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Microrheology of keratin networks in cancer cells To cite this article: T Paust et al 2013 Phys. Biol. 10 065008
View the article online for updates and enhancements.
- Physics of Cancer: Intermediate filaments and nuclear deformability during matrix invasion C T Mierke - Physics of Cancer: Initiation of a neoplasm or tumor C T Mierke - Active microrheology with optical tweezers: a versatile tool to investigate anisotropies in intermediate filament networks T Neckernuss, L K Mertens, I Martin et al.
Recent citations - Oliver Jahnel et al - Active microrheology with optical tweezers: a versatile tool to investigate anisotropies in intermediate filament networks T Neckernuss et al - Discrimination Between Cervical Cancer Cells and Normal Cervical Cells Based on Longitudinal Elasticity Using Atomic Force Microscopy Xueqin Zhao et al
This content was downloaded from IP address 142.132.1.147 on 18/11/2018 at 05:00
IOP PUBLISHING
PHYSICAL BIOLOGY
doi:10.1088/1478-3975/10/6/065008
Phys. Biol. 10 (2013) 065008 (5pp)
Microrheology of keratin networks in cancer cells T Paust 1 , S Paschke 2 , M Beil 3,4 and O Marti 1 1 2 3
Department for Experimental Physics, University of Ulm, D-89069 Ulm, Germany Department of Surgery, University of Ulm, D-89075 Ulm, Germany Department of Medicine I, University of Ulm, D-89081 Ulm, Germany
E-mail: [email protected]
Received 7 June 2013 Accepted for publication 1 October 2013 Published 4 December 2013 Online at stacks.iop.org/PhysBio/10/065008 Abstract Microrheology is a valuable tool to determine viscoelastic properties of polymer networks. For this purpose measurements with embedded tracer beads inside the extracted network of pancreatic cancer cells were performed. Observing the beads motion with a CCD-high-speed-camera leads to the dynamic shear modulus. The complex shear modulus is divided into real and imaginary parts which give insight into the mechanical properties of the cell. The dependency on the distance of the embedded beads to the rim of the nucleus shows a tendency for a deceasing storage modulus. We draw conclusions on the network topology of the keratin network types based on the mechanical behavior.
1. Introduction
the role of keratin networks in this disease and focus on the nanomechanical properties of the keratin cytoskeleton. In general, two different approaches lead to these properties: in vivo measurements of the mechanical properties of the extracted cytoskeleton and measurements of in vitro assembled protein networks. Both approaches have different advantages that shall be discussed briefly. As a top-down approach with the extraction of the keratin cytoskeleton from whole cells [7], the original architecture of the keratin network is conserved. Other parts of the cell, like membrane, organels, actin, microtubuli, etc are removed during the preparation process. Consequently, the mechanical properties of the keratin cytoskeleton can be investigated without any environmental influence. Afterwards the local network topology is determined by SEM [8]. The bottom up approach contains the in vitro assembly of proteins to the intermediate filament network. Since the cytoskeleton of the cell fulfils several special tasks independently [9], it is reasonable to analyze those part of the cytoskeleton as an isolated functional module. This work focuses on the top-down approach where the mechanical properties of the intermediate filament network is investigated.
The active and passive mechanical performance of a cell acting as the smallest biological unit able to move, survive and replicate independently has been of much interest. Most importantly, the motility of malignant cells is an important prognosticator in cancer [1]. The cells movement and response to external mechanical stimuli is a complex process mainly determined by its cytoskeleton. The cytoskeleton is a protein network extending from the cell membrane to the nucleus and filling large parts of the cytoplasm. It mostly consists of three different types of protein fibers: actin filaments, microtubuli and intermediate filaments [2]. Actin filaments, with a persistence length of about 15 μm, are responsible for the movement and deformability of the cell. The stiffer microtubuli, with a persistence length of several millimeters, are responsible for dynamical shape remodeling, which leads to a change in cell motility [3]. Intermediate filaments are more flexible with a persistence length between 500 and 1000 nm [4] their function appears to be to provide the mechanical stiffness and stability of the cell [5]. Thus, they are hypothesized to be the ‘stress-buffering-system’ [6] of cells. Because of the lack in knowledge about the role of keratin networks, we try to further improve the understanding of 4
2. Theoretical aspects Microrheology is a suitable tool for measurements of the mechanical properties of both the extracted cytoskeleton and
Author to whom any correspondence should be addressed.
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1
© 2013 IOP Publishing Ltd
Printed in the UK & the USA
Phys. Biol. 10 (2013) 065008
T Paust et al
of in vitro assembled keratin networks. The possibility to measure over an extended range only by observing thermal fluctuation is an advantage over the traditional measurements [10]. In our model micron-sized spherical beads, act as probes which scan their environment driven by the thermal forces (Brownian motion) dependent on the viscoelastic behavior of the surrounding network. By means of particle tracking the Brownian motion of several beads can be detected over a wide range of frequencies with a high accuracy in resolution (down to 5 nm [11, 12]). The calculation of the mean squared displacement (MSD) is a necessary step for the derivation of the complex shear modulus. The unilateral Laplace transformation relates the MSD with the dynamic shear modulus. Since an exact conversion is not possible due to the lack of an infinite amount of data points, an approximation of the transformation was previously applied to the MSD [13–15]. These methods are optimized for data which is smooth or flattened. In our case the usage of either [13] or [14] led to an insufficient accuracy of the dynamical shear modulus. Alternatively, the usage of a first principle model to fit the MSD was preferred. This first principle model bases on physical considerations which results in a model-based approach of the MSD. Therefore, the usage of analytical functions fitted to the MSD leads to an exact conversion to the dynamic shear modulus. Consequently, general statements about network dynamics are possible. It was shown that results of one-point microrheology compared to two-point microrheology do not differ in systems of assembled proteins and the relatively simple one-particle technique is sufficient to probe the bulk rheological properties of the medium [16, 17]. In our studies we use the single-particle technique which enables to measure for longer times because of smaller screen sizes. The Brownian motion in this model-based method can be described by a model that consists of a linear combination of three terms. In the case of microrheological data it is sufficient to include the time-dependent motion of the particle (MSD) governed by the system’s viscosity (B · t ), by the elasticity (A) and by the spatial confinement of the particles’ diffusion inside the networks’ meshes C·(1 − e−t /τ ). The elasticity is described by a constant value. This is based on a particle motion which is elastically bound in the network. The system’s viscosity can be described by the motion of the meshes the particle is placed in. The third part assumes the particle being in a mesh with a free Brownian motion until it hits the mesh. Then it bounces back elastically to the inside of the mesh (figure 1). The sum of the three parts is fitted to the MSD leading to function f f = A + B · t + C · [1 − exp(−t/τ )].
(A)
(C)
Figure 1. Illustration of the three parts for the model-based fitting function. In this first principle modeling the properties of the medium are considered for the particle motion. This motion is governed by the systems elasticity (A), viscosity and flow properties (B), and the spatial confinement of the meshes (C).
the real parameters E = exp(e), B = exp(b), C = exp(c), and τ = exp(−d). All subsequent steps such as the unilateral transformation and the calculation of the complex shear modulus are based on the fitted model (equation (2)) and the logarithmic coefficients.
3. Setup and materials For the measurements the movements of micro-beads (diameter 1 μm, Cat No. 4009A, Thermo Fisher Scientific, Waltham, MA, USA) were recorded with a microscope equipped with an oil immersion objective (CFI Apo TIRF 100XH, numerical aperture 1.49, Nikon, Tokyo, Japan) and a CCD camera (MotionX Pro 4, Imaging Solutions, Regensdorf, Switzerland) with a frame rate of 5 kHz. The motion was tracked by a MATLAB script [12] with an optical resolution of 5 nm and analyzed with further custom-built scripts of MATLAB and Mathematica. Living carcinoma cells incorporated the beads via phyagocytosis and embedded them into their cytoskeleton. After the extraction of the cell the keratin network, the nucleus and the incorporated beads remained. For further details on the extraction of the cell we refer to Beil et al 2003 [7]. For the achievement of a low uncertainty of the resulting data, numerous measurements were performed. The number of tracked particles in the network exceeded 980, which leads to approximately 80 particles per distance to the nucleus. Every cell included around five particles resulting in measurements at 190 cells. This ensures that the mechanics of intracellular keratin networks with a relatively high validity was achieved by measuring.
4. Measurements
(1)
The extracted cell consists of the nucleus and the intermediate filament network. In the case of pancreatic carcinoma cells of line Panc-1, the network is based on the assembly of human keratin 8 and 18 [7]. The density of the network is dependent on the distance to the rim of the nucleus (figure 2). The beads incorporated in the network are located in different distances to the nucleus. Therefore it is possible to cover the complete range of distances for the determination of the dynamic shear modulus. Since every cell network is arranged slightly different, a high number of measurements are necessary to gain reasonable results.
The fitting of equation (1) to experimental MSD data yields values for the parameter A, B, C and τ . To increase the numerical stability of fitting and to ensure a unique fitting result, a modified fitting function was used for the characterization of the MSD. This function f fit is described by ffit = E + B · t − C · exp(−t/τ )
(B)
(2)
with A = E − C. Fitting parameters are all positive numbers. To enforce this the actual fit was done with the logarithms of 2
Phys. Biol. 10 (2013) 065008
(A)
T Paust et al
and therefore the plateau value appears higher. A Fax´en’s law correction applied to the motion can correct the overestimated value. The local minimum at 2 μm indicates a lower density of the network. Up to 4 μm distance the plateau modulus exhibits a global maximum of 0.65 Pa. For larger distances the plateau decreases to a global minimum of 0.2 Pa. In between the global maximum and the minimum a monotone decrease of the shear modulus is observed. This decrease can be related to a reduced stiffness of the network dependent on the distance. An exemplary cell displayed in the inset of figure 2 shows this fact (B). The local minimum can be explained by a disassembly of the network of the living cell. This behavior was shown by W¨oll et al [20]. The global maximum is reached because of a pushing of the intermediate filament network towards the center of the cell—the cell nucleus. Hence, a shielding of the nucleus is a result of the formation of this dense network. For large distances the network becomes softer until the distance when the network is assembled is reached. The increase to 0.51 Pa at a distance of 12 μm can be explained by the influence of the surface during the measurement. The larger the distance, the lower the network is and therefore the more influence of the substrate is observed. The high value of uncertainty for large distances show, especially in this range, that the network varies a lot for every examined cell although numerous cells were observed. Beside the mechanical properties the determination of the network morphology was investigated. By means of the surface of equal probability of the particle motion the spatial direction of the network was analyzed. For this the particles positions during the motion in the network were used to determine a surface which spans over a specific volume. Therefore a three-dimensional histogram of the positions was calculated which is described by a N × N × N array. Each entry shows how likely the particle moved to this position. The surface of equal probability is the surface contouring all entries with the same probability (for more details the authors refer to [21] and the MATLAB documentation). For a low probability of zero percent, the highest distance of the particle’s positions are covered by the surface, because there the probability approaches zero. Thus, at a chosen probability value of 50 percent, the positions of a higher probability are included. The geometry of the observed surface of equal probability gives an idea about the likelihood of the motion of the particle. This geometry can be related to the confinement geometry and the network’s morphology. Additionally, with this method a classification of the network type—entangled or cross-linked—can be derived [22]. As the network acts like a spring mass system, the occurring repelling force influences the motion of the particle in such that the surface of equal probability approaches an ellipsoidal shape. The calculation of the averaged semi-principal axes in dependency on the density can be used to gather an estimation value for the directionality of the network for this type of cells. A coordinate transformation was considered for the calculation of the surface of equal probability and its semiprincipal axes. In that way the radial, tangential and vertical components in a cylindrical coordinate system with the cell nucleus as center is regarded.
(B )
(C )
Figure 2. Electron microscope image of extracted pancreatic cancer cells. The remaining cell nucleus builds the center of the intermediate filament network (A). The higher the distance to the rim of the nucleus, the lower is the density of the network (B). The beads of 1 μm diameter were embedded in the network via phagocytosis. The positions of the particles cover the complete range of the intermediate network (C). Thus, the local elasticity and viscosity can be measured via the particles’ thermal motion. Since the extraction process removed all cellular components apart from intermediate filament network and nucleus, the mechanical properties of the intermediate filament network can be determined.
Figure 3. Plateau modulus dependent on the distance to the rim of the modulus. The values of G0 were of a frequency of 1 Hz when all observed curves reached a slope of zero. The plateau loss modulus G0 was determined at the same frequency. The distances shown are up to 12 μm. For higher distances the amount of measured particles was too low for a reasonable result.
The extracted cell is assumed to be gel-like viscoelastic [18]. For this case the storage modulus builds a plateau dependent on the viscous and elastic properties of the network [19]. The plateau modulus is used to compare the measurements of particles at specific distances. Furthermore, the loss modulus shows a decrease in value, until at specific frequency a minimum is reached. The shown plateau was determined at a frequency of 1 Hz (figure 3). At a distance of 1 μm the plateau reaches a value of 0.5 Pa, which decreases to a local minimum of 0.3 Pa at 2 μm. The plateau at short distances is governed by the nucleus of the cell. The particle motion in this region is limited by the nucleus 3
Phys. Biol. 10 (2013) 065008
T Paust et al
the cell. This causes an important step in the development of more aggressive cancer, e.g. in case of CRC (colorectal cancer), associated with a shorter patients’ survival [26]. The calculation of the surface of equal probability gives additional insight of how the shape of the confinement can be assumed and also helps to gather the semi-principal axes of the fitted ellipsoids. In that way, a preferred direction of the particle motion can be revealed. In the end it can be shown how inhomogeneous or stressed the networks are. This leads to a hint that a force exerted at the rim of the intermediate filament network is guided towards the nucleus in a channel. Hence, in our opinion the studies provide important information about the spatial organization of keratin networks. In an ongoing study measurements on different substrates are performed. As a result a similar behavior in distance dependency is expected whereas the absolute values of the plateau moduli will differ for every substrate as well as the stiffness of the keratin network.
Figure 4. Calculated semi-principal axes for the surfaces of equal probability with a probability value of 70%. The contribution of the radial motion towards the overall motion of the particle is smaller compared to the perpendicular directions. This indicates an inhomogeneous intermediate filament network with pre-stressed filaments in radial direction.
Acknowledgments
The dependency on the distance to the rim of the nucleus is shown in figure 4, with the semi-principal axes at values of 70 percent position probability. The errors observed can be explained by the fitting of the ellipsoid to the surface of equal probability. The radial semi-principal axis is slightly smaller compared to the other directions. That means that the particles moved less into this direction. This implies a network which is stiffer in the radial direction because of the pre-stressed filaments. The looser connection in tangential direction allowed a higher displacement of the particles.
This project was supported by the German Research Association (DFG) (SFB 569, MA 1297/10-1, BE 2339/3-1) and the Landesstiftung Baden-W¨urttemberg. We thank Harald Herrmann and his group from the DKFZ Heidelberg, Germany for providing the keratin monomers. The help of Ines Martin and Ulla Nolte for preparation and discussions with Kay Gottschalk and Paul Walther are gratefully acknowledged.
References 5. Conclusions
[1] Suresh S, Spatz J, Mills J P, Micoulet A, Dao M, Lim C T, Beil M and Seufferlein T 2005 Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria Acta Biomater. 1 15–30 [2] Fuchs E and Weber K 1994 Intermediate filaments: structure, dynamics, function and diseases Annu. Rev. Biochem. 63 345–82 [3] Lautenschl¨ager F, Paschke S, Schinkinger S, Bruel A, Beil M and Guck J 2009 The regulatory role of cell mechanics for migration of differentiating myeloid cells Proc. Natl Acad. Sci. USA 106 15696–701 [4] M¨ucke N, Kreplak L, Kirmse R, Wedig T, Herrmann H, Aebi U and Langowski J 2004 Assessing the flexibility of intermediate filaments by atomic force microscopy J. Mol. Biol. 335 1241–50 [5] Leitner A, Paust T, Marti O, Herrmann H and Beil M 2012 Properties of intermediate filament networks assembled from keratin 8 and 18 in the presence of Mg2+ Biophys. J. 103 195–201 [6] Herrmann H and Aebi U 2004 Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular scaffolds Annu. Rev. Biochem. 73 749–89 [7] Beil M et al 2003 Sphingosylphosphorylcholine regulates keratin network architecture and visco-elastic properties of human cancer cells Nature Cell Biol. 5 803–11 [8] Beil M, Braxmeier H, Fleischer F, Schmidt V and Walther P 2005 Quantitative analysis of keratin filament networks in scanning electron microscopy images of cancer cells J. Microsc. 220 84–95 [9] Bausch A R and Kroy K 2006 A bottom-up approach to cell mechanics Nature Phys. 2 231–8
Overall, the investigations of measurements at extracted pancreatic cells gave insight into the stiffness of the network, dependent on the distance of the bead to the rim of the nucleus. The measurements showed similar results as shown in [18] and [23]. The novel method could fit the MSD with a high goodness of the fit and R2 values above 0.8. Furthermore, the plateau moduli confirmed the measurements observed by W¨oll et al [20], which showed a pushing of the assembled intermediate filament network towards the nucleus. A lower value in stiffness close to the nucleus indicates a disassembly of the intermediate filament network. In addition the dependency on the distance shows that a comparison with in vitro assembled intermediate filament networks is difficult due to the lack of a nucleus and a radial arrangement of the network. In this regard, other groups have performed similar measurements [24]. In the work of Walter the elastic moduli of Panc-1 cells were determined by using quasistatic indentation and AFM. The diameter of the used tips was 8 μm and differed from the particles of 1 μm diameter used in this work which reduced the spatial resolution. However, their results showed that around 10% of the cell deformability is controlled by the keratin network. This small part is in our opinion important for the fine tuning of cell motility (as shown by studies of our group and other groups (e.g. Rolli et al [25]). Furthermore, a reduced coexpression of the keratin network may indicate an epithelial– mesenchymal transition with a higher metastatic activity of 4
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T Paust et al
[10] Mason T G and Weitz D A 1995 Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids Phys. Rev. Lett. 74 1250–3 [11] Cheezum M K, Walker W F and Guilford W H 2001 Quantitative comparison of algorithms for tracking single fluorescent particles Biophys. J. 81 2378–88 [12] Rogers S S, Waigh T A, Zhao X and Lu J R 2007 Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight Phys. Biol. 4 220–7 [13] Mason T G 2000 Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation Rheol. Acta 39 371–8 [14] Evans R M L, Tassieri M, Auhl D and Waigh T A 2009 Direct conversion of rheological compliance measurements into storage and loss moduli Phys. Rev. E 80 012501 [15] Maier T, Boehm H and Haraszti T 2012 Splinelike interpolation in particle tracking microrheology Phys. Rev. E 86 011501 [16] Crocker J C and Hoffman B D 2007 Multiple-particle tracking and two-point microrheology in cells Methods Cell Biol. 83 141–78 [17] Buchanan M, Atakhorrami M, Palierne J F and Schmidt C F 2005 Comparing macrorheology and one- and two-point microrheology in wormlike micelle solutions Macromolecules 38 8840 [18] Sivaramakrishnan S, DeGiulio J V, Lorand L, Goldman R D and Ridge K M 2008 Micromechanical properties of keratin
[19] [20] [21] [22] [23]
[24]
[25]
[26]
5
intermediate filament networks Proc. Natl Acad. Sci. USA 105 889–94 Wirtz D 2009 Particle-tracking microrheology of living cells: principles and applications Annu. Rev. Biophys. 38 301 W¨oll S, Windoffer R and Leube R E 2005 Dissection of keratin dynamics: different contributions of the actin and microtubule systems Eur. J. Cell Biol. 84 311–28 Hansen C D and Johnson C R 2004 The Visualization Handbook ed C D Hansen and C R Johnson (New York: Academic) pp 7–11 Leitner A 2012 Nanomechanische Eigenschaften von Keratin 8/18—von Einzelfilamenten zu Netzwerken (Ulm: VTS Ulm University) http://vts.uni-ulm.de/doc.asp?id=7819 Kole T P, Tseng Y and Wirtz D 2004 Intracellular microrheology as a tool for the measurement of the local mechanical properties of live cells Methods Cell Biol. 78 45–64 Walter N, Busch T, Seufferlein T and Spatz J P 2011 Elastic moduli of living epithelial pancreatic cancer cells and their skeletonized keratin intermediate filament network Biointerphases 6 79–85 Rolli C G, Seufferlein T, Kemkemer R and Spatz J P 2010 Impact of tumor cell cytoskeleton organization on invasiveness and migration: a microchannel-based approach PLoS ONE 5 e8726 Kn¨osel T, Emde V, Schl¨uns K, Schlag P M, Dietel M and Petersen I 2006 Cytokeratin profiles identify diagnostic signatures in colorectal cancer using multiplex analysis of tissue microarrays Cell Oncol. 28 167–75
Related content
PAPER
Microrheology of keratin networks in cancer cells To cite this article: T Paust et al 2013 Phys. Biol. 10 065008
View the article online for updates and enhancements.
- Physics of Cancer: Intermediate filaments and nuclear deformability during matrix invasion C T Mierke - Physics of Cancer: Initiation of a neoplasm or tumor C T Mierke - Active microrheology with optical tweezers: a versatile tool to investigate anisotropies in intermediate filament networks T Neckernuss, L K Mertens, I Martin et al.
Recent citations - Oliver Jahnel et al - Active microrheology with optical tweezers: a versatile tool to investigate anisotropies in intermediate filament networks T Neckernuss et al - Discrimination Between Cervical Cancer Cells and Normal Cervical Cells Based on Longitudinal Elasticity Using Atomic Force Microscopy Xueqin Zhao et al
This content was downloaded from IP address 142.132.1.147 on 18/11/2018 at 05:00
IOP PUBLISHING
PHYSICAL BIOLOGY
doi:10.1088/1478-3975/10/6/065008
Phys. Biol. 10 (2013) 065008 (5pp)
Microrheology of keratin networks in cancer cells T Paust 1 , S Paschke 2 , M Beil 3,4 and O Marti 1 1 2 3
Department for Experimental Physics, University of Ulm, D-89069 Ulm, Germany Department of Surgery, University of Ulm, D-89075 Ulm, Germany Department of Medicine I, University of Ulm, D-89081 Ulm, Germany
E-mail: [email protected]
Received 7 June 2013 Accepted for publication 1 October 2013 Published 4 December 2013 Online at stacks.iop.org/PhysBio/10/065008 Abstract Microrheology is a valuable tool to determine viscoelastic properties of polymer networks. For this purpose measurements with embedded tracer beads inside the extracted network of pancreatic cancer cells were performed. Observing the beads motion with a CCD-high-speed-camera leads to the dynamic shear modulus. The complex shear modulus is divided into real and imaginary parts which give insight into the mechanical properties of the cell. The dependency on the distance of the embedded beads to the rim of the nucleus shows a tendency for a deceasing storage modulus. We draw conclusions on the network topology of the keratin network types based on the mechanical behavior.
1. Introduction
the role of keratin networks in this disease and focus on the nanomechanical properties of the keratin cytoskeleton. In general, two different approaches lead to these properties: in vivo measurements of the mechanical properties of the extracted cytoskeleton and measurements of in vitro assembled protein networks. Both approaches have different advantages that shall be discussed briefly. As a top-down approach with the extraction of the keratin cytoskeleton from whole cells [7], the original architecture of the keratin network is conserved. Other parts of the cell, like membrane, organels, actin, microtubuli, etc are removed during the preparation process. Consequently, the mechanical properties of the keratin cytoskeleton can be investigated without any environmental influence. Afterwards the local network topology is determined by SEM [8]. The bottom up approach contains the in vitro assembly of proteins to the intermediate filament network. Since the cytoskeleton of the cell fulfils several special tasks independently [9], it is reasonable to analyze those part of the cytoskeleton as an isolated functional module. This work focuses on the top-down approach where the mechanical properties of the intermediate filament network is investigated.
The active and passive mechanical performance of a cell acting as the smallest biological unit able to move, survive and replicate independently has been of much interest. Most importantly, the motility of malignant cells is an important prognosticator in cancer [1]. The cells movement and response to external mechanical stimuli is a complex process mainly determined by its cytoskeleton. The cytoskeleton is a protein network extending from the cell membrane to the nucleus and filling large parts of the cytoplasm. It mostly consists of three different types of protein fibers: actin filaments, microtubuli and intermediate filaments [2]. Actin filaments, with a persistence length of about 15 μm, are responsible for the movement and deformability of the cell. The stiffer microtubuli, with a persistence length of several millimeters, are responsible for dynamical shape remodeling, which leads to a change in cell motility [3]. Intermediate filaments are more flexible with a persistence length between 500 and 1000 nm [4] their function appears to be to provide the mechanical stiffness and stability of the cell [5]. Thus, they are hypothesized to be the ‘stress-buffering-system’ [6] of cells. Because of the lack in knowledge about the role of keratin networks, we try to further improve the understanding of 4
2. Theoretical aspects Microrheology is a suitable tool for measurements of the mechanical properties of both the extracted cytoskeleton and
Author to whom any correspondence should be addressed.
1478-3975/13/065008+05$33.00
1
© 2013 IOP Publishing Ltd
Printed in the UK & the USA
Phys. Biol. 10 (2013) 065008
T Paust et al
of in vitro assembled keratin networks. The possibility to measure over an extended range only by observing thermal fluctuation is an advantage over the traditional measurements [10]. In our model micron-sized spherical beads, act as probes which scan their environment driven by the thermal forces (Brownian motion) dependent on the viscoelastic behavior of the surrounding network. By means of particle tracking the Brownian motion of several beads can be detected over a wide range of frequencies with a high accuracy in resolution (down to 5 nm [11, 12]). The calculation of the mean squared displacement (MSD) is a necessary step for the derivation of the complex shear modulus. The unilateral Laplace transformation relates the MSD with the dynamic shear modulus. Since an exact conversion is not possible due to the lack of an infinite amount of data points, an approximation of the transformation was previously applied to the MSD [13–15]. These methods are optimized for data which is smooth or flattened. In our case the usage of either [13] or [14] led to an insufficient accuracy of the dynamical shear modulus. Alternatively, the usage of a first principle model to fit the MSD was preferred. This first principle model bases on physical considerations which results in a model-based approach of the MSD. Therefore, the usage of analytical functions fitted to the MSD leads to an exact conversion to the dynamic shear modulus. Consequently, general statements about network dynamics are possible. It was shown that results of one-point microrheology compared to two-point microrheology do not differ in systems of assembled proteins and the relatively simple one-particle technique is sufficient to probe the bulk rheological properties of the medium [16, 17]. In our studies we use the single-particle technique which enables to measure for longer times because of smaller screen sizes. The Brownian motion in this model-based method can be described by a model that consists of a linear combination of three terms. In the case of microrheological data it is sufficient to include the time-dependent motion of the particle (MSD) governed by the system’s viscosity (B · t ), by the elasticity (A) and by the spatial confinement of the particles’ diffusion inside the networks’ meshes C·(1 − e−t /τ ). The elasticity is described by a constant value. This is based on a particle motion which is elastically bound in the network. The system’s viscosity can be described by the motion of the meshes the particle is placed in. The third part assumes the particle being in a mesh with a free Brownian motion until it hits the mesh. Then it bounces back elastically to the inside of the mesh (figure 1). The sum of the three parts is fitted to the MSD leading to function f f = A + B · t + C · [1 − exp(−t/τ )].
(A)
(C)
Figure 1. Illustration of the three parts for the model-based fitting function. In this first principle modeling the properties of the medium are considered for the particle motion. This motion is governed by the systems elasticity (A), viscosity and flow properties (B), and the spatial confinement of the meshes (C).
the real parameters E = exp(e), B = exp(b), C = exp(c), and τ = exp(−d). All subsequent steps such as the unilateral transformation and the calculation of the complex shear modulus are based on the fitted model (equation (2)) and the logarithmic coefficients.
3. Setup and materials For the measurements the movements of micro-beads (diameter 1 μm, Cat No. 4009A, Thermo Fisher Scientific, Waltham, MA, USA) were recorded with a microscope equipped with an oil immersion objective (CFI Apo TIRF 100XH, numerical aperture 1.49, Nikon, Tokyo, Japan) and a CCD camera (MotionX Pro 4, Imaging Solutions, Regensdorf, Switzerland) with a frame rate of 5 kHz. The motion was tracked by a MATLAB script [12] with an optical resolution of 5 nm and analyzed with further custom-built scripts of MATLAB and Mathematica. Living carcinoma cells incorporated the beads via phyagocytosis and embedded them into their cytoskeleton. After the extraction of the cell the keratin network, the nucleus and the incorporated beads remained. For further details on the extraction of the cell we refer to Beil et al 2003 [7]. For the achievement of a low uncertainty of the resulting data, numerous measurements were performed. The number of tracked particles in the network exceeded 980, which leads to approximately 80 particles per distance to the nucleus. Every cell included around five particles resulting in measurements at 190 cells. This ensures that the mechanics of intracellular keratin networks with a relatively high validity was achieved by measuring.
4. Measurements
(1)
The extracted cell consists of the nucleus and the intermediate filament network. In the case of pancreatic carcinoma cells of line Panc-1, the network is based on the assembly of human keratin 8 and 18 [7]. The density of the network is dependent on the distance to the rim of the nucleus (figure 2). The beads incorporated in the network are located in different distances to the nucleus. Therefore it is possible to cover the complete range of distances for the determination of the dynamic shear modulus. Since every cell network is arranged slightly different, a high number of measurements are necessary to gain reasonable results.
The fitting of equation (1) to experimental MSD data yields values for the parameter A, B, C and τ . To increase the numerical stability of fitting and to ensure a unique fitting result, a modified fitting function was used for the characterization of the MSD. This function f fit is described by ffit = E + B · t − C · exp(−t/τ )
(B)
(2)
with A = E − C. Fitting parameters are all positive numbers. To enforce this the actual fit was done with the logarithms of 2
Phys. Biol. 10 (2013) 065008
(A)
T Paust et al
and therefore the plateau value appears higher. A Fax´en’s law correction applied to the motion can correct the overestimated value. The local minimum at 2 μm indicates a lower density of the network. Up to 4 μm distance the plateau modulus exhibits a global maximum of 0.65 Pa. For larger distances the plateau decreases to a global minimum of 0.2 Pa. In between the global maximum and the minimum a monotone decrease of the shear modulus is observed. This decrease can be related to a reduced stiffness of the network dependent on the distance. An exemplary cell displayed in the inset of figure 2 shows this fact (B). The local minimum can be explained by a disassembly of the network of the living cell. This behavior was shown by W¨oll et al [20]. The global maximum is reached because of a pushing of the intermediate filament network towards the center of the cell—the cell nucleus. Hence, a shielding of the nucleus is a result of the formation of this dense network. For large distances the network becomes softer until the distance when the network is assembled is reached. The increase to 0.51 Pa at a distance of 12 μm can be explained by the influence of the surface during the measurement. The larger the distance, the lower the network is and therefore the more influence of the substrate is observed. The high value of uncertainty for large distances show, especially in this range, that the network varies a lot for every examined cell although numerous cells were observed. Beside the mechanical properties the determination of the network morphology was investigated. By means of the surface of equal probability of the particle motion the spatial direction of the network was analyzed. For this the particles positions during the motion in the network were used to determine a surface which spans over a specific volume. Therefore a three-dimensional histogram of the positions was calculated which is described by a N × N × N array. Each entry shows how likely the particle moved to this position. The surface of equal probability is the surface contouring all entries with the same probability (for more details the authors refer to [21] and the MATLAB documentation). For a low probability of zero percent, the highest distance of the particle’s positions are covered by the surface, because there the probability approaches zero. Thus, at a chosen probability value of 50 percent, the positions of a higher probability are included. The geometry of the observed surface of equal probability gives an idea about the likelihood of the motion of the particle. This geometry can be related to the confinement geometry and the network’s morphology. Additionally, with this method a classification of the network type—entangled or cross-linked—can be derived [22]. As the network acts like a spring mass system, the occurring repelling force influences the motion of the particle in such that the surface of equal probability approaches an ellipsoidal shape. The calculation of the averaged semi-principal axes in dependency on the density can be used to gather an estimation value for the directionality of the network for this type of cells. A coordinate transformation was considered for the calculation of the surface of equal probability and its semiprincipal axes. In that way the radial, tangential and vertical components in a cylindrical coordinate system with the cell nucleus as center is regarded.
(B )
(C )
Figure 2. Electron microscope image of extracted pancreatic cancer cells. The remaining cell nucleus builds the center of the intermediate filament network (A). The higher the distance to the rim of the nucleus, the lower is the density of the network (B). The beads of 1 μm diameter were embedded in the network via phagocytosis. The positions of the particles cover the complete range of the intermediate network (C). Thus, the local elasticity and viscosity can be measured via the particles’ thermal motion. Since the extraction process removed all cellular components apart from intermediate filament network and nucleus, the mechanical properties of the intermediate filament network can be determined.
Figure 3. Plateau modulus dependent on the distance to the rim of the modulus. The values of G0 were of a frequency of 1 Hz when all observed curves reached a slope of zero. The plateau loss modulus G0 was determined at the same frequency. The distances shown are up to 12 μm. For higher distances the amount of measured particles was too low for a reasonable result.
The extracted cell is assumed to be gel-like viscoelastic [18]. For this case the storage modulus builds a plateau dependent on the viscous and elastic properties of the network [19]. The plateau modulus is used to compare the measurements of particles at specific distances. Furthermore, the loss modulus shows a decrease in value, until at specific frequency a minimum is reached. The shown plateau was determined at a frequency of 1 Hz (figure 3). At a distance of 1 μm the plateau reaches a value of 0.5 Pa, which decreases to a local minimum of 0.3 Pa at 2 μm. The plateau at short distances is governed by the nucleus of the cell. The particle motion in this region is limited by the nucleus 3
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the cell. This causes an important step in the development of more aggressive cancer, e.g. in case of CRC (colorectal cancer), associated with a shorter patients’ survival [26]. The calculation of the surface of equal probability gives additional insight of how the shape of the confinement can be assumed and also helps to gather the semi-principal axes of the fitted ellipsoids. In that way, a preferred direction of the particle motion can be revealed. In the end it can be shown how inhomogeneous or stressed the networks are. This leads to a hint that a force exerted at the rim of the intermediate filament network is guided towards the nucleus in a channel. Hence, in our opinion the studies provide important information about the spatial organization of keratin networks. In an ongoing study measurements on different substrates are performed. As a result a similar behavior in distance dependency is expected whereas the absolute values of the plateau moduli will differ for every substrate as well as the stiffness of the keratin network.
Figure 4. Calculated semi-principal axes for the surfaces of equal probability with a probability value of 70%. The contribution of the radial motion towards the overall motion of the particle is smaller compared to the perpendicular directions. This indicates an inhomogeneous intermediate filament network with pre-stressed filaments in radial direction.
Acknowledgments
The dependency on the distance to the rim of the nucleus is shown in figure 4, with the semi-principal axes at values of 70 percent position probability. The errors observed can be explained by the fitting of the ellipsoid to the surface of equal probability. The radial semi-principal axis is slightly smaller compared to the other directions. That means that the particles moved less into this direction. This implies a network which is stiffer in the radial direction because of the pre-stressed filaments. The looser connection in tangential direction allowed a higher displacement of the particles.
This project was supported by the German Research Association (DFG) (SFB 569, MA 1297/10-1, BE 2339/3-1) and the Landesstiftung Baden-W¨urttemberg. We thank Harald Herrmann and his group from the DKFZ Heidelberg, Germany for providing the keratin monomers. The help of Ines Martin and Ulla Nolte for preparation and discussions with Kay Gottschalk and Paul Walther are gratefully acknowledged.
References 5. Conclusions
[1] Suresh S, Spatz J, Mills J P, Micoulet A, Dao M, Lim C T, Beil M and Seufferlein T 2005 Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria Acta Biomater. 1 15–30 [2] Fuchs E and Weber K 1994 Intermediate filaments: structure, dynamics, function and diseases Annu. Rev. Biochem. 63 345–82 [3] Lautenschl¨ager F, Paschke S, Schinkinger S, Bruel A, Beil M and Guck J 2009 The regulatory role of cell mechanics for migration of differentiating myeloid cells Proc. Natl Acad. Sci. USA 106 15696–701 [4] M¨ucke N, Kreplak L, Kirmse R, Wedig T, Herrmann H, Aebi U and Langowski J 2004 Assessing the flexibility of intermediate filaments by atomic force microscopy J. Mol. Biol. 335 1241–50 [5] Leitner A, Paust T, Marti O, Herrmann H and Beil M 2012 Properties of intermediate filament networks assembled from keratin 8 and 18 in the presence of Mg2+ Biophys. J. 103 195–201 [6] Herrmann H and Aebi U 2004 Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular scaffolds Annu. Rev. Biochem. 73 749–89 [7] Beil M et al 2003 Sphingosylphosphorylcholine regulates keratin network architecture and visco-elastic properties of human cancer cells Nature Cell Biol. 5 803–11 [8] Beil M, Braxmeier H, Fleischer F, Schmidt V and Walther P 2005 Quantitative analysis of keratin filament networks in scanning electron microscopy images of cancer cells J. Microsc. 220 84–95 [9] Bausch A R and Kroy K 2006 A bottom-up approach to cell mechanics Nature Phys. 2 231–8
Overall, the investigations of measurements at extracted pancreatic cells gave insight into the stiffness of the network, dependent on the distance of the bead to the rim of the nucleus. The measurements showed similar results as shown in [18] and [23]. The novel method could fit the MSD with a high goodness of the fit and R2 values above 0.8. Furthermore, the plateau moduli confirmed the measurements observed by W¨oll et al [20], which showed a pushing of the assembled intermediate filament network towards the nucleus. A lower value in stiffness close to the nucleus indicates a disassembly of the intermediate filament network. In addition the dependency on the distance shows that a comparison with in vitro assembled intermediate filament networks is difficult due to the lack of a nucleus and a radial arrangement of the network. In this regard, other groups have performed similar measurements [24]. In the work of Walter the elastic moduli of Panc-1 cells were determined by using quasistatic indentation and AFM. The diameter of the used tips was 8 μm and differed from the particles of 1 μm diameter used in this work which reduced the spatial resolution. However, their results showed that around 10% of the cell deformability is controlled by the keratin network. This small part is in our opinion important for the fine tuning of cell motility (as shown by studies of our group and other groups (e.g. Rolli et al [25]). Furthermore, a reduced coexpression of the keratin network may indicate an epithelial– mesenchymal transition with a higher metastatic activity of 4
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[10] Mason T G and Weitz D A 1995 Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids Phys. Rev. Lett. 74 1250–3 [11] Cheezum M K, Walker W F and Guilford W H 2001 Quantitative comparison of algorithms for tracking single fluorescent particles Biophys. J. 81 2378–88 [12] Rogers S S, Waigh T A, Zhao X and Lu J R 2007 Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight Phys. Biol. 4 220–7 [13] Mason T G 2000 Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation Rheol. Acta 39 371–8 [14] Evans R M L, Tassieri M, Auhl D and Waigh T A 2009 Direct conversion of rheological compliance measurements into storage and loss moduli Phys. Rev. E 80 012501 [15] Maier T, Boehm H and Haraszti T 2012 Splinelike interpolation in particle tracking microrheology Phys. Rev. E 86 011501 [16] Crocker J C and Hoffman B D 2007 Multiple-particle tracking and two-point microrheology in cells Methods Cell Biol. 83 141–78 [17] Buchanan M, Atakhorrami M, Palierne J F and Schmidt C F 2005 Comparing macrorheology and one- and two-point microrheology in wormlike micelle solutions Macromolecules 38 8840 [18] Sivaramakrishnan S, DeGiulio J V, Lorand L, Goldman R D and Ridge K M 2008 Micromechanical properties of keratin
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