J. Phys. Chem. B 2007, 111, 13653-13657
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Entropic and Enthalpic Contributions to the Chair-Boat Conformational Transformation in Dextran under Single Molecule Stretching Richard G. Haverkamp* and Aaron T. Marshall Institute of Technology and Engineering, Massey UniVersity, PriVate Bag 11222, Palmerston North, New Zealand
Martin A. K. Williams Institute of Fundamental Sciences, Massey UniVersity, PriVate Bag 11222, Palmerston North, New Zealand ReceiVed: July 31, 2007; In Final Form: September 21, 2007
The contribution of entropy and enthalpy to the chair-boat conformational changes (clicks) occurring during the force-extension of single molecules of an axially linked polysaccharide, dextran, was investigated. Experimental single molecule force-extension measurements were carried out by atomic force microscopy over the temperature range of 5-70 °C. This enabled the separation of the entropy and enthalpy components of the conformational change. The contribution of entropy to the Gibbs energy of the conformational transformation was found to be small (89%) enthalpic in nature.
Introduction Polysaccharides are an important structural component in nature. They can be structural components in their own right, such as cellulose in plants, or can provide a form of cross-link to proteins, such as dermachondan sulfate in animals, which gives mechanical strength and shape maintenance.1,2 In addition to the entropic and Hookean mechanisms of chain elasticity, certain polysaccharides possess an additional mechanism for generating extra elastic extensibility, involving chair-boat conformational changes that can occur under tension. These polysaccharides have been found particularly to include those for which extra elasticity or flexibility is required, such as those dominant in flexible tissues.3,4 The function of these conformational changes has been proposed to provide a little extra extension during stretching of elastic tissues.3 It is possible to investigate the mechanical properties of single molecules, including biopolymers, using single molecule stretching with atomic force microscopy (AFM).5,6 Studies have included polysaccharide stretching, the interpretation of which requires the combination of statistical mechanical theories of polymer physics with the complexities of possible force-induced conformational transitions of the constituent pyranose rings. There is some debate as to whether the conformational changes that take place in R-linked glycans are chair-boat transformations7,8 or helix-sheet transformations;9 however, for the purpose of this present study, either possibility may be considered. We refer to these force-induced transformations from a shorter to a longer conformation as clicks. These transformations can be observed as a plateau in force-extension curves obtained by AFM.10 A recently developed algorithm enables the force-extension behavior of these R-linked polysaccharides to be modeled.11 Recently, it has been demonstrated that information about the inter-ring hydrogen bonding in many polysaccharide systems can be obtained from a comparison of stretching curves carried out in a range of solvents with different dielectric constants.12 Dextran is one such polysaccharide with axial linkages that exhibits a pronounced click in its single molecule stretching * Corresponding author. E-mail:
[email protected].
curve13 and has been studied extensively both experimentally and in simulations.14 The absence of solvent dependent effects for dextran, and by implication inter-ring hydrogen bonding, means that this is an ideal system in which to study the thermodynamics of the conformational transition in the absence of such complications.15 For polymers that exhibit a click, the Gibbs energy difference between the conformers can be extracted from a fit to the forceextension curve.11,16-18 Gibbs energies can be made up of enthalpic and entropic components, with the entropic contribution being the most temperature dependent. Therefore, the entropic and enthalpic components can be determined from a study of the temperature dependence of stretching. A number of experiments has been reported examining the temperature dependence of single polymer stretching in a range of systems including synthetic polymers,19 a protein system,20 and investigations of the B-S transition in DNA.21 However, the temperature dependence of the clicks in these polysaccharide systems has not been previously studied. Recent theoretical work on single polysaccharide molecules has attempted to predict the energy landscape of these clicking molecules.14,16,17,22 As the molecule transforms from the unclicked to clicked states, it goes through a highly entropic region,14,16,17,22 which is unsurprising since many conformational forms of the skew boat type, all with very similar energies, are possible in the transition state.23 However, the energy difference between the unclicked and the clicked states was not experimentally investigated as a function of temperature in that work. An estimated value for ∆S for the conformational transition state (not the difference between the initial and the final states) has been quoted for R-D-glucose24 of 27 J mol-1 K-1 (based on ab initio calculations for cyclohexane25). Statistical mechanical models have been developed for representing the force-extension behavior of polysaccharides that do not contain a click. These are extensible versions of the worm-like chain model (eWLC)26-29 and the freely jointed chain (FJC) model.10,30-32 These extensible versions allow the chain to be stretched beyond its contour length and account for both the entropic and the enthalpic components in the extension of simple polymers. Extensions to these models have been
10.1021/jp076052t CCC: $37.00 © 2007 American Chemical Society Published on Web 11/08/2007
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developed to represent the force-extension behavior of polysaccharides containing one or two clicks (which we shall call the 1c-WLC and the 2c-WLC models).11 These models incorporate terms containing the Gibbs energy for the conformational changes in the polysaccharide being stretched. The models use the notion of an equilibrium state being maintained during the extension process. The equilibrium constant, K, between the clicked and the unclicked states depends on the Gibbs energy difference between these states (∆G0) according to eq 1, where kB is Boltzmann’s constant and T is the temperature
∆G0 ) -kBT ln K
(1)
∆G varies with temperature due to the entropic component (eq 2)
∆G0 ) ∆H - T∆S
(2)
By measuring the variation in ∆G with temperature, and assuming that the variation of ∆H with temperature is small, we can partition the Gibbs energy into enthalpic and entropic components. We are also interested in understanding the nature of the temperature-induced changes that take place in the mechanical properties of single molecules of clicking polysaccharides to better understand how these materials may influence the function of the organisms in which the polysaccharides are present. Polysaccharides are present in all life forms, and while most organisms survive only at a relatively small range of temperatures, assemblages of polysaccharides can be dramatically affected by small changes in temperature.17,33,34 Here, we provide experimental evidence for the enthalpic and entropic contributions to these conformational transformations by observing this transformation as a function of temperature. We measure the temperature dependence of the conformational change in dextran during single molecule stretching, over the range of 5-70 °C. From these measurements, we are able to partition the Gibbs energy into enthalpic and entropic components.35 Experimental Procedures Dextran (MW 2 000 000 produced by Leuconostoc mesenteriodes, strain B-512, Sigma) was prepared for AFM force measurements by applying 20 µL of 0.01 wt % solution of dextran in deionized water to glass cover slips (cleaned in H2O2/ H2SO4), which were then dried at 11.3% relative humidity overnight. After drying, the sample was mounted in the atomic force microscope, and 100 µL of deionized water was placed on the sample just prior to the force curve measurements. Force-distance curves were recorded by pulling the molecules at approximately 500 nm s-1 using a scanning probe microscope (Asylum Research MFP-3D) with a gold coated Si tip (NTNDT CSG11-Au) calibrated using a thermal excitation method.36 One cantilever was used for all the force curves presented in this paper. The cantilever had a force constant of 51.1((3.7) pN nm-1. The spring constant of silicon varies only slightly over this temperature range with a change of 0.45% from 5 to 70 °C.37 Since the same cantilever was used for all the experiments, the relative precision for the differences between measurements at different temperatures is not limited by the precision in determining the force constant for the cantilever. The cantilever was not recalibrated at the end of the experiments (which would have been a good idea); however, the order in which the measurements at different temperatures was taken was randomized so that any systematic error of varying the
Figure 1. Experimental arrangement for AFM stretching.
spring constant would not be reflected in the data. Measurements were also carried out on a Veeco Nanoscope E with a different cantilever for the 25 °C measurement as a check on the reproducibility of the measurements, which, although not presented here, gave good agreement with the main series of measurements. The single molecule stretching was performed by lowering the atomic force microscope tip to the dextran film under water and raising it. In a small proportion of cases, a single molecule of dextran would attach to the tip and result in a single molecule stretch. As the tip and substrate separation is increased, the molecule straightens and stretches, with the force applied to the molecule determined from the deflection of the flexible atomic force microscope cantilever. The stretch distance is determined by the cantilever holder to substrate distance corrected for the deflection of the cantilever. The stretching rate varies as the cantilever deflects (a slower stretching rate during the maximum cantilever deflection rate). The sample was heated and cooled by a peltier device (Meltech, 33 W, 30 mm × 30 mm) in a custom built arrangement (Figure 1). The peltier device was mounted on a copper plate with water temperature stabilization (gravity fed water at room temperature). The temperature was controlled by a variable power supply adjusted to the appropriate voltage to maintain the required temperature. Temperature control of (0.5 °C or better was achieved at each set point within 10 min. The peltier device expands and contracts on heating or cooling, and this leads to changes in the cantilever-substrate distance, which causes difficulty in stretching measurements. By stabilizing for a few minutes at each set point temperature, we were able to minimize this variation (0.04-1.2 nm s-1 height variation during measurements). In contrast, an on/off temperature controller leads to unacceptable fluctuations in height. When operating at below room temperature, it was found necessary to flow dry air into the scanner head to prevent condensation occurring on the back of the glass window in contact with the drop of water surrounding the cantilever, which otherwise lead to a loss of photodiode signal. Results and Discussion We obtained force-extension curves for dextran at temperatures from 5 to 70 °C. The raw curves are shown in Figure 2a, and the curves normalized for length using the high force region are shown in Figure 2b. About 10 curves were obtained at each temperature, although a total of only five curves are shown in Figure 2 and used in the analysis since many curves either did not have a sufficiently flat baseline or did not pull to an adequately high force. A direct comparison between the normalized curves suggests that there is no obvious shift in the click force, indicating that the Gibbs energy does not change significantly with temperature. To estimate the uncertainty in the experimental data to provide a maximum value for ∆S (from the maximum experimental variation in ∆G), we have generated simulations of force curves at different temperatures from the 1c-WLC model11 (Figure 3). We have also plotted force-extension curves for a clicking
Conformational Transformation Entropy and Enthalpy
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Figure 2. Force-extension curves for stretching of single molecules of dextran at 5 to 70 °C: O 5 °C, b ∼25 °C, 0 50 °C, and 2 70 °C. (a) Raw curves and (b) normalized data.
Figure 3. Simulations of the temperature effect on dextran using 1c-WLC11 with ∆G0 ) 33.1 kJ mol-1 at 298 K, ∆x ) 0.065 nm, ---- 5 °C, and -- 70 °C. (a and c) Force-extension curve and (b and d) fraction clicked vs force. (a and b) ∆S ) 0 J mol-1 K-1 and (c and d) ∆S ) 100 J mol-1 K-1.
polysaccharide with ∆G ) 33.1 kJ mol-1 (which is the value we find and is elsewhere reported15 for dextran) putting ∆S ) 0 J mol-1 K-1 and ∆S ) 100 J mol-1 K-1 (Figure 3). We have chosen 100 J mol-1 K-1, as this would correspond to most or all of the Gibbs energy in the experimental temperature range. If all the Gibbs energy of the conformational transformation consists of enthalpy, then the temperature dependence shown in Figure 3a,b will result. However, if ∆S ) 100 J mol-1 K-1 (providing most of the ∆G), then there will be a clear shift in the force for the click, as shown in Figure 3c,d. This shift is a decrease in force at the midpoint of the click region with 50% clicked of 166 pN at 70 °C as compared to 5 °C (and is larger than this in part of the curve). This shift would easily be observed experimentally if it were present. To estimate the precision with which we can determine the entropy and enthalpy of the conformational change, we need to consider not the absolute accuracy of our measurements (which will include factors such as the force calibration of the
cantilever) but the precision of each measurement and the precision with which we can measure a different force at different temperatures. We have taken the following approach to determining the precision with which we can compare the click force at different temperatures. A 1c-WLC curve was fitted to the concatenated data from the range of temperatures11 (Figure 4a). This curve was then subtracted from the data, and the residuals over the range of 0.85-1.00 were plotted (Figure 4b). We can then analyze the residuals to determine the precision obtained from our measurements. We estimate the average force difference between the fitted curve and for each dataset (corresponding to stretches at each of the four temperature conditions). These provide an average residual force and a standard deviation (Table 1). The difference between the lowest and the highest mean is 27 pN. A t-test on pairs of these curves enables us to obtain a statistical estimate of whether the differences between these mean residuals are significant (Table
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Figure 4. (a) Expanded section of the normalized force-extension curves around click region for all data sets with 1c-WLC fitted curve and (b) residuals after subtraction of fitted curve.
TABLE 1: Statistics on Residuals for Each Temperature Plot over the Range 0.85-1.00 Normalized Extension temp (°C)
av residual force (pN)
SD in residual force (pN)
no. of data points (n)
5 25 50 70
-8 -3 12 -15
3 2 2 3
44 199 72 76
TABLE 2: t-Test on Pairs of Residuals from Table 1 data pair tested 5 °C, 25 °C 5 °C, 50 °C 5 °C, 70 °C 25 °C, 50 °C 25 °C, 70 °C 50 °C, 70 °C
force difference (pN) -5 -4 7 -15 12 27
probability means are different (%) 81 >99 76 >99 >99 >99
2). Taking an overall view of the t-test probabilities allows us to estimate that differences in the click force of greater than 20 pN will be clearly detectable in our measurements. This analysis of the residuals is a way of determining the precision of a region of the force curve. It should be noted that the scatter will be higher in areas of the curve that have a small slope (which the click region has) than in areas with a large slope because for a given thermal energy distribution of the cantilever, larger variations in the stretched length of the molecule can be encompassed in a region of low slope.17 The extension length normalization procedure does not contribute significantly to the error in defining ∆G of the click since the slope of the click region is almost orthogonal to the extension length, while the slope of the high force region is almost parallel to the extension length. We therefore conservatively take the maximum force variation between the data recorded at different temperatures to be less than 20 pN representing 0.783 kJ mol-1 in ∆G. This puts an upper limit on the entropy contribution to the Gibbs energy of 12 J mol-1 K-1, representing about 11% of the total energy of the click. The Gibbs energy of the conformational transformation is therefore largely (or wholly) enthalpic in nature. The largely or wholly enthalpic nature of the click has consequences for the heat balance of a molecule being stretched. When a non-clicking polysaccharide is stretched, initially the extension is an entropic process at low force becoming enthalpic at higher force with the force range at 1-2 nN having contributions from both. For a typical clicking polysaccharide
molecule, if the click were entropic, the work to stretch a single molecule to 1-2 nN should be sufficient, in an adiabatic system, to raise the temperature of the molecule by over 100 K. Obviously in nature, and in most experimental arrangements, a stretched molecule is far from being in an adiabatic system with good heat transfer possible to the surrounding tissue, nevertheless the heat input would be significant. Such a heat input could have a dramatic destructive effect on the polymer and hence on the elastic tissue of which it is a part. However, we have shown that the click is largely enthalpic, so the heating on stretching will be considerably reduced as a large portion of the force-extension work goes into the enthalpic conformational change of the click. It has been observed that these axially linked (clicking) polysaccharides tend to dominate over other polysaccharides in elastic tissues, while equatorially linked (nonclicking) polysaccharides dominate in biological materials not required to be elastic. Having an ethalpic click may therefore enable the extra elasticity apparently required in nature for elastic tissues without a destructive heating effect. Conclusion By using an existing model for clicking (axially linked) polysaccharides, it has been possible to model the effect of temperature on the force-extension behavior around the plateau region. Experimental AFM force measurements over the temperature range of 5-70 °C on the model compound dextran enabled the separation of the entropy and enthalpy components of the conformational change. The contribution of entropy to the Gibbs energy of the conformational transformation is small (89%) enthalpic in nature. Therefore, while clicking polysaccharides have been demonstrated previously to be used in nature for flexible materials, possibly for the extra extensibility they impart at lower force, the ability of the click to absorb the energy of stretching may enable this. References and Notes (1) Scott, J. E.; Heatley, F. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 4850-4855. (2) Scott, J. E.; Stockwell, R. A. J. Physiol. (Oxford, U.K.) 2006, 574, 643-650. (3) Haverkamp, R. G.; Williams, M. A. K.; Scott, J. E. Biomacromolecules 2005, 6, 1816-1818. (4) Scott, J. E. J. Physiol. (Oxford, U.K.) 2003, 553, 335-343. (5) Janshoff, A.; Neitzert, M.; Oberdo¨rfer, Y.; Fuchs, H. Angew. Chem., Int. Ed. 2000, 39, 3212-3237. (6) Butt, H.-J.; Cappella, B.; Kappl, M. Surf. Sci. Rep. 2005, 59, 1-152.
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