Characterizing experimental binding isotherms

The protein lysozyme was object of many different protein adsorption studies since it is stable and very well characterized [172, 173]. For this reason, lysozyme appears to be a suitable choice, which was also selected by the experimenters to investigate in detail the adsorbing process on the CSM. In the following paragraphs, we first compare the experimental binding isotherms of lysozyme at different salt concentrations to the Langmuir and CB model, while the adsorption behavior of the other proteins to the CSM are discussed afterwards.

Langmuir model

The evaluation of the ITC data by the standard Langmuir binding model at 7 mM, 17 mM, and 32 mM ionic strength is presented in Figure 4.4 (a). As mentioned before, the Langmuir binding model is very sensitive in the pre-saturation region. The resulting fitting parameters are summarized in Table 4.1. From looking at the fits by eye and judging from the overall least square deviation (LSD) to the ITC data (cf. Table 4.1), all fits look comparably well.

Here, we observe that the number of Langmuir binding sites N_S decreases with increasing ionic strength. The reason isa priori unclear as the Langmuir model assumes a fixed number of binding sites independent of ionic strength. We further notice that the heat of adsorption ΔH_ITC slightly increases with ionic strength. More importantly, K or rather ΔG₀ stays fairly independent of c_s.

Cooperative binding model

The fitting of the same ITC data set by the CB model including the volume change of the CSM is presented in Figure 4.4 (b). The corresponding fitting parameters are listed in Table 4.2. Note again that the initial CSM volume at x = 0 decreases for increasing ionic strengths (see Figure 4.3 (a)). For the data set measured at 17 mM and 32 mM ionic strength no DLS data were available. Thus, V_M is obtained by using the known R_max from Figure 4.3 (a) and x₀ = N_P, while R_min = 129 nm is used from the 7 mM fit. The only free variable Δ is employed as an additional fit parameter obtained by least square fitting to ITC data. We find that Δ appears to be correlated with the change of the sharpness of the binding isotherms N_P with c_s.

Table 4.2: Results of fitting the same ITC data set to the CB model withR_P = 1.9nm and Z_P = +7 e at T = 298K. The change of the CSM volume was considered in the fit according to Eq. (4.35).

c_s ΔH_ITC ΔG₀

[mM] [kJ/mol] [kBT] LSD

7 59.1 -6.3 46

17 62.1 -6.7 38

32 70.1 -6.5 153

Like for the Langmuir binding model, the binding isotherms are described excellent with the CB model according the LSD to the experimental data. The resulting values for the heat ΔH_ITC are also consistent with the Langmuir fits except for the 32 mM data set. This is not surprising, as this value is determined by the plateau in Q(x) for small x, far away from the saturation regime. For that reason, ΔH_ITC = 70.1 _mol^kJ for the 32 mM date set is more reasonable instead of 83.8 _mol^kJ obtained from the Langmuir binding model. The fitting parameterN_P is now directly calculated in the CB model, depending on the packing fraction η and thus on R_P, the effective hard core radius of the protein. The agreement is remarkable and justifies the assumptions leading to the CB model, i.e., the packing picture of globular proteins. A very small salt dependency of ΔG₀ remains, indicating a slightly inaccurate subtraction of the nonspecific effects in this model. However, the salt concen-tration dependency is low and on average we find ΔG₀ −6.5 kBT. This value might be attributed to hydrophobic interactions or possibly other local binding effects. We also note that the effective net charge of chicken egg white lysozyme as used in this experiments may be slightly larger on average due to protonation effects within the CSM [22]. However, using Z_P = +7.5e or+8e for lysozyme in our analysis we end up with a similar ΔG₀ −6.5kBT.

The reason is that while the prefactor in the electrostatic contribution (4.20) rises, the Don-nan potential (4.3) decreases quicker with load. These effects roughly cancel each other for our particular system.

A conspicuous point is the difference in the magnitude of the intrinsic adsorption energy ΔG₀ in both models. At 7 mM ionic strength, we obtain from the Langmuir binding model roughly ΔG₀ −15 kBT and from the CB model ΔG₀ −6.3 kBT. The volume change has a considerable effect on the electrostatic contribution which grows by several kBT (see Section 4.3.3). This trend can be understood by the fact that the monomer charge density c_M = ^N_V^M

M increases with CSM shrinking due to protein adsorption and the contributions in ΔG_elas given by Eq. (4.20) rise. Considering volume changes in charged systems is important for quantitative fitting, especially in those systems where deswelling is significant. In contrast to the standard Langmuir binding model, the nonspecific electrostatic contributions have been consistently separated and the remainingΔG₀ becomes salt concentration independent.

Furthermore, we would like to comment on the magnitude of ΔG₀ −6.5 kBT for the intrinsic interaction of lysozyme with the pNiPAm network. If methane-methane interactions are taken as reference with attractions on the order of 2-3 kBT, then 6.5 kBT correspond to

0

Figure 4.5: (a) Binding isotherms of papain, cytochrome c, and RNAse A onto the CSM at 7 mM ionic strength and T = 298 K. (b) Change of the hydrodynamic radius of the CSM during protein uptake as obtained by DLS measurements. The DLS data are fitted by Eq. (4.35) and used as input in the CB model to fit the binding isotherms.

3 hydrophobic protein-pNiPAm contacts on average which seems reasonable. Increasing the temperature leads to an increase inΔG₀, which is conform with the signature of hydrophobic interactions [174]. A recent study on a similar system showed hardly uptake of lysozyme by an uncharged pNiPAm microgel [30]. Reasons for this discrepancy may be the different batches of CSM which may differ, e.g. in larger pore sizes within the CSM. Alternatively, we overestimate the effects of hydrophobicity and other local effects, such as salt bridges.

Other proteins

In the previous paragraph we have successfully separated the salt-independent intrinsic free energy. This advantage enables us to study the adsorption for other proteins at one single salt concentration.

The single adsorption of papain, cytochrome c, and RNAse A to the CSM at 7 mM ionic strength by ITC demonstrates also a strong binding. The resulting binding isotherms are presented in Figure 4.5 (a), while the corresponding thermodynamic parameters are summa-rized in Table 4.3. The uptake of all proteins by the CSM is endothermic sinceΔH_ITC>0. A particular point is the order of the binding enthalpies. Those are associated apparently with the net charges Z_i, because the magnitude of ΔG₀ is almost same for all proteins. Pa-pain possesses the largest net charge and consequently the largest enthalpy change, followed by cytochrome c and RNAse A. Hence, protein adsorption onto oppositely charged CSM particles is due to electrostatics and essentially determined by the net charge of the proteins.

The ionizable groups on the protein surface play certainly a significant role in the binding process. This is the most likely reason why the swelling state of the CSM is different for all investigated proteins as shown in Figure 4.5 (b). For example, the adsorption of papain lead to a deswelling of roughly 65% of the core-shell particles, while for cytochrome c and RNAse A the effect is less pronounced. This indicates that shrinkage is due to specific bind-ing effects between CSM network monomers and adsorbed proteins. The protein radii R_P

-22 Partial free energies [kBT]

x

(a) (b)

μlys(x) ΔG0,lys ΔG_el,lys(x)

Figure 4.6: (a) Total binding energy ΔG_tot as a function of the molar ratio of the respective proteins at c_s= 7mM andT = 298K. (b) Decomposition of the total binding energy for lysozyme into its contributions;

intrinsic adsorption free energy ΔG_0,lys, electrostatic contribution ΔG_el,lys, and configurational chemical potentialμ_lys

used in this model show a very good agreement with hydrodynamic radii known from litera-ture [175–178]. The same is true for the protein chargeZ_P. The values were calculated from experimentally determined protein crystal structures provided by the Protein Data Bank (PDB) [179] or in case of RNAse A from literature [180]. Table 4.3 summarizes all model parameters. The experimenters observed aggregation in adsorption experiment with papain at molar ratios x >80000 (data not shown). Further experiments with papain were carried out not exceeding x≈80000.