According to polymer science, we know that a condensation polymerization comprises 2 kinds of reactions - linear polymerization and three-dimensional polymerization. The difference between the two reaction types is that the former can lead to the formation of covalently linked one-dimensional polymers, while the latter can lead to the formation of high-dimensional linkage hydrogel. To increase the contact area and the strength of the polymer, we decided to use monomers containing more than 3 functional groups, i.e., the multi-branched monomer Af (f>=3). We attempted to anticipate the gel point specific for the three-dimensional polymerization (TDP) with reaction extent p through Flory Theory and Carothers Theory.
In Flory’s description, the sol becomes a gel when its reaction extent reaches the gel point Pc. For a more direct route from initial experimental parameter configuration to its prediction, the linkage between the initial solution state and final reaction extent (when it reaches stability) must be established. A simple way to do this, with enough qualitative credibility, is to use the concentrations of A and B, together with the dissociation constant Kd (1).
The gel point also limits the obtainable states by confining Pf. Any gelation is not acceptable for the reasons described earlier. In Flory’s theory, the formula used to calculate the gel point is well described. We have therefore derived for our own case (2):
Assuming that the total number of a and b is unchanged, the differences of the propensities towards different kinds of configurations can easily be compared via their respective gel points. Hereby a tetrad SpyTag-SUP and double SpyTag reaction is a different configuration from a triple SpyTag-SUP and triple SpyTag reaction. The corresponding comparison chart is shown in Fig. 1.
— differences between 3A-SUP and 3A-mSA
It has been witnessed that changing the protein attached to the 3A part can notably affect the polymerization reaction. The result could be easily understood based on the corresponding SDS-PAGE picture (Fig. 2).
The figure illustrates the reaction process from 10-120 min after mixing of the reactants 3A and 3B. Both of these pre-experiments were done at 25 centigrade, pH=7.4 and an initial concentration of 1mg/ml for both 3A and 3B. The difference was that in the first group each 3A module was attached to an SUP module while in the second group mSA was substituted for SUP. The red vector in Fig. 3 indicates the passage of time and also a sharp decrease of the relevant band. Briefly, the decreasing band on the left represents 3B (55.4 kDa) and the one on the right represents 3A_mSA (24.2 kDa).
Such differences could be attributed to the effect of steric hindrance. Based on such a presumption, the terms and would change accordingly. Additionally, one of Flory’s assumptions must be reconsidered. That assumption is that all individual representatives of a single type of functional group in the system have the same probability of reacting. We thus developed a new method to deal with the probability terms , which can be expressed simply as “if one of the functional groups on a 3A or 3B monomer has already reacted, then a residual functional group has a lower/higher probability of reacting”. If the lower/higher probability has the format of min (1, Pa_d · Pa), the formula will change into (3):
Hereby a Pa_d larger than 1 indicates a recruiting effect of the first reacted “AB” of 3A on the rest of its functional groups. Conversely, a Pa_d lower than 1 indicates that the first “AB” bond hinders further reaction of functional groups in its immediate vicinity (the reaction of the rest of functional groups on its parent 3A monomer). This new approach has been programmed into the web-calculator “MWCal”. A monomer ratio experiment shows the validity of the formula via weight distribution analysis (Fig. 3).
Based on the experiment shown in Fig. 3, for the monomer functionalized with the SUP module, this ratio ranged from 1:1 to 1:3, and for mSA the ratio ranged from 1:1 to 3:1. The total initial mass concentrations (3A+3B) in the two experiments were set to 1mg/ml. The SDS-PAGE experiments were analyzed via densitometry, whereby each OD value roughly represents the protein mass located in a particular band. Hence we can get a coarse molecular weight distribution line graph with the help of gel analysis tools. Since there is no quantitative access to the mass concentrations from the light absorbance data, the shape and area of each peak (relative intensity) needs to be taken into account.
The bar charts below the line graphs were generated using the software “MWCal”. The blue bar charts have the same vertical values as the yellow bar charts below them, but with logarithmic coordinates, which helps when comparing them with the experimental results. The calculations in Figs. 28(A) and (B) share the following parameters: fa=3, fb=3 and Kd=4.64e-5. The molar concentrations and monomer weights correspond to the experimental facts. The Pa_d and Pb_d values were set to 0.9 and 1.38 for SUP, and 1.5 and 0.8 for mSA, respectively, which optimized the similarity between the relative intensities of the experimental and theoretical peaks, since said values were fitted based on this similarity. It is essential to bear in mind that proper choice of values for these two parameters can produce good similarity over a wide range (1:1 to 1:3) of cases, with 4 to 5 peaks in each case. This indicates the effectiveness of eq. (5).
The experiment shown in Fig. 28(C) is the same as the one in 28(B), while the calculation uses Pa_d=1, Pb_d=1. In other words, Fig. 6 shows the calculation without any correction for the Pa_d and Pb_d terms, from which we can see the limitation of the original eq. (4) (see below).
The result of this fitting work can be rough due to the low accuracy of the line graph. One can nevertheless qualitatively estimate the recruiting or hindering effect of the attached protein from the values of the optimized Pa_d and Pb_d terms. For example, in the SUP experiment, Pa_d=0.9 and Pb_d=1.38 indicate that the SUP protein reduces the likelihood of reaction for the second bond on its 3A monomer, and conversely makes it more likely that any 3B directly linked to this 3A monomer will react with another 3A.
Based on the definition of orthogonality for biological parts, the design of the SpyTag - SpyCatcher pair, which are the structural molecules, should ideally make this hindrance/recruiting effect negligible for any attached protein. In other words, whether it is SUP or mSA, the value Pa_d and Pb_d should remain unchanged. Otherwise, the resulting weight distribution will be uncontrollable, together with any related mechanical traits such as viscosity. We thus planned to optimize the design using Pa_d and Pb_d as index values.
The adsorption capacities of 10μM proteins and hydrogel were measured in TBS buffer against uranyl in equimolar quantities. In very short time, 3A-SUP alone showed an adsorption capacity of up to 87% and cross-linked 3A-SUP+3B could effectively sequester 96% of the total uranyl (Fig. 6).
Furthermore, we measured the adsorption capacities of other kinds of fusion constructs and polymers, such as 4A-SUP (84%), 6A-SUP (87%), 4A-SUP+3B (88%), 6A-SUP+3B (63%) (Fig. 7). All of these were less efficient but they also could sequester at least 60% of the total uranyl. The standard deviations were calculated from triplicate experiments (n=3). These results were promising since different kinds of fusion proteins and protein constructs were able to adsorb uranyl with great efficiency. Among these, 3A-SUP+3B (96%) showed the best adsorption capacity and was consequently used for all further experiments.
We next wondered whether the adsorption capacity of 3A-SUP+3B would increase with an increased protein-uranyl ratio. We thus tested the adsorption capacity of 3A-SUP+3B at different protein-uranyl ratios in TBS buffer. In these experiments, the concentration of uranyl ions was kept at 10μM.
The 3A-SUP+3B hydrogel could sequester 89% and 93% of the total uranyl when the protein to uranyl ratio was one and ten, respectively (Fig.8). The standard deviations were calculated from triplicate experiments
The results thus showed that when the protein-uranyl ratio was increased tenfold, the adsorption rate increased as well. However, the rate of increase was less than 5% and was furthermore not statistically significant.
According to these results, the adsorption rate did not increase significantly when the protein to uranyl ratio was increased to ten. The reason might be that 3A-SUP+3B can sequester almost all of the available uranyl already when the ratio is 1:1, making the increase inconsequential. In conclusion, a protein-uranyl ratio of 1:1 was enough to sequester most uranyl at a concentration of 10μM.
The protein constructs showed a great uranyl adsorption capacity in TBS buffer, therefore we wondered whether they could work just as well in other conditions. We prepared two experimental scenarios simulated real-life pollution, using fresh water from Weiming Lake on campus and artificial seawater, respectively.
At the protein-uranyl ratio of 10:1, 3A-SUP+3B could sequester 93%, 67% and 83% of total uranyl in TBS buffer, fresh water and artificial seawater, respectively (Fig.9). The standard deviations were calculated from triplicate experiments.
When 3A-SUP+3B was used in fresh water, the adsorption capacity dropped sharply. It is possible that carbonate and other species found in the fresh water might have interfered with 3A-SUP+3B and led to the decrease. It is also possible that the proteins are unstable under low-salt conditions, as opposed to the NaCl-rich environments of TBS buffer or artificial seawater.
The adsorption capacity of 3A-SUP+3B against 13nM uranyl was tested at a protein-uranyl ratio of 6000:1, and it was able to sequester 48% and 35% of the total uranyl in TBS buffer and artificial seawater, respectively (Fig. 10). That means that the functional hydrogel can not only adsorb uranyl at high concentrations of uranium pollution, but can also bind uranyl at very low concentrations - as low as 13nM - which equals the uranyl concentration in natural seawater.
Triple SpyTag-SUP (3A-SUP) was able to adsorb uranyl with great efficiency, and the cross-linked product of 3A-SUP+3B showed an even better adsorption capacity. What’s more, 3A-SUP+3B can also perform its function well in contaminated conditions, and can thus be used to detoxify the environment. Furthermore, we confirmed that the biological functional hydrogel could indeed adsorb uranyl ions from seawater, and might even be employed to gather uranium directly from seawater in the future. Thus, our biological functional hydrogel has broad potential application fields.
References:
[1] Lu, Z. et al. A protein engineered to bind uranyl selectively and with femtomolar affinity. Nature chemistry 1856, 236-241 (2014).
[2] Laura, G, et al. UO22+ Uptake by Proteins: Understanding the Binding Features of the Super Uranyl Binding Protein and Design of a Protein with Higher Affinity. J. Am. Chem. Soc 136, 17484−17494 (2014).
