The volume occupancy of p-NIPAm-co-AAc solutions defines the degree of crowding. Using a hydrodynamic radius of 312 nm and a molecular weight of 1 GDa, the microgel in a 10 g/L solution occupies ~70% of the solution volume at pH 5.4 and 37°C (the conditions used in our experiments). The practical limit of spherical packing is 64% volume occupancy [15], but soft materials such as microgels can be "overpacked" [16]. Our solutions, however, were still in the liquid state, meaning our value for volume occupancy is likely an overestimate. The high value does, however, suggest that experimental conditions were within the realm of crowding, as other systems show crowding effects at less than 20% volume occupancy [17, 18].
Although the microgel slowed exchange (Figure 3), it was necessary to perform control experiments to ensure that stability values could be obtained under both sets of conditions. First, we confirmed that amide proton exchange from the open state (k
int
, Scheme 1) is rate limiting. Under this condition, pairs of proximal amide protons, A and B, open with the same frequency, but with different k
int
values. That is, amide proton exchanges for A and B are uncorrelated. By observing the decay of an amide-amide NOESY crosspeak corresponding to a resonance coupling between A and B, it is possible to determine whether their exchange is correlated or uncorrelated. If the exchange is uncorrelated, the decay curve of the amide-amide crosspeak should equal the product of the individual amide proton decay curves [19, 20],
In this instance, the overall exchange rate of the amide-amide crosspeak will correspond to the sum of the individual exchange rate constants,
All these rates can be assessed from a series of 15N-filtered 1H-1H NOESY spectra acquired under exchange conditions [10].
As shown in Table 1, the exchange rates observed for the amide-amide crosspeaks for CI2 in both dilute solution and in 10 g/L p-NIPAm-co-AAc are, within the uncertainty of the experiment, the sums of their respective individual exchange rates, indicating that the exchanges are uncorrelated. We conclude that exchange from the open state is rate limiting, allowing determination of stability from amide proton exchange rates.
Second, we must determine if the microgel changes k
int
from the values determined in dilute solution. The dilute solution value for each residue is calculated by using the computer program, SPHERE [14] (http://www.fccc.edu/research/labs/roder/sphere/). The program uses values from the exchange of free peptides [21], and relies solely on the primary structure of the test protein. We assessed whether k
int
is affected by adding p-NIPAm-co-AAc by using the CLEANEX-PM experiment [13]. We measured the exchange rate of the His37 amide proton, which is fully exposed in the flexible loop region of CI2 (residues 35-44). The data indicated that the intrinsic rate of exchange in 10 g/L p-NIPAm-co-AAc (8 ± 2 s-1) is within uncertainty of the value in dilute solution (11 ± 2 s-1). These results suggest that k
int
values can be used without alteration. Having shown that it is valid to use k
obs
and k
int
values to obtain opening free energies, we constructed histograms of ΔG0*
op
values versus residue number (Figure 4).
Dynamics and Stability
Crowding involves two different types of effects on protein stability: volume exclusion and chemical interactions. Volume exclusion is expected to stabilize protein native states, whereas chemical interactions can be stabilizing or destabilizing [6]. Attractive chemical interactions are expected to impede rotational dynamics, and the microgel used here is known to have favorable electrostatic interactions with proteins at low ionic strength [22]. Our data were collected at pH 5.4, where the microgel is negatively charged. The truncated form of CI2 we use has an isoelectric point (pI) of 6. Therefore, the polymer and CI2 are oppositely charged, and one might expect an attractive interaction.
Our observation that the order parameters (S2), the timescale of internal motion (τ
e
), and the rotational correlation time (τ
m
), are unchanged by the polymer indicates the absence of significant chemical interactions between the polymer and CI2. The lack of interaction probably arises because we used an ionic strength of 50 mM, which minimizes binding [22]. Therefore, we only consider contributions from volume exclusion effects.
The patterns of ΔG0*
op
values along the amino acid sequence (Figure 4) are the same in dilute solution as they are in the microgel solution, suggesting that the microgel does not alter the open states of CI2. The ΔG0*
op
values in the microgel are uniformly larger than the values for dilute solution, indicating the polymer stabilizes the protein with a maximal stability increase of approximately 0.4 kcal/mol. Averaging the ΔG0*
op
values from residues known to be implicated in global unfolding [20] show that the microgel increases the overall stability from 4.9 kcal/mol to 5.2 kcal/mol. We cannot state with certainty that the increased stability arises from the polymeric nature of the microgel because its crosslinked nature makes determination of a suitable monomer unit difficult.
Considering the volume fraction estimate of ~70%, a 0.3 kcal/mol stability increase is quite small. A modest increase is anticipated, however, because the hydrodynamic radius of CI2 is only 1% that of the p-NIPAm-co-AAc microgels (Figure 5). In such a system, CI2 can occupy interstitial spaces between p-NIPAm-co-AAc microgels, putting CI2 in a dilute solution environment. Alternatively, the microgel particles probably have pores large enough to accommodate CI2 and water.
Next, we try to relate the stability change to the backbone dynamics data (Figure 2). The data indicate that the increased stability does not alter the ps-ns backbone dynamics. It has been proposed that stability changes are associated with alterations of ps-ns backbone dynamics [23, 24]. Our results do not indicate a connection, because we observe increased stability without a change in ps-ns timescale dynamics. The most straightforward conclusion is that stability is not linked to backbone ps-ns dynamics. It is possible, however, that stability is reflected in slower (ms-s) motions [25].