant-pH (CpH) (Barroso da Silva and Dias, 2017; Barroso Da Silva and Jönsson, 2009; de Vos et al., 2010; Jönsson et al., 2007; Kirkwood and Shumaker, 1952). The binding free energy of proteins onto nano surfaces such as titanium dioxide, can depend on the local charge on the surface due to the binding, for example, of hydroxyl ions, which in turn depends on the relative concentrations of hydroxyl ions in water and cannot be fully described in systems where particle number cannot fluctuate. Similarly, the binding of antibodies to antigens or nanocarriers (in the context of drug delivery systems) strongly depends on electrostatic effects (Gunner and Baker, 2016; Han et al., 2010; Ivanov et al., 2017; Li et al., 2015; Poveda-Cuevas et al., 2018). These sorts of effects are important for nano-toxicology, food processing, immuno-diagnostics, and drug delivery. Their study through simulation is further complicated when large free energy barriers exist between key metatable states corresponding, for example, to bound and unbound configurations configurations of a ligand to a binding site; or a crystal phase and an amorphous phase; or folded and unfolded protein;or different charge configuration of titratable sites of pH-sensitive proteins in solution (Barroso da Silva and MacKernan, 2017; Barroso da Silva et al., 2019, p. 6; Barroso Da Silva and Jönsson, 2009; Jönsson et al., 2007).
In recent years there have been many developments on methods to study rare events, but these methods usually rely on biasing molecular dynamics with fixed particle number, and are difficult to adapt to ensembles where numbers of particles fluctuate.
Recently, some emerging approaches have tackled the question of modeling rare events at constant chemical potential, for example using the String Method in Collective Variables in the osmotic ensemble to model crystal nucleation at constant supersaturation, but these approaches are still in their infancy. There is a clear need to further develop these approaches and come up with new ideas to study rare events in open systems. In a similar way, the modeling of pH-related processes has been attracting scientific interests, and nowadays a diversity of CpH methods and protocols are available from DFT molecular dynamics to coarse-grained Monte Carlo simulations (Baptista et al., 2002; Bennett et al., 2013; Srivastava et al., 2017). Indeed a key difficulty for many CpH methods of macromolecules with explicit solvents is the presence of very high free energy barriers existing between different charge configurations...
Given the importance of open systems including CpH to industrial processing, and at the same time, the fundamental questions these pose to rare-event methods, the current proposal envisages a combined E-CAM industry scoping and research workshop.
The objectives of this meeting are: (i) provide industry participants a summary of the state of the art simulation and rare-event methods at fixed chemical potential; (ii) provide academic research scientists a perspective of the key challenges in this context that industry faced. (iii) allow for a fundamental review of the statistical foundations of rare-event methods in the context of fixed chemical potentials; (iv) determine the means by which corresponding simulations in the condensed phase can be practically implemented using or adapting popular community simulation engines such as LAMMPS, Gromacs or NAMD, and free energy software such as PLUMED. The possibility of also implementing such methods for ab-initio molecular dynamics will also be assessed.