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* Biophysical Engineering Lab, Institute for Medicine and Engineering, and School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania;
Structural Biology Program, The Wistar Institute, Philadelphia, Pennsylvania; and
Department of Physics, Drexel University, Philadelphia, Pennsylvania
Correspondence: Address reprint requests to Dennis E. Discher, Biophysical Engineering Lab., Department of Chemical and Biomolecular Engineering, 112 Towne Building, University of Pennsylvania, Philadelphia, PA 19104-6315. Tel.: 215-898-4809; Fax: 215-573-6334; E-mail: discher{at}seas.upenn.edu.
| ABSTRACT |
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-actinin homolog. The major unfolding length corresponds to unfolding of a single repeat, and a minor peak at twice the length corresponds to tandem repeats. Increasing temperature shows fewer tandem events but has no effect on unfolding intervals. As T approaches Tm, however, mean unfolding forces in atomic force microscopy also decrease; and circular dichroism studies demonstrate a nearly proportional decrease of helical content in solution. The results imply a thermal softening of a helical linker between repeats which otherwise propagates a helix-to-coil transition to adjacent repeats. In sum, structural changes with temperature correlate with both single-molecule unfolding forces and shifts in unfolding pathways. | INTRODUCTION |
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-helical proteins such as spectrin show helical fraying and fragmented unfolding at high temperature in contrast to forced stretching where helix unwinding is described as cooperative in its propagation. A major qualification on such simulation predictions is that they lack any collective hydrodynamics and are performed at rates, and therefore forces, that are orders-of-magnitude greater than experimental rates of heating or extension (Evans, 2001
How forced unfolding is influenced by temperature, especially as the transition temperature of a protein is approached, is the focus of the AFM studies here on ß-spectrin. We show that cooperativity indeed decreases with temperature as pathways of unfolding shift for the first four i.e., ß14, (of 17) tandem repeats studied here. We also show that unfolding forces decrease in almost direct proportion to loss of helix in the folded state of each three-helix repeat at a given temperature. Similar temperature studies of DNA stretching have already shown that the force needed to alter interstrand interactions and drive a transition from B-DNA to S-DNA (S for stretched) decreases nonlinearly with temperature (Clausen-Schaumann et al., 2000
; Williams et al., 2001
). Moreover, the transition force F is most simply approximated by the known temperature-dependent basepairing
G(T) divided by the molecular-scale gain in length per basepair (x = 0.24 nm) during the DNA transition, i.e., F(T)
G(T)/x. Whether simple relations between rupture forces and energy increments also apply to forced unfolding of a protein domain is one motivation for the work here.
Among protein, spectrin is highly suited for temperature studies because its three-helix repeats display relatively low and accessible (by AFM) midtransition or "melting" (MacDonald and Pozharski, 2001
) temperatures, Tm. With intact erythrocyte spectrin composed of both
- and ß- chains, transitions have been reported at temperatures close to 40°C (Minetti et al., 1986
; Grimaldi et al., 1989
), whereas the Tm of various short constructs of
-spectrin have been reported to be near 50°C (DeSilva et al., 1997
; Menhart et al., 1996
; MacDonald and Pozharski, 2001
). Melting is thus close to 37°C and therefore potentially relevant to spectrin pathophysiology (Zhang et al., 2001
).
Forced extension of various native spectrin family proteins off various substrates has already shown that the characteristic three-helix repeats can unfold independently and at much lower forces compared to most ß-sheet proteins studied at similar extension rates (Rief et al., 1999
). Tandem repeat unfolding (Fig. 1 A) occurs frequently with the four-repeat erythroid ß-spectrin construct here as well as with ß13 and ß12 truncations (Law et al., 2003
). Perhaps surprising, these tandem repeat unfolding events occur at the same level of average force as the single repeat unfolding events. Partial unfolding events shorter than a single repeat have also been reported to occur with a flexibly linked concatemer of a chicken brain
-spectrin repeat (Lenne et al., 2000
; Altmann et al., 2002
) upon initial extensionwhere proximity to the substrate can complicate analyses. Partial unfolding is not seen with the present erythroid ß14 protein in thorough ensemble-scale studies (Law et al., 2003
). Tandem events that do occur with ß12 spectrin constructs in the latter work have suggested, in particular, that cooperative propagation of tandem unfolding occurs via a helix-to-coil transition through inter-repeat helical linkers. Inter-repeat helices are indeed believed to be present a significant fraction of the time in these ß-spectrin constructs due to their high homology (Ursitti et al., 1996
) to
-actinin, for which a crystal structure shows four repeats interconnected by three contiguous helical linkers (Ylanne et al., 2001
). A helical linker is also seen in crystal structures of a tandem repeat of chicken brain
-spectrin (Grum et al., 1999
). However, nuclear magnetic resonance studies of at least one erythroid
-spectrin construct in solution (Park et al., 2000
) also offer some evidence that the inter-repeat linker can be disordered. Whereas AFM results for the flexibly linked concatemers of Lenne et al. (2000)
reportedly show no evidence of tandem repeat unfolding, a roughly similar proportion of single and tandem unfolding events were reported for ß14 in Law et al. (2003)
. This suggests that the linker between repeats is sometimes helical and sometimes unstructured at room temperature.
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| MATERIALS AND METHODS |
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Dynamic force spectroscopy
Two AFMs were used with similar results: 1), a Nanoscope IIIa Multimode AFM (Digital Instruments, Santa Barbara, CA) equipped with a liquid cell; and 2), an Epi-Force Probe (Asylum Research, Santa Barbara, CA). Sharpened silicon nitride (Si3N4) cantilevers (Park Scientific, Sunnyvale, CA) of nominal spring constant kC = 10 pN/nm were commonly used, with equivalent results obtained using 30-pN/nm cantilevers. kC was measured for each cantilever using the manufacturer's directions at each temperature, and additional calibrations were performed as described previously (Carl et al., 2001
). Temperatures in the range used seemed to have little effect on the kC and this was confirmed with the Digital Instruments equipment. Experiments were done at imposed displacement rates of 1 nm/ms. For the high temperature experiments, samples were first studied at 23°C, and the temperature was then raised. These experiments were challenging due to the propensity of the bilayered (gold and silicon nitride) cantilever to bend. The laser had to be realigned each time after raising the temperature to 37 and 42°C, and only the rare cantilever that yielded a high laser sum and low data noise was used. Temperatures >42°C caused the cantilever to bend so much that the laser would not deflect off the tip. Low temperature experiments (10°C) were done inside a cold room. The desired temperatures for both high and low temperature studies were controlled and monitored using the Nanoscope Heater Controller (Digital Instruments). For any one temperature, thousands of surface-to-tip contacts were collected and later analyzed with the aid of a semiautomated, visual analysis program custom-written in C++. Since protein unfolding events are stochastic and the experiment intrinsically random in many ways, collecting and analyzing thousands of peaks is necessary to provide an accurate statistical survey of the unfolding possibilities. Initial results at the beginning of an experiment lasting many hours were similar to those obtained at the end of the experiment. Nearly all of the data was thus analyzed.
Circular dichroism measurements
Circular dichroism spectra were measured at a number of temperatures using a 1-mm pathlength cell on a J715 spectropolarimeter (Jasco, Easton, MD) in the same buffer (PBS, pH 7.4) as that used in AFM experiments. The instrument was calibrated with d-10-camphorsulfonic acid. Samples were equilibrated at each temperature for 20 min before taking measurements.
| RESULTS AND DISCUSSION |
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2. These correspond to tandem repeat unfolding as events elaborated further below. Regardless, the maximum number of peaks per force-extension curve for this four-repeat spectrin construct is no more than six, as reported earlier for our room temperature studies (Law et al., 2003The exponentially increasing portions of the asymmetric force-extension curves are fit well by the wormlike chain (WLC) model for entropic elasticity and correspond, as is typical in such experiments, to extension of an unfolded domain up to the point where another (hitherto folded) domain in the chain unfolds. The last spectrogram in Fig. 1 B illustrates how a four-peak spectrogram is analyzed. The first peak and the height of the last peak are ignored in the analyses as desorption events, and peak forces and peak-to-peak (lpk-pk) lengths were analyzed as illustrated. The total unfolding length is the sum of all the lpk-pk values, and this sum is found to never exceed the molecule's total contour length (Table 1).
Tandem repeat unfolding events are cumulated in the lpk-pk histograms of Fig. 2 A for the extremes in temperature studied, 10°C and 42°C. Both histograms appear bimodal with principal means differing by a factor of 2.0 (within 5%) per earlier measurements at 23°C (Law et al., 2003
). The major peaks in the distributions are fit with sums of Gaussians that reflect proportional contour lengths for each repeat as listed in Table 1; the minor peaks are likewise fit but with contour lengths of tandem repeats. The 10°C distribution clearly shows a more distinct and prominent tandem repeat peak at 4144 nm compared to that for 42°C or any of the other intermediate temperatures studied. This indicates that tandem unfolding events are more frequent and energetically favored at lower temperatures.
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20% at 42°C. The dashed line in this same figure illustrates the reversible effect of cooling the sample back down to 23°C from 42°C and repeating the collection of unfolding spectrograms. The result demonstrates the reversible reproducibility of temperature effects in AFM.
Although temperature has no significant effect on the unfolding lengths (Fig. 2 B), it does have a dramatic effect on the unfolding forces as T approaches Tm. Unfolding force histograms were fitted with two Gaussians of the same width (Fig. 3 A), where the second, minor Gaussian at nearly twice the force reflects the extension of two molecules or a loop (Law et al., 2003
). Mean forces for the major peaks (and their variances) at 10°C and 23°C are statistically the same 2122 pN (Fig. 3 B), which is in close agreement with previous measurements on this and related spectrin constructs (Rief et al., 1999
; Law et al., 2003
). However, the average force is seen to decrease significantly and nonlinearly with temperature to 16 pN at 37°C and to 11 pN at 42°C. The force that drives DNA's B-S transition is also found to decrease nonlinearly with temperature (Clausen-Schaumann et al., 2000
; Williams et al., 2001
), although the approach to Tm seems far less sharp compared to here. The change in force is nonetheless reversible (Fig. 3 B, dashed line) as reported above (Fig. 2 C) for the tandem event frequency.
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-helical structure is halfway to baseline at Tm
43°C (Fig. 3 C). By 50°C, CD shows ß14 spectrin has lost most of its helix content in a complete helix-to-coil transition. Such nonlinear changes are consistent with results of others near 40°C or slightly higher (Minetti et al., 1986
9% (dotted line in Fig. 3 C). This is probably because aggregation of thermally unfolded protein in solution inhibits proper refolding. In contrast, the AFM experiments are performed on surface immobilized proteins that clearly limit diffusion and aggregation. With AFM, however, higher temperatures are not easily attained due to severe bending of the soft cantilevers needed.
The AFM and CD measurements here show that increasing temperature yields nonlinear reductions in the respective force and percentage of initial helix. Fig. 4 shows that the relationship between normalized changes in average force versus helix content deviates only slightly from a line (using physiological 37°C as a reference temperature). Fig. 4 also plots the percentage change in tandem events versus the percentage of initial helix, and indicates a similar correlation as the force except at low temperature: from 10°C to 23°C, a few-percent helix is lost in heating but the frequency of tandem events decreases substantially more. This indicates, we propose, that a small helical linker (
1015 residues) seen in various crystal structures of related spectrin family proteins (e.g., Grum et al., 1999
) is melting earliest, and its loss buffers against helix-to-coil transitions that cooperatively propagate unfolding from a single repeat to a tandem pair. A helical linker here is also implicated by the fact that AFM results for flexibly linked concatemers of spectrin repeats (Lenne et al., 2000
) show no evidence of tandem repeat unfolding. The high frequency of either tandem or single repeat pathway being taken here (e.g., 37% tandem events at 10°C; Fig. 2 C) further implies that the putative linking helix is intact only for a finite fraction of the time to propagate unfolding. This softness of the linker at all temperatures may explain why no ßI-spectrin crystal structures have yet been reported, whereas several other spectrin family tandem repeat structures are published.
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If the linkers are indeed weaker and unfolded at elevated temperatures, the protein should have a longer unfolded length before unfolding with the AFM. We therefore analyzed the l02 length (defined in Fig. 1 B) for the longest extension curves with five or more peaks. The l02 length at 10°C is close to the estimated folded length of 26 nm for a four-repeat spectrin (based on
-actinin's structure; Ylanne et al., 2002), and this length increases gradually to
1.5x that value at 42°C. This increase includes contributions from extension due to initial desorption, stretching of any unfolded structure, and also unfolding of weakened and disrupted regions of the protein. Per each of the three linkers, the measured increase in length l02 corresponds to the contour length of
12 amino acids or, if folded, an
2-nm helical linker between repeats.
Energetic considerations
In addition to cited temperature studies of forced transitions in double-stranded DNA, a recent temperature-dependent study of biotin-avidin bond rupture forces by Lo et al. (2002)
concluded that temperature has a significant cooperative effect on the rupture forces. At higher T, it takes less time for thermal fluctuations to induce rupture under an applied bias force. The argument should, in principle, extend to fold-stabilizing interactions and protein unfolding. However, contrasting with the linear dependence of rupture force F vs. T shown by Lo and co-workers, we find here that unfolding force is increasingly nonlinear as T approaches Tm (Fig. 3 B). A hybrid kinetic-thermodynamic theory of Lo and co-workers predicts Fb = c1 - c2 T (T in Kelvin), where b = 2 for Hookean-type models of cantilever and bond elasticity, and the ci values are constants related, among other factors, to the activation energy
G* governing kinetics. Fitting Lo and co-workers' most general form to our force-versus-temperature results of Fig. 3 B yields a very different exponent of b = 6.64 (as well as c1 = 73 x 108, c2 = 0.23 x 108; fit R = 0.95). The Hookean-type model of Lo and co-workers clearly does not fit here. Although different models for elasticity may prove predictive one day, the notion of integrating or comparing equilibrium results (from CD) with kinetics (from AFM) does prove useful below in a simpler analysis of our spectrin measurements.
An equilibrium difference in free energy between folded and unfolded states,
Geq(T), is provided by our CD measurements. In particular, the CD experiments were performed over a period of hours, allowing the protein solution to equilibrate at each temperature. In contrast, the subsecond unfolding times forced on a protein in the AFM experiments imply a well-known rate dependence to the unfolding force and also that AFM provides insight into the free energy difference,
G*(T), between folded and transition states (Rief et al., 1998
; Evans, 2001
). Given this distinction in measurements, suppose that both the unfolded state and the transition state are invariant, but that the free energy of the folded state increases with temperature. Fig. 5 A provides a sketch of relevant energy landscapes for both low T and high T. For the two different temperatures, the difference in equilibrium free energies is given by 
Geq =
Geq(T2) -
Geq(T1). Likewise, the difference in free energies from the folded states to the common transition state is 
G* =
G*(T2) -
G*(T1). Clearly, in the case, it is supposed to be 
Geq = 
G* (see Fig. 5 A). We show that this relation holds approximately for the temperature results here.
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Geq(T) (Cantor and Schimmel, 1980
![]() | (1) |
![]() | (2) |

Geq clearly becomes more negative with increasing T.
In calculating 
G*, we exploit prior demonstrations (Carl et al., 2001
) that show the linear approximation of Bell (Bell, 1978
; Evans and Ritchie, 1999
; Rief et al., 1998
) for work done by a force leads to
![]() | (3) |
1.2 nm at 23°C (Law et al., 2003
5-nm length of the three-helix repeat, xu
1.2 nm suggests significant helix displacement before unfolding. Preliminary results imply a similarly weak dependence of F on extension rate at 37°C, which is consistent with a single transition state at xu
1.2 nm as sketched in Fig. 5 A (see Carl et al., 2001
G*(T) per Eq. 3, Fig. 5 B shows that 
Geq

G*, suggesting consistency between CD and AFM measurements. The principal discrepancy is the 10°C result, but this would fit well within uncertainties given the error bars for the unfolding force (see Fig. 3 B).
Relation to thermal softening of red cell shear elasticity
The decrease in both unfolding force F and 
G with temperature provide a basis for better understanding the long-established temperature-dependent deformability of the red cell membrane. Using a shear flow to distort red blood cells, Rakow and Hochmuth (1975)
showed an irreversible transition in red cell deformability at 4650°C. Waugh and Evans (1979)
subsequently showed, using a micropipette to aspirate individual red cells, that the shear elastic modulus, µ, decreases linearly with temperature up to at least 42°C. The latter study concluded that the entropy of the spectrin network in extension increases at higher temperatures, i.e., spectrin becomes more disordered by stretching. As recognized by Waugh and Evans, this is not consistent with the widely presumed entropic chain elasticity such as WLC elasticity where F simply scales as T. The cell measurements are consistent, however, with processes such as protein unfolding. The thermal elasticity data is seen to correlate nonlinearly with the temperature-dependent unfolding force as well as 
G (Fig. 6). Just as the membrane becomes softer with temperature, both the free energy differences for spectrin unfolding and the unfolding force itself decreases. The inset to Fig. 6 shows a relative elastic length, (
G/
µ)1/2, for the red cell membrane; this is seen to increase above the 10°C reference. At 37°C, for example, an incremental length of
65 nm approximates the length of three unfolded spectrin repeats (see Fig. 1 B). Thermal softening in red cell membrane elasticity may thus be due to spectrin unfolding.
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| CONCLUSION |
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| ACKNOWLEDGEMENTS |
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This work was supported by grants from the National Institutes of Health, the National Science Foundation, and the Muscular Dystrophy Association to D.W.S. and D.E.D.
Submitted on April 21, 2003; accepted for publication August 8, 2003.
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