Difference between revisions of "Template:Team:Groningen/CONTENT/ARTICLES/Modeling poly-gamma-glutamic acid as a cation exchange membrane"

Some bacteria naturally have the first property. In this case they usually form a biofilm, which is an aggregate of bacteria in the slime they produce. One example of such a bacteria is the wild type Bacillus subtilis. While this bacteria makes a biofilm, our experiments show that this biofilm is not robust enough to withstand being in water for an extended period. In addition for the time that the biofilm is still intact it does not function as an ion exchange membrane.

Now, if one wants to add or improve the desirable properties to the biofilm, it is required to understand how the biofilm works. After all if one does not, then it is hard (if not impossible) to make a decent hypothesis to base the experiments in the lab on. What makes understanding the biofilm hard is that the exact composition of the the biofilm is not known, since it depends on the Bacillus Subtilis strain, what genes are expressed, how the bacteria specialize and how heterogeneous the biofilm is.<a href="#reps" class="cite">1</a> In addition, some genes related to the production of the biofilm are not well understood. While some are known to be responsible for the production of extracellular polymers, the length of the polymers in the biofilm varies a lot. This varying length makes characterization of these polymers hard.

While studying the literature on Bacillus Subtilis biofilms we found that poly-γ-glutamic acid (PGA) might help us with both properties. It helps B. Subtilis stick together, because PGA helps with the underwater growth.<a href="#runw" class="cite">2</a> This happens probably by increasing the number of sites available for salt bridges. It may also help the aggregation of B. Subtilis, because PGA forms aggregates even in dilute solutions.<a href="#rdilsol" class="cite">3</a> Poly-γ-glutamic acid may also form an obstacle for some ions, because is has a high number of fixed charges (as can been seen in its structure as shown in Figure <a href="#pgachem">1</a>). With a model of PGA one could gain insight in how it aggregates and how it could improve ion conductivity. Naturally there are multiple ways to approach modeling, usually though one takes a top-down approach or a bottom-up approach.

When using the top-down approach, the models are usually based on the biomass, individuals (bacteria) or particles. These are useful to study the detachment, mass transfer and species distributions in biofilms, but fail when they are applied in bigger systems like whole reactors.<a href="#rbiomod" class="cite">4</a><a href="#rbiomod2" class="cite">5</a> Furthermore, many parameters required for such models are hard to gather experimentally. Since this project is concerned with a complete system like a reverse electrodialysis cell and the electrostatic interactions, which are not included, this type of model would not be a good fit. While there are models for the growth of the biofilm, there are also models about the ion permeability of membranes. These models give good results with materials that have known geometries, but are less reliable for materials with pore sizes that are small relative to the Debye length or if the materials in question are heterogeneous.

Our model is based on the the bottom-up approach. Since poly-γ-glutamic acid was identified as a molecule that might have a positive contribution to our modified biofilm, the properties of this polymer were modeled. With molecular dynamics one is able to model the interactions between molecules and atoms. Thus molecular dynamics is able to simulate the interactions between the PGA molecules and to simulate the interaction of PGA with ions. Unfortunately, these simulations take a lot of time and computational power. Luckily it is possible to reduce the time needed by using the MARTINI coarse grained force field due to Marrink et al.<a href="#rmartini" class="cite">6</a> While ion exchange membranes and proton exchange membranes have been studied using molecular dynamics before, this has never been done using MARTINI, and certainly not for poly-γ-glutamic acid.<a href="#rnafion" class="cite">7</a><a href="#rproton" class="cite">8</a>

An introduction to molecular dynamics can be found in the supporting material, as well as some additional information on the creation of the protocols in the methods. In the methods section (<a href="#smethods">link</a>) protocols are detailed for the parameterize poly-γ-glutamic acid, the aggregation molecules, the membrane formation and the reverse electrodialysis cell simulations. In the results section we will report our findings and discuss them, and we will also mention possible future work. In the appendix an overview is given of the specific tools and scripts we have written to create, modify or analyse topologies and trajectories.

The modeling of poly-γ-glutamic acid consisted of the carrying out the following steps in order: parameterization of PGA, aggregation of PGA, membrane formation and ion flow simulations with PGA, cellulose and cellulose phosphate. Our main efforts in the parameterization of poly-γ-glutamic acid were focussed on the bonded parameters. Interactions are bonded if they are part of a bond, an angle or a dihedral. Note that this property is not transitive.

The final parameters for bonded interactions of PGA in the coarse grained model can be seen in Table <a href="#tparam">1</a>, while corresponding mapping can be seen in Figure <a href="#fmbeads">2</a>. The bead types were chosen based on expected interaction strength. However changing the bead types of the backbone of the monomer did not have any effect on the end-to-end distance, bond and angle distributions(data not shown). In addition the shape of the bond distributions is similar but shifted, since the average bond lengths are a little bit higher in the coarse grained case (data not shown).

The angle distributions are shown in Figure <a href="#fangles">3</a>. The fit is not perfect, but it should be sufficient. Changing the force constants of the angles did not affect the distributions much, except if the constants were changed to a big value like 500 kJ/mol. However if the angle force constants are this big, then the distributions are too narrow. The distribution of the end-to-end distances, as can be seen in Figure <a href="#fe2e">4</a>, are comparable with each other. The only differences are that the the peak around 0.9 nm in the coarse grained graph is more distinct than in the all atomic one. Furthermore, the distribution is narrower. The latter difference together with the angle distributions indicates that either the interactions between beads are too strong or the interactions of the backbone with the water is too weak. To fix this one would have to change the nonbonded interactions of the beads in PGA.

Next, if multiple molecules are simulated together, they aggregate (as shown in Movie <a href="#movaggr">1</a>). As can be seen in the movie a shell of sodium ions forms around the polymers and some ions stay in position for a while. If the recidency time is high enough, then this is counterion condensation. This phenomenon is usually observed if the coulomb interactions are stronger than the thermal interactions.

From an aggregate membranes were made and the water-holding capacity of the membrane made of poly-γ-glutamic acid was compared with values found in literature.<a href="#rwhc" class="cite">9</a> As can be seen in Figure <a href="#fcross">5</a> the amount of water for PGA is approximately in agreement with the expected water-holding capacity of 56.9%. This property was not checked for cellulose and cellulose phosphate membranes. Comparing the other two cross sections with PGA one can see that the PGA membrane contains more water than one from cellulose, but less than one from cellulose phosphate.

Finally simulations were prepared with two membranes consisting of a single type of molecule. A typical example of this kind of system can be seen in Movie <a href="#movboxrot">2</a>. The concentrations in the simulations are equal to the concentrations used in the lab. In Movies <a href="#movpga">3</a>, <a href="#movcel">4</a> and <a href="#movcelp">5</a> the first 50 ns of the simulations are shown. These simulations show what kind of influence the fixed charges have on the ion conductivity. Based on these movies the sodium ions seem to be able to hop between the charge groups and move through the counterion shells in the membrane to the fresh water.

While the effectiveness of PGA can be compared based on these videos, it is hard to make definitive statements about the flow rate of ions. Therefore we also calculated the net number of ions moving from salt water to fresh water and vice versa and then normalized the resulting value over the total number of the respective ions. The result can be seen in Figure <a href="#fnaclw">6</a>. As is shown PGA and cellulose phosphate let only sodium ions through while blocking the chloride ions. The cellulose allows both sodium and chloride ions to pass through. Another noteworthy thing is that in the beginning the PGA lets through the sodium at the same rate as cellulose. It is unclear if this is so because of the different charge, pore size or width in comparison with cellulose phosphate. In the figure the water flow is also shown. The graphs show that the water moves from the fresh water to the salt water. The main reason for this effect is that the water has to fill the space left by the ions moving from salt to fresh water.

Before these results can be taken as granted, some points have to be addressed. Firstly, since the electrostatic interactions are not well represented in MARTINI, the ion flow simulations should be validated by backmapping the system to an all atom model and simulating the result. This would give insight in how well the MARTINI CG force field works for this type of simulation, since the interactions between the ions and the membrane is more accurate in the all atom simulation.

Secondly, since the properties of the poly-γ-glutamic acid model do not fit the ones calculated from the all atomic simulations and experimental data, it would be nice if the parameterization is improved. For example the non-bonded interaction parameters could be investigated, since they also play an important role in the molecular behavior and were neglected in our parameterization.

Thirdly, the influence of charges in the membrane is not clear, since different charge configurations were not investigated. It might be that only charges at the surface of the membrane are important, or maybe denser or stronger charges improve the flux and/or selectivity.

Fourthly, the results of aggregation were not thoroughly checked. The length of the simulated polymers is rather small in comparison with the length of polymers used in experiments, which could lead the simulated molecules to exhibit different behavior. For example materials can behave quite differently at a nanoscopic scale then at a mesoscopic scale, because at mesoscopic scale the properties of the material is mainly defined by the properties of the aggregate rather than on the properties of single molecules. Therefore the aggregate of PGA should be checked for the properties it exhibits at mesoscopic scale.

Lastly, while poly-γ-glutamic acid is a promising substance, others might also provide the same benefits. Based on the result that charges in the molecule are important, one could come up with a few other molecules to build a membrane with. One interesting option would be polyacrylic acid, since it has a higher charge density than PGA. Or maybe one could try to make a AEM instead by using ε-polylysine, because its structure is similar to PGA but with positive functional groups.

Extended explanations for the chosen methodology can be found in the supplementary material.

The parameterization of poly-γ-glutamic acid is based on the general procedure to parameterize a new molecule in MARTINI. In essence the following steps are performed:

The timestep used in these simulations was 40 fs in the case of the MARTINI CG force field and 20 fs for the all atomic simulation. These simulations ran for 40 ns and 45 ns respectively. The correctness of the fit was based on the distributions of the angles, bonds and end-to-end distance.

The parameters for the monomer of cellulose is taken from the paper due López et al.<a href="#rmartcarbo" class="cite">10</a> Like they did for the hexamer of amylose, the topology of the monomer of cellulose was extended by adding bonds, angles and dihedrals. The angle over the backbone is based on the paper on cellulose fibers, while the other extensions are based on the similarities in the cellulose monomer.<a href="#rmartcellfiber" class="cite">11</a> The parameter extensions are given in Table <a href="#tcelparam">2</a>. The timestep used in all cellulose simulations was 20 fs.

The definition of cellulose phosphate is based on the definition of cellulose. The main difference is that the bead type of bead B1 and B5 are changed to Qa with a charge of -2. All simulations with cellulose phosphate use a timestep of 20 fs.

For aggregation a box size of 10 nm x 10 nm x 10nm is used, except for cellulose phosphate the box was 15 nm wide in the z axis direction. In such a box 35 molecules with 20 monomers (including terminals) are placed. The general procedure is as follows:

The procedure to make the membranes is as follows:

For this last phase a semiisotropic pressure coupling type is used instead an isotropic type. The procedure is as follows: