Introduction {#sec1}
============

The link between structure and function in biological molecules is well-established and raises important questions given that proteins are dynamic in the solution phase. This means that having the ability to follow the mechanisms of structural change in real time is imperative if we are to understand and modify protein behavior *in vivo*. Observing protein structural transitions is technologically challenging, however, due to the complexity of the associated macromolecular potential energy surfaces, which are multidimensional in terms of both degrees of structural freedom and the range of time scales over which transitions occur.

Temperature-jump (T-jump) initiation offers a powerful approach to understanding biomolecular dynamics.^[@ref1]−[@ref4]^ T-jump pump--probe methodology exploits infrared wavelength excitation of water to create a fast rise in temperature in an aqueous biomolecular system, followed by a time delayed probe of the evolving system. The probe method employed to study proteins or peptides includes fluorescence,^[@ref5]^ circular dichroism,^[@ref6]^ and infrared spectroscopy.^[@ref3]^ The latter is particularly attractive because of the sensitivity of the amide I vibrational mode of the peptide backbone link to protein secondary structure and local molecular environment.

T-jump methods have been used to access time scales ranging from the nanosecond pulse duration of the excitation laser to the milliseconds required for the temperature-jump to dissipate.^[@ref1]−[@ref4],[@ref6]−[@ref16]^ An alternative strategy employed solvated dyes to achieve a rapid temperature change,^[@ref17]^ while jumps in pH have also been used to study peptide structural transitions.^[@ref18]^ An advantage in using temperature or pH to perturb proteins is the ability to explore their potential energy surface in the absence of structural modifications or non-natural entities.^[@ref19]−[@ref22]^

In the case of protein or peptide systems, T-jump IR methods have largely been applied to short chain peptides, where unfolding time scales are on the order of a few microseconds for typical α-helical and β-turn systems.^[@ref1]−[@ref3],[@ref23]^ More recently, T-jumps combined with vibrational echo probing have been applied to study processes involving larger proteins, including ubiquitin unfolding and insulin dimer formation.^[@ref8],[@ref11],[@ref13],[@ref24]^ It was reported that protein unfolding occurs on two time scales. Hundreds of microsecond dynamics were assigned to the crossing of energetic barriers in response to the elevated temperature, but rapid unfolding processes taking just a few microseconds were also observed and attributed to downhill unfolding, constituting the first steps of the structural rearrangement.^[@ref11]^

We report the use of high pulse repetition rate T-jump pump-IR probe spectroscopy^[@ref25]^ to target the fastest steps in the unfolding of the human calmodulin protein (CaM). CaM is a multifunctional calcium-binding messenger protein found in many eukaryotic cells. At room temperature in solution, the CaM structure is largely conserved across a range of organisms,^[@ref26]−[@ref29]^ consisting of α-helical sections organized into two (C- and N-terminal) globular domains, each containing helix--loop--helix E-F hand motifs ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}a,b, red). Each domain houses a pair of Ca^2+^ ion binding sites. In the absence of Ca^2+^ the two domains are connected by a central linker, which features two α-helices ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}a, orange) joined by a short random coil ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}a, blue). Upon uptake of four Ca^2+^ ions, the random coil element becomes helical leading to the fully extended *holo*-CaM structure ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}b).^[@ref30],[@ref31]^ While the *apo--holo* structural transition is well-understood,^[@ref29],[@ref32]−[@ref44]^ the presence of significant structural plasticity in both states^[@ref31],[@ref35],[@ref45]−[@ref48]^ is believed to contribute to CaM function *in vivo.*([@ref49]−[@ref53])

![Structures of (a) *apo*-CaM and (b) *holo*-CaM showing α-helices (red), β-strands (yellow), flexible central linker (orange and blue), and Ca^2+^ ions (gray). (c, d) IR absorption spectra of *apo*-CaM (c) and *holo*-CaM (d) as a function of temperature. (e, f) Difference IR absorption spectra of *apo*-CaM (e) and *holo*-CaM (f) as a function of temperature relative to the spectrum obtained at 20 °C. The spectra are labeled using the convention of *T*~0~, which indicates the starting temperature of the solution, and Δ*T*, which indicates the size of the temperature increase.](jp9b08870_0001){#fig1}

The application of T-jump methods to CaM will shed important new light on the stability of the structure and the mechanism of unfolding. Recently, we demonstrated that ultrafast IR spectroscopy provides a sensitive probe of the structural changes occurring in CaM, using 2D-IR methods at a range of temperatures to probe the equilibrium structures of *apo*- and *holo*-CaM.^[@ref54]^ Our work showed that CaM exhibits temperature sensitive IR spectra in both *apo* and *holo* states and that the thermodynamically more stable *holo*-CaM can be used to provide a benchmark for changes in solvation of the protein that accompany heating without a structural transition. By contrast, the IR spectrum of *apo*-CaM contains contributions from both changes in solvation and domain melting. These results form the basis of this time-resolved study of CaM unfolding in which a 9 °C T-jump was used to observe *apo*-CaM domain melting, using *holo*-CaM as a reference. With a focus on time scales shorter than 100 μs, our results develop upon the single previous time-resolved study of CaM, which reported two-state unfolding of the C-terminal domain on several hundred microsecond time scales.^[@ref35]^

Results and Discussion {#sec2}
======================

Infrared absorption spectra of *apo*- and *holo*-CaM show that the amide I band of both proteins shifts to a higher wavenumber upon heating ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}c--f). Difference IR absorption spectra relative to the spectrum at 20 °C are shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}e,f. In preparation for discussion of T-jump data below, these are labeled using the convention of *T*~0~, to indicate the starting temperature of the solution, and Δ*T*, to indicate the size of the temperature increase. For T-jump measurements discussed below, Δ*T* will remain constant at 9 °C, while *T*~0~ will vary.

The IR absorption difference spectra ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}e) show that the amide I band of *apo*-CaM undergoes a decrease in intensity at 1636 cm^--1^ and a gain of intensity in a well-defined band centered at 1671 cm^--1^ (blue arrows and gray dashed lines).^[@ref54]^ In the case of *holo*-CaM ([Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}f), a loss of intensity near 1635 cm^--1^ was accompanied by a broad and rather featureless gain in intensity peaking near 1658 cm^--1^ but extending toward 1700 cm^--1^. These results have been assigned previously, with the aid of circular dichroism, differential scanning calorimetry (DSC), and 2D-IR spectroscopy, to the effects of increased temperature of the solvent combined, in the case of *apo*-CaM, with a helix-to-coil transition consistent with C-terminal domain melting at 46 °C.^[@ref54]^

Representative T-jump pump-IR probe spectroscopy results are shown for *apo*-CaM ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}a--c) and *holo*-CaM ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}d--f) at *T*~0~ values of 20, 40, and 60 °C. The design and implementation of the spectrometer were reported recently.^[@ref25]^ The temporal profile of the T-jump was calibrated using the asymmetric carboxylate stretching mode of trifluoroacetic acid (TFA) solutions (see [SI Figures S1--S3](http://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.9b08870/suppl_file/jp9b08870_si_001.pdf)),^[@ref25]^ revealing a 9 °C T-jump within the 4 ns pulse duration of the pump laser that relaxed in a manner well-described by a stretched exponential functionwith a lifetime of τ~1~ ∼ 47 μs and β parameter of 0.54 ([Figure [3](#fig3){ref-type="fig"}](#fig3){ref-type="fig"}, black). In the equation, Δ*A* indicates the measured change in absorbance, τ~pp~ the T-jump-probe delay time, and α the amplitude of the signal. The stretched exponential character originates largely from a heterogeneous temperature-jump distribution across the sample cell caused by absorption of the T-jump pulse by the OD stretching vibration.^[@ref25]^

![T-jump pump-IR probe spectra for *apo*-CaM (a--c) and *holo*-CaM (d--f). Data are shown for three representative values of *T*~0~: 20, 40, and 60 °C in the left, center, and right columns, respectively. Gray spectra show IR absorption difference spectra corresponding to a rise in temperature of 9 °C from *T*~0~ for comparison. (g--i) Double difference spectra showing \[*S*~*apo*~ -- *S~holo~*\] T-jump data for each value of *T*~0~ and T-jump pump-IR probe delay time (τ~pp~).](jp9b08870_0002){#fig2}

![Temporal response of the T-jump as calibrated using a trifluoroacetic acid (TFA) solution (black), see text. This is compared to the results obtained for *apo*-CaM with a *T*~0~ value of 20 °C (red). Results of fitting the temporal dynamics of the TFA T-jump data to a stretched exponential function (see text) are shown as a solid black line.](jp9b08870_0003){#fig3}

At *T*~0~ = 20 °C, the T-jump-IR spectrum of the *apo*-CaM sample ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}a) shows an instantaneous response consisting of a negative peak, indicating a decrease in absorbance, near 1635 cm^--1^ (gray dashed line). This is present from the shortest measured values of τ~pp~ (∼1 ns) ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}, dark red) and is superimposed upon a negative shift in the baseline of the difference spectrum that masks a small, almost flat, positive response to the high wavenumber side of the 1635 cm^--1^ peak. Both the baseline shift and the negative peak relax to zero intensity over a period of 1 ms ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}, green) without any significant evolution in shape.

The response of the *apo*-CaM sample at *T*~0~ = 20 °C is assigned to the result of the T-jump-induced perturbation. This is supported by comparison of the T-jump results with those from IR absorption spectroscopy (solid gray line, [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}a). Applying a Δ*T* of 9 °C to a sample with a *T*~0~ of 20 °C gave an IR absorption difference profile that was almost identical in shape to the T-jump data. Furthermore, the relaxation dynamics of the T-jump spectral features in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}a closely match those of the TFA calibration sample ([Figure [3](#fig3){ref-type="fig"}](#fig3){ref-type="fig"}, red).

For *holo*-CaM at *T*~0~ values of 20 °C, the response to the T-jump ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}d) is almost identical to that of *apo*-CaM ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}a). Raising the starting temperature of the sample to 40 °C leads to differences being observed between the *apo*- and *holo*-CaM samples. While the *holo*-CaM data at *T*~0~ = 40 °C ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}e) closely resembled that at *T*~0~ = 20 °C ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}d), we observe the growth of a new spectral feature in the *T*~0~ = 40 °C *apo*-CaM spectrum ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}b, black dashed oval). This positive peak is most clearly visible in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}b near 1670--1680 cm^--1^ at τ~pp~ values of ∼100 μs, before it relaxes to the baseline by τ~pp~ = 1 ms.

The results at a *T*~0~ value of 60 °C for *apo*-CaM were similar to those at *T*~0~ = 40 °C. Once again, an additional positive feature was present in the *apo*-CaM data ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}c, black dashed oval), though this was smaller than that observed at *T*~0~ = 40 °C, and the peak extended to a slightly higher wavenumber. By contrast, the *T*~0~ = 60 °C *holo*-CaM spectra ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}f) showed little variation from the *T*~0~ = 20 °C result ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}d).

To analyze the T-jump data in more detail, double difference spectra were created by subtracting the response of the *holo*-CaM sample from that of the *apo*-CaM sample, \[*S*~*apo*~*-- S*~*holo*~\], for given values of *T*~0~ and τ~pp~. This approach has twin benefits. First, the response of the solvent is expected to be similar in both cases, and so, its effect is removed from the T-jump data. Second, it has been demonstrated previously that the *holo*-CaM sample does not undergo a melting transition below 80 °C, and so the *holo*-CaM sample acts as a convenient reference for the impact of elevated solvent temperature on the protein amide I band.^[@ref54]^ Thus, any differences in the resultant double difference spectrum, \[*S*~*apo*~*-- S*~*holo*~\], can be confidently assigned to additional temperature-induced processes present in the former protein. The results are shown in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}g--i, where the \[*S*~*apo*~*-- S*~*holo*~\] spectra are shown as a function of τ~pp~ for *T*~0~ values of 20, 40, and 60 °C.

At *T*~0~ = 20 °C, the \[*S*~*apo*~*-- S*~*holo*~\] spectrum shows that there is little variation in the responses of *apo*- and *holo*-CaM ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}g) as would be expected given that the first structural transition occurs at 46 °C.^[@ref54]^ However, at *T*~0~ = 40 °C ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}h) it is clear that *apo*-CaM responds differently to the T-jump than the *holo*-CaM sample. The differences were characterized by fitting to Gaussian line shape functions, revealing negative and positive peaks at 1640 and 1671 cm^--1^, respectively. These are present from early values of τ~pp~ ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}h, dark red), indicating an effectively instantaneous response of *apo*-CaM to the increase in temperature of the solvent, but they subsequently grow in amplitude, peaking at τ~pp~ of ∼10 μs ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}h, orange) before relaxing by τ~pp~ = 1 ms ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}h, dark green). This is the same feature described in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}b,c, but the spectral positions and temporal dependences are more clearly identified following the \[*S*~*apo*~*-- S*~*holo*~\] analysis.

Similar results were obtained at *T*~0~ = 60 °C ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}i), though the negative peak at 1640 cm^--1^ was smaller than that observed at *T*~0~ = 40 °C, while the positive feature at 1675 cm^--1^ (black arrow) was broader with greater contributions at frequencies near 1700 cm^--1^. Once again, the peak in the T-jump double difference spectra \[*S*~*apo*~*-- S*~*holo*~\] occurred at τ~pp~ ∼10 μs, with all features relaxing to the baseline by τ~pp~ = 1 ms.

Prior studies of the temperature dependence of the CaM IR spectrum have shown that melting of the C-terminal domain of CaM is accompanied by spectral density loss at 1636 cm^--1^ and a gain at 1671 cm^--1^.^[@ref54]^ It is thus reasonable to conclude that the differences between the *apo*- and *holo*-CaM T-jump responses stem from domain melting in *apo*-CaM. This is further supported by examination of the amplitude of the \[*S*~*apo*~*-- S*~*holo*~\] double difference feature as a function of *T*~0~. [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}a shows the T-jump double difference spectra obtained at τ~pp~ = 100 μs at a range of *T*~0~ values. It can be seen that the spectral form of the response does not change dramatically with *T*~0~, but the amplitude shows a strong correlation with a previously reported differential scanning calorimetry (DSC) temperature profile of *apo*-CaM ([Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}b).^[@ref54]^ On this basis, the double difference spectral feature is assigned to a helix-to-coil process associated with melting of the C-terminal domain of *apo*-CaM induced by the 9 °C T-jump.

![(a) Double difference \[*S*~*apo*~ -- *S*~*holo*~\] T-jump spectra at a range of *T*~0~ values for τ~pp~ = 100 μs. (b) Comparison of the amplitude of the T-jump double difference response shown in part a (black) with the results of DSC data obtained for *apo*-CaM (red).^[@ref54]^ The *y*-axis label "normalized response" refers to the magnitude of the T-jump double difference \[*S*~*apo*~ -- *S*~*holo*~\] signal at 1640 cm^--1^ (as in part a) and *C*~p~ (μCal/°C) from DSC data. (c) Temporal dependence of the T-jump double difference response \[*S*~*apo*~ -- *S*~*holo*~\] as a function of *T*~0~. (d) Results of fitting the data in part c to a stretched biexponential function (see text).](jp9b08870_0004){#fig4}

For *T*~0~ = 54 and 60 °C, an increased amplitude was observed at higher wavenumber (∼1700 cm^--1^) in the \[*S*~*apo*~*-- S*~*holo*~\] spectrum ([Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}a) and is tentatively assigned to the beginnings of the N-terminal domain melting process expected at 58 °C leading to a more unstructured *apo*-CaM protein and broader amide I signature.

Upon assignment of the T-jump spectra, it is instructive to consider the dynamics observed for the process. The temporal dependence of the \[*S*~*apo*~*-- S*~*holo*~\] double difference feature is shown in [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}c, which plots the magnitude of the α-helix feature near 1640 cm^--1^; the results obtained for the peak-to-peak (1640--1671 cm^--1^) magnitude were in close agreement. It can be seen that the peak is present from early values of τ~pp~, reaches a maximum at around 10 μs, and relaxes by τ~pp~ = 1 ms. Fitting these dynamics to a stretched biexponential function ([Figure S4](http://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.9b08870/suppl_file/jp9b08870_si_001.pdf)) showed that the behavior is well-represented by a rising component with a time scale of ∼5 μs and a decay of ∼40 μs ([Table [1](#tbl1){ref-type="other"}](#tbl1){ref-type="other"} and [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}d). These time scales were largely constant with *T*~0~ ([Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}d), though the longer time scale observed at *T*~0~ = 60 °C was shorter, possibly due to the smaller amplitude of the melting process at an elevated temperature.

###### Results of Fitting \[*S*~*apo*~ -- *S*~*holo*~\] Dynamics to Stretched Double Exponential Function

  *T*~0~ (°C)   τ~1~ (μs)   τ~2~ (μs)   β~1~   β~2~
  ------------- ----------- ----------- ------ ------
  40            5.3         41          0.46   0.36
  44            4.7         38          0.46   0.35
  54            5.8         36          0.53   0.39
  60            4.1         25          0.53   0.35

The longer time scale is very similar to that obtained in the TFA calibration experiments (47 μs) and is therefore assigned to the effects of cooling of the sample following the T-jump. In the current spectrometer configuration, the high T-jump pulse repetition rate (0.5 kHz, [Supporting Information](http://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.9b08870/suppl_file/jp9b08870_si_001.pdf)) provides more rapid data acquisition compared to lower repetition rate experiments, but it also requires the sample to have cooled by τ~pp~ = 2 ms in order to prevent gradual temperature buildup in the sample.^[@ref25]^ To avoid this, a short sample path length (6 μm) was employed, although one impact of this is that the excess temperature dissipates more rapidly than for longer path length samples. The result is that the spectrometer is optimized to observe the faster (\<100 μs) melting dynamics, which complements techniques able to extend the visible window to tens of milliseconds.

The presence of a fast rising component in the \[*S*~*apo*~*-- S*~*holo*~\] signal shows that melting-related processes are occurring in the *apo*-CaM sample on ∼5 μs time scales and that these are not present in the *holo*-CaM data (see also [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}). The time scales involved are comparable to previous observations of helical peptide melting and hairpin unfolding.^[@ref1]−[@ref4]^ While such time scales may seem too fast for domain melting, we stress that the signals observed are small and the observations of these experiments represent the very fastest steps in a domain melting that does not go fully to completion. Justification for this can be found in the much greater magnitude of the IR absorption difference spectral signature, where equilibration at the new elevated temperature is achieved, relative to the T-jump difference spectra ([Figures [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"} and [2](#fig2){ref-type="fig"}). Indeed, the time scales observed in the T-jump melting experiments are comparable with fast steps reported in the melting of ubiquitin, which were assigned to initial "burst phase" or downhill melting of the protein following T-jump perturbation of the potential energy surface for some of the proteins.^[@ref11]^ In those experiments, slower time scale dynamics on hundreds of microsecond time scales were assigned to activated barrier crossing caused by proteins re-equilibrating to the new temperature. In our current study, although the early processes are visible, sample cooling competes with any activated barrier crossing such that the results are dominated by the fast initial phase of the unfolding. This is supported by the lack of a *T*~0~ dependence of the 5 μs unfolding time scale in all except for the *T*~0~ = 20 °C data (where unfolding is not detected).

It is interesting to note that *apo*-CaM unfolding appears to begin with destabilization of α-helical components of the C-terminal domain. In a previous study, the results of molecular dynamics simulations were reported, which showed that the *apo*-CaM protein is significantly more flexible than its *holo* counterpart.^[@ref54]^ Indeed, the most flexible residues were reported to lie between positions 90 and 148 in the C-terminal domain. Although these were largely located in the coil sections between the helical parts of the C-terminal domain, it is reasonable to suggest, on the basis of prior studies of short chain peptides, that helix melting begins at the ends of the short helical sections, which link to the random coil units. Thus, the concept of domain unfolding beginning with fraying of the ends of helical sections would be consistent with both our results and other studies.^[@ref2],[@ref3]^

Concluding Remarks {#sec3}
==================

Comparison with the only other T-jump study of CaM unfolding shows a marked disparity in time scales.^[@ref35]^ An experiment using changes in the absorbance of tyrosine residues in CaM to probe melting observed processes on hundreds of microsecond time scales. As explained above, however, on the basis of this new information these are most likely to be assignable to the activated barrier crossing processes such as those reported for ubiquitin.^[@ref11]^ Thus, by probing the fastest steps in CaM domain melting, our new results complement this prior study to produce an overall picture of CaM domain melting. Taken jointly, these two studies also reinforce the need to observe protein dynamics over as wide a range of time scales as possible to gain a complete molecular picture.

The Supporting Information is available free of charge on the [ACS Publications website](http://pubs.acs.org) at DOI: [10.1021/acs.jpcb.9b08870](http://pubs.acs.org/doi/abs/10.1021/acs.jpcb.9b08870).Details of materials and methods, including calibration of the T-jump spectrometer and additional fitting of dynamic data ([PDF](http://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.9b08870/suppl_file/jp9b08870_si_001.pdf))

Supplementary Material
======================

###### 

jp9b08870_si_001.pdf

The authors declare no competing financial interest.

Funding from STFC is gratefully acknowledged for program access to the Central Laser Facility ULTRA spectrometer. L.M. gratefully acknowledges studentship support from STFC Central Laser Facility and the University of Strathclyde. R.F. gratefully acknowledges studentship support from the University of Strathclyde.
