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Nanomechanical analysis of Clostridium tyrobutyricum spores
Micron 41 (2010) 945–952
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Nanomechanical analysis of Clostridium tyrobutyricum spores N. Andreeva a , D. Bassi b , F. Cappa b , P.S. Cocconcelli b , F. Parmigiani c , G. Ferrini a,∗ a
Dipartimento di Matematica e Fisica, Università Cattolica, I-25121 Brescia, Italy Istituto di Microbiologia, Università Cattolica, I-29100 Piacenza, Italy c Dipartimento di Fisica, Università degli Studi di Trieste, I-34127 Trieste, Italy and Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy b
a r t i c l e
i n f o
Article history: Received 1 May 2010 Received in revised form 12 July 2010 Accepted 12 July 2010 Keywords: Atomic force microscopy Clostridium tyrobutyricum spores Young modulus
a b s t r a c t In this work we report on the measurement of the Young modulus of the external surface of Clostridium tyrobutyricum spores in air with an atomic force microscope. The Young modulus can be reliably measured despite the strong tip-spore adhesion forces and the need to immobilize the spores due to their slipping on most substrates. Moreover, we investigate the disturbing factors and consider some practical aspects that influence the measurements of elastic properties of biological objects with the atomic force microscopy indentation techniques. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The investigation of mechanical properties of biological samples with atomic force microscopy (AFM) has received considerable attention in the past years (Radmacher et al., 1996; Rosenbluth et al., 2006; Cross et al., 2007). In addition to fundamental research interests, monitoring local mechanical properties of cells allows a better understanding of the mechanism of some diseases causing cell stiffness changes (Costa, 2003). The elastic properties of bacteria or cell walls can be determined by taking force curves using AFM, measuring the stiffness of the exterior cell surfaces by indenting them with a cantilever tip, achieving a lateral resolution of few tens of nm (Butt et al., 2005). Despite AFM force spectroscopy methods are well developed, there are situations in which the presence of adhesion, attraction or repulsion forces between tip and sample may results in the impossibility of retrieving information on the elastic properties of cell walls. In the literature there are examples of force spectroscopy applied to cell walls or soft samples in the absence of strong interaction between the tip and the surface. In this case soft cantilevers can be used for indentation studies without taking into account instabilities caused by jump-to-contact or force modulations due to the interactions between tip and surface. However, in the natural environment, the presence of strong adhesion to cell surface is often found (Vadillo Rodriguez, 2004; Dufrêne, 2001). In this situation, it is not clear if it is possible at all to obtain information on the local mechanical properties. Even if detailed theoretical descriptions of tip interaction in the pres-
∗ Corresponding author. Fax: +39 030 2406742. E-mail address: [email protected] (G. Ferrini). 0968-4328/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2010.07.006
ence of adhesion forces (Johnson et al., 1971; Derjaguin et al., 1975) have been devised, it is important to know if it is possible to obtain reproducible results in experiments. In this work, we demonstrate that the Young modulus of the external layer of spores of the anaerobic bacterium Clostridium tyrobutyricum (Andreeva et al., 2009) can be reliably measured in air despite the strong tip-spore adhesion forces and the need to immobilize the spores due to their slipping on most substrates. Moreover, we investigate the disturbing factors that influence the measurements of viscoelastic properties of biological objects with AFM indentation technique and consider some practical aspects of the elasticity investigation with AFM. 2. Materials and methods 2.1. Sample preparation C. tyrobutyricum ATCC 25755 (T) spores were used for AFM investigation. Spores were prepared according to the protocol described previously (Bassi et al., 2009). These spores have bad adhesion both to hydrophilic and hydrophobic surfaces, preventing investigation of their elastic properties by AFM without a proper strategy of sample immobilization. We avoided to use substrates covered with biological “glues” like polypeptides and aldehydeslike fixatives by glutaraldehyde since it is known that this kind of fixation could influence the elastic modulus of biological samples (Moloney et al., 2004; Braet et al., 1998; Velegol and Logan, 2002), Instead of this, we choose a mechanical immobilization technique. A drop of ∼3 l of spore suspension in water (1.8 × 107 ml−1 ) was put on polycarbonate Isopore DTTP (Millipore, USA) membrane and dried in air. During the drying process, spores partially fell
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into membrane pores immobilizing them inside the membrane. The correct size of membrane pores was approximately equal to the size of the spore coat (about 1.5 m), determined by preliminary AFM measurements of spores dried in air taken in non-contact mode. The polycarbonate is known to be an extremely stiff material (e.g. see the “polycarbonate” article on www.wikipedia.org), with Young modulus of the order of few GPa, so that the membrane elastic compliance do not alter the force curves taken on the spores. 2.2. Instrumentation All measurements were carried out with an AFM (NT-MDT, Russia), working in contact mode to measure samples topography, immediately before taking force curves. We use contact mode silicon nitride cantilevers CSC 17 with nominal spring constant of 0.15 N/m and tip curvature radius of 10 nm (MMasch, Lithuania). The spring constant kc of the cantilever was determined by the Sader method (Sader et al., 1999), implemented in AFM software, obtaining kc = 0.14 N/m. The estimated error of spring constant calibration with Sader method is 5% (Gibson et al., 2005). The cantilever deflection during force curves is monitored by the offset current from the quadrant photodiode, which is correlated to the calibrated piezotube extension. The deflection calibration of the cantilever (deflection sensitivity calibration) is done on a hard surface, assuming a negligible indentation and thus equal distances spanned by the cantilever tip and the piezotube. As test surface we used highly oriented pyrolitic graphite (HOPG). In our point of view, HOPG is an ideal substrate for the cantilever deflection calibration due to its inertness and hydrophobicity, avoiding a significant influence of the surface water layer on the calibration. To prevent damaging of the cantilever tip and to fulfill the assumption of linear elasticity theory, the range of cantilever deflection during calibration did not exceed the value of the tip curvature radius. It is important to consider the influence of changes in the sensitivity of the AFM optical beam deflection system on viscoelastic measurements. Fig. 1 shows a scheme of a standard AFM optical beam deflection system. The displacement of the laser spot on the photodiode a related to the cantilever displacement z as (Fukuma et al., 2005): a = 3(s/l)z, where l and s are the effective cantilever length and the distance between the tip and photodiode, respectively. Note that the position of the laser beam spot influences both the cantilever effective length l and the measured cantilever displacement z. Moreover, the change of the cantilever length is not proportional to the change of the cantilever displacement, as far as the cantilever bends in the force gradient acting near the sample surface (Mironov, 2004). This means that changing of
the laser beam spot position on the cantilever alters the calibration of the cantilever deflection sensitivity and care must be used during measurement regarding the stability of laser alignment. 2.3. Indentation geometry and force–displacement relations When the surface of a biological object is deformed by the pressure exerted by the tip of an AFM cantilever, the amount of displacement with respect to the undeformed surface (the indentation) carries information on its elastic properties. The deflection of the cantilever as its tip indents an object is usually described with models of linear elasticity theory (Landau et al., 1959). The predictions from these approximate models are accurate when the linear dimensions of the contact area between bodies upon deformation is small in comparison with the sizes of the bodies. This restriction poses strict limitations on the depth of the indentation made with the cantilever tip on soft samples. The geometry which is frequently used for calculation of elastic properties of biological objects is the contact problem between a sphere and a semi-infinite plane (Hertz, 1881). In the case of an infinitely stiff sphere of radius R that indents a plane, the loading force F depends on the indentation ı as: F = ı3/2 (2/3) (E/(1 − 2 )) R1/2 , where E is the Young’s modulus and is the Poisson ratio of the indented material. According to this model the value of the indentation should not be more then the curvature radius of the (spherical) cantilever tip and the thickness of the isotropic layer under indentation. Using a conical geometry of the indenter (Radmacher et al., 1996), with a cone opening angle ˛, the loading force depends on indentation as F = ı2 (/2) (E/(1 − 2 )) tan ˛. The two indenter geometries describe distinct physical situations. When indentation is comparable or smaller than the radius of curvature of the cantilever tip, the interaction is well described by a spherical indenter on a flat surface. Instead, when indentation is greater than the radius of curvature of the cantilever tip, then the conical shape of the indenter has much more influence on the contact area than the tip radius of curvature. In this situation, a better description of the interaction is given by the conical indenter geometry, where the tip is considered to be point-like in comparison with the size of the indenter. The proper application of the contact problem demands preliminary knowledge about the morphology of the biological object under investigation. For example, knowing that the thickness of the cell wall is varying in the range of 10–50 nm (Jackson, 2006), it is correct to apply the model with conical geometry only assuming that the cell content beyond the cell wall is isotropic and has the same elastic properties of the cell wall. On the other hand, the spherical symmetric indenter describes well the tip–surface interaction when indentation lengths are less than the tip curvature radius (i.e. few nanometers). Otherwise it is necessary to solve the contact problem numerically in the assumption of finite thickness layers (Chen and Engel, 1972). 3. Results 3.1. Measurements of elastic properties by force spectroscopy curves
Fig. 1. Scheme of the AFM optical beam deflection system: a—displacement of the laser spot on the photodiode; z—cantilever displacement; l—effective cantilever length; s—distance between the tip and photodiode.
The cantilever deflection measures the force exerted on the sample by the cantilever tip. The dependence of the cantilever deflection on the piezotube extension is called a force curve. In a single force spectroscopy measurement, two main parts could be distinguished, that convey different physical information, the approach curve and the retraction curve. Below we comment on the approach and retraction force curves taken on C. tyrobutyricum spores, shown in Fig. 2. An approach curve can be approximately
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Fig. 2. Approach and retraction force curves taken on Clostridium tyrobutyricum spores. On the inset: an approach curve divided into the following parts. (1) Free cantilever, far from the surface, in the absence of force gradient. (2) The cantilever is subject to attractive forces, often causing the so-called “jump-to-contact” regime, a known mechanical instability of the cantilever that can be avoided choosing a sufficiently stiff cantilever. (3) Intermediate regime between long and short-range surface forces, it is the most complicated part from the analytical point of view. (4) Short-range surface forces dominates. (5) Contact regime, where adhesion can be considered negligible.
divided into five main parts (refer to the numbering in the inset of Fig. 2): (1) corresponds to a free cantilever which is far from the surface in the absence of force gradient; (2) describes the cantilever while attractive forces act on it, often causing the so-called “jump-to-contact”; (3) gives an idea on intermediate case between long and short-range surface forces and it is the most complicate part from the analytical point of view; (4) represents the action of short-range surface forces; (5) is the contact part of the curve, where adhesion could be considered negligible. In the absence of strong interaction between the cantilever and the sample, caused for example by adhesion or high humidity, the retract curve (dotted line in Fig. 2) precisely reproduces the approach curve. This ideal situation is almost never realized in practice. According to Fig. 2, two main differences between approach and retraction force curves could be highlighted. First, a slight hysteresis between approach and retract curves could be noticed in the contact part (known as loading–unloading hysteresis, Butt et al., 2005). This difference can be explained by the plastic and/or viscoelastic deformation of the sample or by a friction mechanism. We exclude the possibility of piezo hysteresis because the piezo elongation is monitored independently by capacitive sensors. The AFM cantilever is tilted typically by 7–20◦ with respect to the sample surface to prevent touching the sample with the cantilever base instead of tip when approaching the sample. The cantilever tilt causes the tip to slip in the longitudinal direction during loading. In the retract curve the tip slides over the sample surface and bends due to the friction forces, causing the hysteresis between the contact parts of the approach/retract force curves. Since the kind of hysteresis observed is similar in all the force curves taken in different points of the samples, the influence of friction is the probable cause of the hysteresis seen in the experimental data. Second, the adhesion part of the force curve on approach and retraction curves is different. On the approach curve adhesion provokes the tip “jump-to-contact”. This instability takes place when the gradient of attractive surface forces exceeds the spring constant of the cantilever. On the retraction curve the adhesion keeps the tip in contact with the surface until the retracting force exceeds the adhesion force. It also should be noted that adhesion force strongly changes from point to point on the sample surface. Since it appears
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that approach curves are reproducible experimentally, even when a great variability in retract curves is present, it makes sense to analyze elastic properties of the sample through data acquired during approach. The next step of the elastic properties investigation with AFM is the correct interpretation of the data from an approach curve. For force curves analysis taken on biological samples it is convenient to apply the Hertzian approach due to its simplicity. However, this mechanical model predicts correct results only for a contact problem in the absence of adhesion. In practice almost all biological samples have an adhesion to the AFM tip. To take into account adhesion, models that describe the situation in two limiting cases of short- and long-range surface forces have been developed. The Johnson–Kendall–Roberts (JKR) model (Johnson et al., 1971) gives a solution to the contact problem with adhesion when surface forces are short range in comparison to the elastic deformation they produce (as in the part of the approach curve marked with (4) in the inset of Fig. 2). The Derjaguin–Muller–Toropov (DMT) model (Derjaguin et al., 1975) treats well the contact problem with adhesion when surface forces are long-range (part (2) of the approach curve). The general solution of the contact problem in the presence of adhesion demands a numerical simulation or cumbersome equations from Maugis theory (Maugis, 1992) (part (3) of the approach curve). All these models were developed with the assumptions of normal cantilever load and in the absence of lateral forces. In practice, experimental force curves are greatly influenced by lateral forces, and the condition of normal applied load is not always satisfied due to topographical features of the sample. Thus, even the results from complicated and thorough models often are greatly affected by experimental errors which could not be eliminated. So, for the sake of simplicity, it is preferable to use the simpler Hertzian approach, but it is necessary to determine correct conditions for its application. 3.2. Measurements of the Young modulus of the outer surface of C. tyrobutyricum spores After calibrating the AFM deflection sensitivity on HOPG, we carried out the measurements of the elastic properties of C. tyrobutyricum spores immobilized on Isopore DTTP membrane (see Section 2.1). Previous studies have shown that C. tyrobutyricum spores consist of a dark spore core, surrounded by a dense cortex transparent to electron beams in transmission electron spectroscopy and a multilayered spore coat (Plomp et al., 2007). Many clostridia have spores surrounded by large portions of amorphous and soft material, the exosporium. This can take a large volume around the spores, in many cases more than 100% of the spore volume itself (Plomp et al., 2007). To determine the spore distribution on Isopore DTTP membrane we acquired the topography of our samples in contact mode. According to preliminary images of C. tyrobutyricum spores, we found that spores are covered with a soft and very reactive material, as expected. To prevent damaging the sample and the contamination of the cantilever, we acquired images in contact mode and under low loading force, using the deflection signal from the photodiode as a feedback signal. The loading force was gradually increased and the topography was acquired with the smallest force needed to avoid significant image distortions. The value of the force applied to the cantilever during scanning was 0.70 nN. The elastic properties of C. tyrobutyricum spores were measured on the area above the coat and on the spore “tail” formed by the external amorphous material. The points where the force curves have been acquired are shown in Fig. 3. In each zone we acquired 9 points to estimate the possible range of Young’s modulus values. To avoid the influence of cantilever deformations during repeated spectroscopy, we per-
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Fig. 3. (a) Topography of Clostridium tyrobutyricum spores distributed on Isopore DTTP membrane taken with AFM in contact mode. Membrane pores are shown with white arrows and spore core with its surrounded coat (Co) and exosporium (Ex) are indicated. The force curves have been acquired on the points shown by the square grids of numbers on the spore core and exosporium. (b) The error signal is displayed to underline topographic features of Clostridium tyrobutyricum spore. (c) Topographic profiles along the horizontal lines of the grids on the top of the spore coat and exosporium tail. The points indicate where spectroscopic measurements have been taken.
formed the measurements slowly (a measurement, approach and retraction force curves, takes several seconds). To determine the initial conditions to apply the Hertz model, we used the following procedure. The zero-deflection reference of the cantilever is set when it is far from the surface and no forces act on it. No hysteresis between approach and retract force curves in the zero-deflection level is observed. Near the surface, in the presence of long-range attractive force and liquid meniscus, the tip “jumps” into contact and the deflection of the cantilever becomes negative (downward deflection). Actually, the point with greatest negative deflection corresponds to the contact point; in this point the surface acts on the cantilever forcing it to press the sample and possibly to indent it. Further approaching leads to decreasing the attractive forces and increasing the repulsive forces acting on the tip. At some point, the attractive and repulsive forces are balanced and the cantilever deflection becomes equal to zero, i.e. its deflection is equal to the cantilever deflection when it is far away from the surface, defining the zero-deflection point in Fig. 2. The initial conditions to apply the Hertz model are determined in this point. We assume that at the zero-deflection level the indentation is zero. Even though the “zero-deflection level” point belongs to the part of the force curve
described by the JKR model, due to the reproducibility of the results, we are led to conclude that, even in the presence of strong adhesion, which is true for most biological samples, attractive forces do not have a strong influence on the cantilever indentation after it reaches the zero-deflection level. Moreover, it is evident that the force curve between the contact point and the zero-deflection point, which is actually provoked by adhesion forces, is relatively small on the approach curves compared with the same part on the retraction curve. In Fig. 4 we show a sample of force curves and loading force versus indentation for four experimental points, chosen to demonstrate all the possible range of differences between approach and retraction curves observed experimentally. For each force curve we determined the dependence of loading force and indentation on piezomovement. We calculated the indentation as a difference between contact parts of force curve taken on HOPG and those taken on spore (at constant piezo height). Loading force was calculated as a product of cantilever deflection and k-constant of the cantilever, determined by the Sader method. Then for each force curve we reconstructed the dependence of loading force versus indentation. The experimental loading force curves were
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Fig. 4. Force spectroscopy measurements obtained in four points shown in Fig. 3 as 2, 3, 4, 6 on the spore coat (Co), to demonstrate the possible variations between approach and retraction curves. In each graph is reported the specification of the point where the spectroscopy has been measured. On the right, there are the results of fitting experimental data with spherical and conical indenters.
fitted with the analytical functions reported in Section 2.3 with the Young’s modulus as the only fitting parameter. As usual in biological contact problems (Butt et al., 2005), we set the Poisson ratio to 0.5, as for water and other incompressible materials. The fitting results are presented in the right column of Fig. 4, assuming a tip curvature radius of 10 nm and an aperture angle of 40◦ . The initial conditions (after jump-to-contact) are chosen so that at zero-deflection (i.e. no force applied on the cantilever) the tip do not indent the sample. In this case a good fitting of experimental data with the spherical indenter geometry is achieved, while the conical indenter geometry gives evidently unacceptable
results. Good reproducibility of Young’s modulus determination with the spherical indenter model allows us to conclude that, even in the presence of strong adhesion, it is possible to retrieve elastic modulus of the upper layer of biological samples. The error from the fitting procedures on the Young’s modulus (reported in the figures only for the spherical indenter model) are small, indicating that this model is well suited to describe the experimental data. These results are in agreement with the previous discussion, indicating that the conical geometry is better suited to describe indentations larger that the tip radius of curvature (typically 10 nm) while the spherical indenter geometry is better suited
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Table 1 Value of Young’s modulus determined with the spherical indenter model on the coat and exosporium.
Young’s modulus, MPa
Coat
Exosporium
26 ± 8
44 ± 20
for indentations smaller than the tip radius of curvature, as in our case. The values of the Young’s modulus have been averaged over 9 points on the top of the spore above the coat and on the area of the exosporium “tail” (see Fig. 3) and reported in Table 1. The exosporium Young modulus can be influenced by either the substrate stiffness or the stiffness of the internal structure of the spore. While we exclude an influence of the polycarbonate millipore substrate, that is so much stiffer than the spore structures to be considered as indeformable (see previous observations in Section 2.1), the same cannot be taken for granted for the internal structures as the core. In the literature, to analyze the spore coat architecture of other types of clostridia similar to that studied here, the exosporium is removed by physical means using, for example, a French press treatment; applying a pressure of 120 MPa to a water suspension of clostridia spores, it is possible to strip them of their amorphous exosporium (Plomp et al., 2007). In this case, only 15% of the treated spores appear to have damaged internal structures, showing that the coat is resistant under pressures much higher than those used in this experiment, that are in the range of tens of MPa (i.e. one tenth of the pressure applied by the French press during the exosporium stripping process). On these basis, we suggest that the measured Young modulus in different parts of the dried exosporium is related to the exosporium different biological conditions, such as water content, proximity to different structures and so on, and only in minor degree the Young modulus is influenced by the compliance of internal structures, that appear to be capable of withstanding much higher pressure. While the choice of a particular tip do not influence the agreement between the theoretical and the experimental curve, to obtain a quantitative estimate of the Young’s modulus from the experimental data it is necessary to know the tip radius R for the spherical indenter model and the aperture angle ˛ of the conical tip for the conical indenter model. These parameters (R = 10 nm and ˛ = 40◦ ) have been taken from the manufacturer data, and the estimated uncertainty of 30% must be considered when estimating the uncertainty on the absolute value of the Young’s modulus. The errors reported in the table represent the dispersion of the experimental data and take into account the uncertainty on the tip parameters (R or ˛). Fig. 5 shows the theoretical dependences of loading force on indentation for both models in the range of 1–100 nm. When the indentation is lower than 20 nm, for the same loading force, the value of indentation for the spherical geometry is bigger than for conical geometry. This explains the lower Young’s modulus values predicted by the spherical indenter for indentations below 20 nm. On contrary for values of indentation bigger than 20 nm the conical indenter gives bigger indentation for the same loading force. Note that smaller values of indentation allow achieving better lateral resolution in the elastic properties measurements. In fact, if the value of sample indentation exceeds the tip radius of curvature, the measured elastic properties of the object are not determined only by a vertical compression of the sample and are not described in the framework of linear elastic theory. Moreover, in this case, lateral forces, arising from a bigger area around the point of contact, will significantly influence the results of measurements and the lateral resolution will be decreased due to an increased effective contact area.
Fig. 5. Theoretical dependences of loading force on indentation for spherical and conical geometries in the range of 1–100 nm.
4. Discussion 4.1. Which viscoelastic properties does AFM measure? All living cells, prokaryotic and eukaryotic, consist of a nucleus and different organelles immersed in a liquid cell matrix, the cytoplasm. All these internal cell structures are surrounded by the plasma membrane that encloses their contents and serves as a semi-porous barrier to the outside environment. The plasma membrane is composed of a double layer (bilayer) of lipids, more precisely described as phospholipids. In bacteria, the plasma membrane is an inner layer of protection since a rigid cell wall made up of peptidoglycan forms the outside boundary. Moreover, the bacterial spore produced by Clostridium species has a more complex structure; it is composed of a central core, which is surrounded by various protective layers. The outermost layer is the exosporium which is the primary site of contact with the environment; it is apparently formed by a single collagen-like glycoprotein, whereas the basal layer is composed of a number of different proteins in tight and loose associations. Below this is the spore coat which is made up of highly cross-linked keratin and layers of spore-specific proteins. The innermost spore cell, the core, is surrounded by the cortex of loosely cross-linked peptidoglycan and contains the components of the vegetative bacterial cell (the cell wall, cytoplasmic membrane, cytoplasm, DNA, ribosomes, etc.) Analyzing a biological model like a cell, the first structure indented with an AFM cantilever tip in force spectroscopy measurements is the cell surface. In case of plasma membrane the thickness is often no more than 10–20 nm, while when we deal with bacteria the thickness of cell wall range from 5 nm to 80 nm. According to measurements with micropipette method of phospholipids membrane, values of stretching elastic modulus vary in range of 0.135–0.19 N/m (Evans and Rawicz, 1990), that corresponds to Young’s modulus values in the range of 27–38 MPa for a 5 nm thick membrane. Measurements of elastic properties of Escherichia coli sacculi dried in air with AFM give a Young’s modulus of 300–400 MPa (Yao et al., 1999). On the other hand, measurements of the elasticity of a cell as whole with other methods like micropipette aspiration, optical tweezers, microplates and others, give a cell elasticity modulus of the order of 10 Pa to 100 kPa (see for example, Hochmuth, 2000). Thereby, the elastic properties determined with AFM force spectroscopy depends on the experimental conditions and indentation depth.
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Fig. 6. (a) Small indentations with AFM tip allow to measure the elastic properties of the cell wall itself, while (b) under indentations greater than the cell wall thickness, force curves are influenced by the underlying structures of the cell.
In the case of small indentation, less then the thickness of the cell wall, we have a contact problem in which spherical geometry is a good approximation and the retrieved Young’s modulus corresponds to the elastic properties of the cell wall, with values most likely in the range of tens of MPa (see Table 1). For indentation greater than the cell wall thickness, force curves are influenced by the underlying structures (Fig. 6) and in this case the conical indenter model is more adequate. However, if the membrane underlying
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structures have different elastic properties, it is necessary to introduce a finite layer approach (Chen and Engel, 1972). Considering the Young’s modulus retrieved with a conical indenter model, in the case of a membrane with an isotropic cell content, its value will be in the kPa range (Radmacher et al., 1996), representing the elastic properties of the whole cell. Moreover, a big indentation often is not admissible for biological samples, because of high pressure surface damage and because biological surfaces are usually very reactive and the risk of cantilever contamination is high under big indentations. 4.2. What happens when the tip of the cantilever becomes contaminated? To assess the influence of tip contamination on force spectroscopy curves, we used first the HOPG monoatomic steps as a calibration for the tip sharpness. The image of HOPG shown in Fig. 7a are obtained with an uncontaminated tip, showing the error signal to enhance the finer details. After scanning the sample of C. tyrobutyricum spores, we acquired a HOPG topography, shown
Fig. 7. Topography of HOPG obtained with the error signal before (a) and after (b) tip contamination; (c) force spectroscopy curves acquired with contaminated tip; (d) measurements of elastic properties with AFM could be represented as a determination of the sample spring constant k2 from known value of the cantilever spring constant k1 . In case of contaminated tip, the contamination could be considered as an additional spring with unknown spring constant k3 added to the sample-cantilever spring system. Thus, it becomes impossible to determine the proper value of the sample spring constant using data from force spectroscopy measurements.
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in Fig. 7b. In this case the edges of the HOPG steps are wider and in some cases are doubled, due to tip contamination. Force spectroscopy curves acquired using a contaminated tip are shown in Fig. 7c. Comparison of two force curves on HOPG sample before and after tip contamination shows that the slope of the curve is the same for both curves in the contact region. However, in the adhesion region the “jump-to-contact” is less sharp with the contaminated tip. Considering the force curves acquired with the contaminated tip both on the spores and on HOPG, it results that the measured Young modulus is the same for both samples, a result that can be explained by a modified cantilever k-constant due to tip contamination, as shown in Fig. 7d. 5. Conclusions The measurement of elastic properties via AFM force curves demands a stable optical beam deflection system and a correct choice of the model to interpret the contact problem. The choice of the theoretical model for the interpretation of the experimental results relies on preliminary knowledge of the sample morphology and surface structure. In this work we investigated the elastic properties of C. tyrobutyricum spores, in the presence of high adhesion forces. Using a small indentation range, comparable with the size of the cantilever tip, we found that the Young modulus of the spore surface is independent on the topography and that the underlying spore‘s structures do not influence the upper layer elastic response. The determined values of C. tyrobutyricum spores Young moduli are in the range of 25 MPa for the spore’s coat and 42 MPa for the exosporium, which is in good agreement with the theoretical estimation of the area-stretching elastic modulus for lipid bilayer based on the free energy theory and experimental results for cell walls Young’s modulus obtained with other techniques. Acknowledgement This work has been partially funded by Fondazione Cariplo. References Andreeva, N., Ferrini, G., Bassi, D., Cappa, F., Cocconcelli, P.S., Prato, S., Troian, B., Parmigiani, F., 2009. Preliminary results of combined scanning near-field optical microscopy and atomic force microscopy applied to a model biological system: Clostridium tyrobutyricum spores. Boll. Geof. Teor. Appl. 50, 396. Bassi, D., Cappa, F., Cocconcelli, P.S., 2009. A combination of a SEM technique and X-ray microanalysis for studying the spore germination process of Clostridium tyrobutyricum. Res. Microbiol. 160, 322–329.
Braet, F., Rotsch, C., Wisse, E., Radmacher, M., 1998. Comparison of fixed and living liver endothelial cells by atomic force microscopy. Appl. Phys. A 66, S575–S578. Butt, H.-J., Cappella, B., Kappl, M., 2005. Force measurements with the atomic force microscope: technique, interpretation and applications. Surf. Sci. Rep. 59, 1–152. Chen, W.T., Engel, P.A., 1972. Impact and contact stress analysis in multilayer media. Int. J. Solids Struct. 8, 1257–1281. Cross, S.E., Jin, Y.-S., Rao, J., Gimzewski, J.K., 2007. Nanomechanical analysis of cells from cancer patients. Nat. Nanotechnol. 2, 780–783. Costa, K.D., 2003. Single-cell elastography: probing for disease with atomic force microscope. Dis. Markers 19, 139–154. Derjaguin, B.V., Muller, V.M., Toropov, Y.P., 1975. Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53, 314–326. Dufrêne, Y.F., 2001. Application of atomic force microscopy to microbial surfaces: from reconstituted cell surface layers to living cells. Micron 32, 153–165. Evans, E., Rawicz, W., 1990. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett. 64, 2094–2097. Fukuma, T., Kimura, M., Kobayashi, K., Matsushige, K., Yamada, H., 2005. Development of low noise cantilever deflection sensor for multienvironment frequency-modulation atomic force microscopy. Rev. Sci. Instrum. 76, 0537041–053704-8. Gibson, C.T., Smith, D.A., Roberts, C.J., 2005. Calibration of silicon atomic force microscope cantilevers, Gibson. Nanotechnology 16, 234–238. Hertz, H., 1881. Uber den Kontakt elastischer Korper. J. Reine Angew. Math. 92, 156. Hochmuth, R.M., 2000. Micropipette aspiration on living cells. J. Biomech. 33, 15–22. Jackson, M.B., 2006. Biophysics. Cambridge University Press, 504 pp. Johnson, K.L., Kendall, K., Roberts, A.D., 1971. Surface energy and the contact of elastic solids. Proc. R. Soc. London A 324, 301–313. Landau, L.D., Pitaevskii, L.P., Kosevich, A.M., Lifshitz, E.M., 1959. Theory of Elasticity. Pergamon Press Ltd., Oxford, UK, 185 pp. Maugis, D., 1992. Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J. Colloid Interf. Sci. 150, 243–269. Mironov, V.L., 2004. Fundamentals of scanning probe microscopy. The Russian Academy of Sciences. Institute of Physics of Microstructures, Nizhniy Novgorod, 97 pp. Moloney, M., McDonnel, L., O’Shea, H., 2004. Atomic force microscopy of BHK-21 cells: an investigation of cell fixation techniques. Ultramicroscopy 100, 153–161. Plomp, M., McCaffery, J.M., Cheong, I., Huang, X., Bettegowda, C., 2007. Spore coat architecture of Clostridium novyj NT spores. J. Bacteriol. 189, 6457–6468. Radmacher, M., Fritz, M., Kacher, C.M., Cleveland, J.P., Hansma, P.K., 1996. Measuring the viscoelastic properties of human platelets with the atomic force microscope. Biophys. J. 70, 556–567. Rosenbluth, M.J., Lam, W.A., Fletcher, D.A., 2006. Force microscopy of nonadherent cells: a comparison of leukemia cell deformability. Biophys. J. 90, 2994–3003. Sader, J.E., Chon, J.W.M., Mulvaney, P., 1999. Calibration of rectangular atomic force microscope cantilevers. Rev. Sci. Instrum. 70, 3967–3969. Vadillo Rodriguez, V., 2004. Macroscopic and microscopic approaches toward bacterial adhesion. Dissertation in Medical Sciences, University of Groningen, 142 pp. Velegol, S.B., Logan, B.E., 2002. Contributions of bacterial surface polymers, electrostatics, and cell elasticity to the shape of AFM force curves. Langmuir 18, 5256–5262. Yao, X., Jericho, M., Pink, D., Beveridge, T., 1999. Thickness and elasticity of gramnegative murein sacculi measured by atomic force microscopy. J. Bacteriol. 181, 6865–6875.
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Nanomechanical analysis of Clostridium tyrobutyricum spores N. Andreeva a , D. Bassi b , F. Cappa b , P.S. Cocconcelli b , F. Parmigiani c , G. Ferrini a,∗ a
Dipartimento di Matematica e Fisica, Università Cattolica, I-25121 Brescia, Italy Istituto di Microbiologia, Università Cattolica, I-29100 Piacenza, Italy c Dipartimento di Fisica, Università degli Studi di Trieste, I-34127 Trieste, Italy and Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy b
a r t i c l e
i n f o
Article history: Received 1 May 2010 Received in revised form 12 July 2010 Accepted 12 July 2010 Keywords: Atomic force microscopy Clostridium tyrobutyricum spores Young modulus
a b s t r a c t In this work we report on the measurement of the Young modulus of the external surface of Clostridium tyrobutyricum spores in air with an atomic force microscope. The Young modulus can be reliably measured despite the strong tip-spore adhesion forces and the need to immobilize the spores due to their slipping on most substrates. Moreover, we investigate the disturbing factors and consider some practical aspects that influence the measurements of elastic properties of biological objects with the atomic force microscopy indentation techniques. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The investigation of mechanical properties of biological samples with atomic force microscopy (AFM) has received considerable attention in the past years (Radmacher et al., 1996; Rosenbluth et al., 2006; Cross et al., 2007). In addition to fundamental research interests, monitoring local mechanical properties of cells allows a better understanding of the mechanism of some diseases causing cell stiffness changes (Costa, 2003). The elastic properties of bacteria or cell walls can be determined by taking force curves using AFM, measuring the stiffness of the exterior cell surfaces by indenting them with a cantilever tip, achieving a lateral resolution of few tens of nm (Butt et al., 2005). Despite AFM force spectroscopy methods are well developed, there are situations in which the presence of adhesion, attraction or repulsion forces between tip and sample may results in the impossibility of retrieving information on the elastic properties of cell walls. In the literature there are examples of force spectroscopy applied to cell walls or soft samples in the absence of strong interaction between the tip and the surface. In this case soft cantilevers can be used for indentation studies without taking into account instabilities caused by jump-to-contact or force modulations due to the interactions between tip and surface. However, in the natural environment, the presence of strong adhesion to cell surface is often found (Vadillo Rodriguez, 2004; Dufrêne, 2001). In this situation, it is not clear if it is possible at all to obtain information on the local mechanical properties. Even if detailed theoretical descriptions of tip interaction in the pres-
∗ Corresponding author. Fax: +39 030 2406742. E-mail address: [email protected] (G. Ferrini). 0968-4328/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2010.07.006
ence of adhesion forces (Johnson et al., 1971; Derjaguin et al., 1975) have been devised, it is important to know if it is possible to obtain reproducible results in experiments. In this work, we demonstrate that the Young modulus of the external layer of spores of the anaerobic bacterium Clostridium tyrobutyricum (Andreeva et al., 2009) can be reliably measured in air despite the strong tip-spore adhesion forces and the need to immobilize the spores due to their slipping on most substrates. Moreover, we investigate the disturbing factors that influence the measurements of viscoelastic properties of biological objects with AFM indentation technique and consider some practical aspects of the elasticity investigation with AFM. 2. Materials and methods 2.1. Sample preparation C. tyrobutyricum ATCC 25755 (T) spores were used for AFM investigation. Spores were prepared according to the protocol described previously (Bassi et al., 2009). These spores have bad adhesion both to hydrophilic and hydrophobic surfaces, preventing investigation of their elastic properties by AFM without a proper strategy of sample immobilization. We avoided to use substrates covered with biological “glues” like polypeptides and aldehydeslike fixatives by glutaraldehyde since it is known that this kind of fixation could influence the elastic modulus of biological samples (Moloney et al., 2004; Braet et al., 1998; Velegol and Logan, 2002), Instead of this, we choose a mechanical immobilization technique. A drop of ∼3 l of spore suspension in water (1.8 × 107 ml−1 ) was put on polycarbonate Isopore DTTP (Millipore, USA) membrane and dried in air. During the drying process, spores partially fell
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into membrane pores immobilizing them inside the membrane. The correct size of membrane pores was approximately equal to the size of the spore coat (about 1.5 m), determined by preliminary AFM measurements of spores dried in air taken in non-contact mode. The polycarbonate is known to be an extremely stiff material (e.g. see the “polycarbonate” article on www.wikipedia.org), with Young modulus of the order of few GPa, so that the membrane elastic compliance do not alter the force curves taken on the spores. 2.2. Instrumentation All measurements were carried out with an AFM (NT-MDT, Russia), working in contact mode to measure samples topography, immediately before taking force curves. We use contact mode silicon nitride cantilevers CSC 17 with nominal spring constant of 0.15 N/m and tip curvature radius of 10 nm (MMasch, Lithuania). The spring constant kc of the cantilever was determined by the Sader method (Sader et al., 1999), implemented in AFM software, obtaining kc = 0.14 N/m. The estimated error of spring constant calibration with Sader method is 5% (Gibson et al., 2005). The cantilever deflection during force curves is monitored by the offset current from the quadrant photodiode, which is correlated to the calibrated piezotube extension. The deflection calibration of the cantilever (deflection sensitivity calibration) is done on a hard surface, assuming a negligible indentation and thus equal distances spanned by the cantilever tip and the piezotube. As test surface we used highly oriented pyrolitic graphite (HOPG). In our point of view, HOPG is an ideal substrate for the cantilever deflection calibration due to its inertness and hydrophobicity, avoiding a significant influence of the surface water layer on the calibration. To prevent damaging of the cantilever tip and to fulfill the assumption of linear elasticity theory, the range of cantilever deflection during calibration did not exceed the value of the tip curvature radius. It is important to consider the influence of changes in the sensitivity of the AFM optical beam deflection system on viscoelastic measurements. Fig. 1 shows a scheme of a standard AFM optical beam deflection system. The displacement of the laser spot on the photodiode a related to the cantilever displacement z as (Fukuma et al., 2005): a = 3(s/l)z, where l and s are the effective cantilever length and the distance between the tip and photodiode, respectively. Note that the position of the laser beam spot influences both the cantilever effective length l and the measured cantilever displacement z. Moreover, the change of the cantilever length is not proportional to the change of the cantilever displacement, as far as the cantilever bends in the force gradient acting near the sample surface (Mironov, 2004). This means that changing of
the laser beam spot position on the cantilever alters the calibration of the cantilever deflection sensitivity and care must be used during measurement regarding the stability of laser alignment. 2.3. Indentation geometry and force–displacement relations When the surface of a biological object is deformed by the pressure exerted by the tip of an AFM cantilever, the amount of displacement with respect to the undeformed surface (the indentation) carries information on its elastic properties. The deflection of the cantilever as its tip indents an object is usually described with models of linear elasticity theory (Landau et al., 1959). The predictions from these approximate models are accurate when the linear dimensions of the contact area between bodies upon deformation is small in comparison with the sizes of the bodies. This restriction poses strict limitations on the depth of the indentation made with the cantilever tip on soft samples. The geometry which is frequently used for calculation of elastic properties of biological objects is the contact problem between a sphere and a semi-infinite plane (Hertz, 1881). In the case of an infinitely stiff sphere of radius R that indents a plane, the loading force F depends on the indentation ı as: F = ı3/2 (2/3) (E/(1 − 2 )) R1/2 , where E is the Young’s modulus and is the Poisson ratio of the indented material. According to this model the value of the indentation should not be more then the curvature radius of the (spherical) cantilever tip and the thickness of the isotropic layer under indentation. Using a conical geometry of the indenter (Radmacher et al., 1996), with a cone opening angle ˛, the loading force depends on indentation as F = ı2 (/2) (E/(1 − 2 )) tan ˛. The two indenter geometries describe distinct physical situations. When indentation is comparable or smaller than the radius of curvature of the cantilever tip, the interaction is well described by a spherical indenter on a flat surface. Instead, when indentation is greater than the radius of curvature of the cantilever tip, then the conical shape of the indenter has much more influence on the contact area than the tip radius of curvature. In this situation, a better description of the interaction is given by the conical indenter geometry, where the tip is considered to be point-like in comparison with the size of the indenter. The proper application of the contact problem demands preliminary knowledge about the morphology of the biological object under investigation. For example, knowing that the thickness of the cell wall is varying in the range of 10–50 nm (Jackson, 2006), it is correct to apply the model with conical geometry only assuming that the cell content beyond the cell wall is isotropic and has the same elastic properties of the cell wall. On the other hand, the spherical symmetric indenter describes well the tip–surface interaction when indentation lengths are less than the tip curvature radius (i.e. few nanometers). Otherwise it is necessary to solve the contact problem numerically in the assumption of finite thickness layers (Chen and Engel, 1972). 3. Results 3.1. Measurements of elastic properties by force spectroscopy curves
Fig. 1. Scheme of the AFM optical beam deflection system: a—displacement of the laser spot on the photodiode; z—cantilever displacement; l—effective cantilever length; s—distance between the tip and photodiode.
The cantilever deflection measures the force exerted on the sample by the cantilever tip. The dependence of the cantilever deflection on the piezotube extension is called a force curve. In a single force spectroscopy measurement, two main parts could be distinguished, that convey different physical information, the approach curve and the retraction curve. Below we comment on the approach and retraction force curves taken on C. tyrobutyricum spores, shown in Fig. 2. An approach curve can be approximately
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Fig. 2. Approach and retraction force curves taken on Clostridium tyrobutyricum spores. On the inset: an approach curve divided into the following parts. (1) Free cantilever, far from the surface, in the absence of force gradient. (2) The cantilever is subject to attractive forces, often causing the so-called “jump-to-contact” regime, a known mechanical instability of the cantilever that can be avoided choosing a sufficiently stiff cantilever. (3) Intermediate regime between long and short-range surface forces, it is the most complicated part from the analytical point of view. (4) Short-range surface forces dominates. (5) Contact regime, where adhesion can be considered negligible.
divided into five main parts (refer to the numbering in the inset of Fig. 2): (1) corresponds to a free cantilever which is far from the surface in the absence of force gradient; (2) describes the cantilever while attractive forces act on it, often causing the so-called “jump-to-contact”; (3) gives an idea on intermediate case between long and short-range surface forces and it is the most complicate part from the analytical point of view; (4) represents the action of short-range surface forces; (5) is the contact part of the curve, where adhesion could be considered negligible. In the absence of strong interaction between the cantilever and the sample, caused for example by adhesion or high humidity, the retract curve (dotted line in Fig. 2) precisely reproduces the approach curve. This ideal situation is almost never realized in practice. According to Fig. 2, two main differences between approach and retraction force curves could be highlighted. First, a slight hysteresis between approach and retract curves could be noticed in the contact part (known as loading–unloading hysteresis, Butt et al., 2005). This difference can be explained by the plastic and/or viscoelastic deformation of the sample or by a friction mechanism. We exclude the possibility of piezo hysteresis because the piezo elongation is monitored independently by capacitive sensors. The AFM cantilever is tilted typically by 7–20◦ with respect to the sample surface to prevent touching the sample with the cantilever base instead of tip when approaching the sample. The cantilever tilt causes the tip to slip in the longitudinal direction during loading. In the retract curve the tip slides over the sample surface and bends due to the friction forces, causing the hysteresis between the contact parts of the approach/retract force curves. Since the kind of hysteresis observed is similar in all the force curves taken in different points of the samples, the influence of friction is the probable cause of the hysteresis seen in the experimental data. Second, the adhesion part of the force curve on approach and retraction curves is different. On the approach curve adhesion provokes the tip “jump-to-contact”. This instability takes place when the gradient of attractive surface forces exceeds the spring constant of the cantilever. On the retraction curve the adhesion keeps the tip in contact with the surface until the retracting force exceeds the adhesion force. It also should be noted that adhesion force strongly changes from point to point on the sample surface. Since it appears
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that approach curves are reproducible experimentally, even when a great variability in retract curves is present, it makes sense to analyze elastic properties of the sample through data acquired during approach. The next step of the elastic properties investigation with AFM is the correct interpretation of the data from an approach curve. For force curves analysis taken on biological samples it is convenient to apply the Hertzian approach due to its simplicity. However, this mechanical model predicts correct results only for a contact problem in the absence of adhesion. In practice almost all biological samples have an adhesion to the AFM tip. To take into account adhesion, models that describe the situation in two limiting cases of short- and long-range surface forces have been developed. The Johnson–Kendall–Roberts (JKR) model (Johnson et al., 1971) gives a solution to the contact problem with adhesion when surface forces are short range in comparison to the elastic deformation they produce (as in the part of the approach curve marked with (4) in the inset of Fig. 2). The Derjaguin–Muller–Toropov (DMT) model (Derjaguin et al., 1975) treats well the contact problem with adhesion when surface forces are long-range (part (2) of the approach curve). The general solution of the contact problem in the presence of adhesion demands a numerical simulation or cumbersome equations from Maugis theory (Maugis, 1992) (part (3) of the approach curve). All these models were developed with the assumptions of normal cantilever load and in the absence of lateral forces. In practice, experimental force curves are greatly influenced by lateral forces, and the condition of normal applied load is not always satisfied due to topographical features of the sample. Thus, even the results from complicated and thorough models often are greatly affected by experimental errors which could not be eliminated. So, for the sake of simplicity, it is preferable to use the simpler Hertzian approach, but it is necessary to determine correct conditions for its application. 3.2. Measurements of the Young modulus of the outer surface of C. tyrobutyricum spores After calibrating the AFM deflection sensitivity on HOPG, we carried out the measurements of the elastic properties of C. tyrobutyricum spores immobilized on Isopore DTTP membrane (see Section 2.1). Previous studies have shown that C. tyrobutyricum spores consist of a dark spore core, surrounded by a dense cortex transparent to electron beams in transmission electron spectroscopy and a multilayered spore coat (Plomp et al., 2007). Many clostridia have spores surrounded by large portions of amorphous and soft material, the exosporium. This can take a large volume around the spores, in many cases more than 100% of the spore volume itself (Plomp et al., 2007). To determine the spore distribution on Isopore DTTP membrane we acquired the topography of our samples in contact mode. According to preliminary images of C. tyrobutyricum spores, we found that spores are covered with a soft and very reactive material, as expected. To prevent damaging the sample and the contamination of the cantilever, we acquired images in contact mode and under low loading force, using the deflection signal from the photodiode as a feedback signal. The loading force was gradually increased and the topography was acquired with the smallest force needed to avoid significant image distortions. The value of the force applied to the cantilever during scanning was 0.70 nN. The elastic properties of C. tyrobutyricum spores were measured on the area above the coat and on the spore “tail” formed by the external amorphous material. The points where the force curves have been acquired are shown in Fig. 3. In each zone we acquired 9 points to estimate the possible range of Young’s modulus values. To avoid the influence of cantilever deformations during repeated spectroscopy, we per-
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Fig. 3. (a) Topography of Clostridium tyrobutyricum spores distributed on Isopore DTTP membrane taken with AFM in contact mode. Membrane pores are shown with white arrows and spore core with its surrounded coat (Co) and exosporium (Ex) are indicated. The force curves have been acquired on the points shown by the square grids of numbers on the spore core and exosporium. (b) The error signal is displayed to underline topographic features of Clostridium tyrobutyricum spore. (c) Topographic profiles along the horizontal lines of the grids on the top of the spore coat and exosporium tail. The points indicate where spectroscopic measurements have been taken.
formed the measurements slowly (a measurement, approach and retraction force curves, takes several seconds). To determine the initial conditions to apply the Hertz model, we used the following procedure. The zero-deflection reference of the cantilever is set when it is far from the surface and no forces act on it. No hysteresis between approach and retract force curves in the zero-deflection level is observed. Near the surface, in the presence of long-range attractive force and liquid meniscus, the tip “jumps” into contact and the deflection of the cantilever becomes negative (downward deflection). Actually, the point with greatest negative deflection corresponds to the contact point; in this point the surface acts on the cantilever forcing it to press the sample and possibly to indent it. Further approaching leads to decreasing the attractive forces and increasing the repulsive forces acting on the tip. At some point, the attractive and repulsive forces are balanced and the cantilever deflection becomes equal to zero, i.e. its deflection is equal to the cantilever deflection when it is far away from the surface, defining the zero-deflection point in Fig. 2. The initial conditions to apply the Hertz model are determined in this point. We assume that at the zero-deflection level the indentation is zero. Even though the “zero-deflection level” point belongs to the part of the force curve
described by the JKR model, due to the reproducibility of the results, we are led to conclude that, even in the presence of strong adhesion, which is true for most biological samples, attractive forces do not have a strong influence on the cantilever indentation after it reaches the zero-deflection level. Moreover, it is evident that the force curve between the contact point and the zero-deflection point, which is actually provoked by adhesion forces, is relatively small on the approach curves compared with the same part on the retraction curve. In Fig. 4 we show a sample of force curves and loading force versus indentation for four experimental points, chosen to demonstrate all the possible range of differences between approach and retraction curves observed experimentally. For each force curve we determined the dependence of loading force and indentation on piezomovement. We calculated the indentation as a difference between contact parts of force curve taken on HOPG and those taken on spore (at constant piezo height). Loading force was calculated as a product of cantilever deflection and k-constant of the cantilever, determined by the Sader method. Then for each force curve we reconstructed the dependence of loading force versus indentation. The experimental loading force curves were
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Fig. 4. Force spectroscopy measurements obtained in four points shown in Fig. 3 as 2, 3, 4, 6 on the spore coat (Co), to demonstrate the possible variations between approach and retraction curves. In each graph is reported the specification of the point where the spectroscopy has been measured. On the right, there are the results of fitting experimental data with spherical and conical indenters.
fitted with the analytical functions reported in Section 2.3 with the Young’s modulus as the only fitting parameter. As usual in biological contact problems (Butt et al., 2005), we set the Poisson ratio to 0.5, as for water and other incompressible materials. The fitting results are presented in the right column of Fig. 4, assuming a tip curvature radius of 10 nm and an aperture angle of 40◦ . The initial conditions (after jump-to-contact) are chosen so that at zero-deflection (i.e. no force applied on the cantilever) the tip do not indent the sample. In this case a good fitting of experimental data with the spherical indenter geometry is achieved, while the conical indenter geometry gives evidently unacceptable
results. Good reproducibility of Young’s modulus determination with the spherical indenter model allows us to conclude that, even in the presence of strong adhesion, it is possible to retrieve elastic modulus of the upper layer of biological samples. The error from the fitting procedures on the Young’s modulus (reported in the figures only for the spherical indenter model) are small, indicating that this model is well suited to describe the experimental data. These results are in agreement with the previous discussion, indicating that the conical geometry is better suited to describe indentations larger that the tip radius of curvature (typically 10 nm) while the spherical indenter geometry is better suited
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Table 1 Value of Young’s modulus determined with the spherical indenter model on the coat and exosporium.
Young’s modulus, MPa
Coat
Exosporium
26 ± 8
44 ± 20
for indentations smaller than the tip radius of curvature, as in our case. The values of the Young’s modulus have been averaged over 9 points on the top of the spore above the coat and on the area of the exosporium “tail” (see Fig. 3) and reported in Table 1. The exosporium Young modulus can be influenced by either the substrate stiffness or the stiffness of the internal structure of the spore. While we exclude an influence of the polycarbonate millipore substrate, that is so much stiffer than the spore structures to be considered as indeformable (see previous observations in Section 2.1), the same cannot be taken for granted for the internal structures as the core. In the literature, to analyze the spore coat architecture of other types of clostridia similar to that studied here, the exosporium is removed by physical means using, for example, a French press treatment; applying a pressure of 120 MPa to a water suspension of clostridia spores, it is possible to strip them of their amorphous exosporium (Plomp et al., 2007). In this case, only 15% of the treated spores appear to have damaged internal structures, showing that the coat is resistant under pressures much higher than those used in this experiment, that are in the range of tens of MPa (i.e. one tenth of the pressure applied by the French press during the exosporium stripping process). On these basis, we suggest that the measured Young modulus in different parts of the dried exosporium is related to the exosporium different biological conditions, such as water content, proximity to different structures and so on, and only in minor degree the Young modulus is influenced by the compliance of internal structures, that appear to be capable of withstanding much higher pressure. While the choice of a particular tip do not influence the agreement between the theoretical and the experimental curve, to obtain a quantitative estimate of the Young’s modulus from the experimental data it is necessary to know the tip radius R for the spherical indenter model and the aperture angle ˛ of the conical tip for the conical indenter model. These parameters (R = 10 nm and ˛ = 40◦ ) have been taken from the manufacturer data, and the estimated uncertainty of 30% must be considered when estimating the uncertainty on the absolute value of the Young’s modulus. The errors reported in the table represent the dispersion of the experimental data and take into account the uncertainty on the tip parameters (R or ˛). Fig. 5 shows the theoretical dependences of loading force on indentation for both models in the range of 1–100 nm. When the indentation is lower than 20 nm, for the same loading force, the value of indentation for the spherical geometry is bigger than for conical geometry. This explains the lower Young’s modulus values predicted by the spherical indenter for indentations below 20 nm. On contrary for values of indentation bigger than 20 nm the conical indenter gives bigger indentation for the same loading force. Note that smaller values of indentation allow achieving better lateral resolution in the elastic properties measurements. In fact, if the value of sample indentation exceeds the tip radius of curvature, the measured elastic properties of the object are not determined only by a vertical compression of the sample and are not described in the framework of linear elastic theory. Moreover, in this case, lateral forces, arising from a bigger area around the point of contact, will significantly influence the results of measurements and the lateral resolution will be decreased due to an increased effective contact area.
Fig. 5. Theoretical dependences of loading force on indentation for spherical and conical geometries in the range of 1–100 nm.
4. Discussion 4.1. Which viscoelastic properties does AFM measure? All living cells, prokaryotic and eukaryotic, consist of a nucleus and different organelles immersed in a liquid cell matrix, the cytoplasm. All these internal cell structures are surrounded by the plasma membrane that encloses their contents and serves as a semi-porous barrier to the outside environment. The plasma membrane is composed of a double layer (bilayer) of lipids, more precisely described as phospholipids. In bacteria, the plasma membrane is an inner layer of protection since a rigid cell wall made up of peptidoglycan forms the outside boundary. Moreover, the bacterial spore produced by Clostridium species has a more complex structure; it is composed of a central core, which is surrounded by various protective layers. The outermost layer is the exosporium which is the primary site of contact with the environment; it is apparently formed by a single collagen-like glycoprotein, whereas the basal layer is composed of a number of different proteins in tight and loose associations. Below this is the spore coat which is made up of highly cross-linked keratin and layers of spore-specific proteins. The innermost spore cell, the core, is surrounded by the cortex of loosely cross-linked peptidoglycan and contains the components of the vegetative bacterial cell (the cell wall, cytoplasmic membrane, cytoplasm, DNA, ribosomes, etc.) Analyzing a biological model like a cell, the first structure indented with an AFM cantilever tip in force spectroscopy measurements is the cell surface. In case of plasma membrane the thickness is often no more than 10–20 nm, while when we deal with bacteria the thickness of cell wall range from 5 nm to 80 nm. According to measurements with micropipette method of phospholipids membrane, values of stretching elastic modulus vary in range of 0.135–0.19 N/m (Evans and Rawicz, 1990), that corresponds to Young’s modulus values in the range of 27–38 MPa for a 5 nm thick membrane. Measurements of elastic properties of Escherichia coli sacculi dried in air with AFM give a Young’s modulus of 300–400 MPa (Yao et al., 1999). On the other hand, measurements of the elasticity of a cell as whole with other methods like micropipette aspiration, optical tweezers, microplates and others, give a cell elasticity modulus of the order of 10 Pa to 100 kPa (see for example, Hochmuth, 2000). Thereby, the elastic properties determined with AFM force spectroscopy depends on the experimental conditions and indentation depth.
N. Andreeva et al. / Micron 41 (2010) 945–952
Fig. 6. (a) Small indentations with AFM tip allow to measure the elastic properties of the cell wall itself, while (b) under indentations greater than the cell wall thickness, force curves are influenced by the underlying structures of the cell.
In the case of small indentation, less then the thickness of the cell wall, we have a contact problem in which spherical geometry is a good approximation and the retrieved Young’s modulus corresponds to the elastic properties of the cell wall, with values most likely in the range of tens of MPa (see Table 1). For indentation greater than the cell wall thickness, force curves are influenced by the underlying structures (Fig. 6) and in this case the conical indenter model is more adequate. However, if the membrane underlying
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structures have different elastic properties, it is necessary to introduce a finite layer approach (Chen and Engel, 1972). Considering the Young’s modulus retrieved with a conical indenter model, in the case of a membrane with an isotropic cell content, its value will be in the kPa range (Radmacher et al., 1996), representing the elastic properties of the whole cell. Moreover, a big indentation often is not admissible for biological samples, because of high pressure surface damage and because biological surfaces are usually very reactive and the risk of cantilever contamination is high under big indentations. 4.2. What happens when the tip of the cantilever becomes contaminated? To assess the influence of tip contamination on force spectroscopy curves, we used first the HOPG monoatomic steps as a calibration for the tip sharpness. The image of HOPG shown in Fig. 7a are obtained with an uncontaminated tip, showing the error signal to enhance the finer details. After scanning the sample of C. tyrobutyricum spores, we acquired a HOPG topography, shown
Fig. 7. Topography of HOPG obtained with the error signal before (a) and after (b) tip contamination; (c) force spectroscopy curves acquired with contaminated tip; (d) measurements of elastic properties with AFM could be represented as a determination of the sample spring constant k2 from known value of the cantilever spring constant k1 . In case of contaminated tip, the contamination could be considered as an additional spring with unknown spring constant k3 added to the sample-cantilever spring system. Thus, it becomes impossible to determine the proper value of the sample spring constant using data from force spectroscopy measurements.
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in Fig. 7b. In this case the edges of the HOPG steps are wider and in some cases are doubled, due to tip contamination. Force spectroscopy curves acquired using a contaminated tip are shown in Fig. 7c. Comparison of two force curves on HOPG sample before and after tip contamination shows that the slope of the curve is the same for both curves in the contact region. However, in the adhesion region the “jump-to-contact” is less sharp with the contaminated tip. Considering the force curves acquired with the contaminated tip both on the spores and on HOPG, it results that the measured Young modulus is the same for both samples, a result that can be explained by a modified cantilever k-constant due to tip contamination, as shown in Fig. 7d. 5. Conclusions The measurement of elastic properties via AFM force curves demands a stable optical beam deflection system and a correct choice of the model to interpret the contact problem. The choice of the theoretical model for the interpretation of the experimental results relies on preliminary knowledge of the sample morphology and surface structure. In this work we investigated the elastic properties of C. tyrobutyricum spores, in the presence of high adhesion forces. Using a small indentation range, comparable with the size of the cantilever tip, we found that the Young modulus of the spore surface is independent on the topography and that the underlying spore‘s structures do not influence the upper layer elastic response. The determined values of C. tyrobutyricum spores Young moduli are in the range of 25 MPa for the spore’s coat and 42 MPa for the exosporium, which is in good agreement with the theoretical estimation of the area-stretching elastic modulus for lipid bilayer based on the free energy theory and experimental results for cell walls Young’s modulus obtained with other techniques. Acknowledgement This work has been partially funded by Fondazione Cariplo. References Andreeva, N., Ferrini, G., Bassi, D., Cappa, F., Cocconcelli, P.S., Prato, S., Troian, B., Parmigiani, F., 2009. Preliminary results of combined scanning near-field optical microscopy and atomic force microscopy applied to a model biological system: Clostridium tyrobutyricum spores. Boll. Geof. Teor. Appl. 50, 396. Bassi, D., Cappa, F., Cocconcelli, P.S., 2009. A combination of a SEM technique and X-ray microanalysis for studying the spore germination process of Clostridium tyrobutyricum. Res. Microbiol. 160, 322–329.
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