How strong is an individual living cell? How is it moving and deforming? How can the cell fulfil its mechanical tasks? How is it communicating with its environment? The answer to such questions can be found in the interface between physics, cell biology and molecular biology – an internationally strongly growing research field. In this article we will focus on the first of the questions asked above. We demonstrate how physical methods are applied to the investigation of mechanical properties of a living cell.
Written by: Kirstine Berg-Sørensen, Mario Fischer, Poul Martin Hansen and Lene Oddershede
This article was originally published in the Danish journal for physics and astronomy "Kvant" . It was based on the scientific work in the research groups of Prof. L.Oddershede of the Niels Bohr Institute, Copenhagen, Denmark and of Prof. K. Berg-Sørensen of the Technical University of Denmark, Lyngby, Denmark. The study was in collaboration with their two students M. Fischer and P.M. Hansen . The authors kindly provided a translation of the original article to xscience.info.
Physics of living systems
A living organism is highly complicated and much of the knowledge we have, e.g., about our body, is based on observations rather than on understanding. In physics we primarily want to achieve understanding which is delicate in a complex living organism, since it is difficult to separate the most important from the less important parameters. Within the last decade the development of physical methods that enable us to study individual biological molecules has revolutionized our understanding of the working principles of individual molecules. However, once the function of an individual molecule is understood, the understanding of how many individual molecules form a living organism together and how they function within that organism poses an even greater challenge. Here, physicists can contribute for example with their knowledge about methods from statistical physics and complexity theory.
For instance, for the investigation of the mechanical forces which an individual molecule can exert, first steps typically involve taking the molecule out of its biological context, diminishing the number of unknown parameters, and getting it to work in vitro, i.e., in artificial environments, typically in a sample chamber. For the individual molecule the induced dipole moment is mostly not so large that the optical tweezers could hold and detect it. Therefore one attaches a “handle”, typically a micrometer-sized bead of a dielectric material like glass or polystyrene.
Another possibility is to use metallic nano-particles. For small bead radii, metallic particles exhibit an induced dipole moment which is large compared to the scattering force which the laser light is also exerting [4]. The potential of the optical tweezers can be described in a good approximation as being harmonic, i.e., like the potential of a spring. In order to find the forces which are exerted on the dielectric bead in this potential and thereby to determine the forces which are exerted on the biological system, it is necessary to perform a precise determination of the spring constant. This characterization of the spring constant can be performed with high precision in a simple system, where a spherical bead is moving in water or a similar fluid [5]. The situation immediately becomes much more complicated if the bead is moving in a medium with both elastic and viscous properties.
The next step, following the understanding of the functionality of the molecule in vitro, is to try to understand how the molecule works in a living organism. In the optical tweezers group at the Niels Bohr Institute in Copenhagen we have worked on this problem for the past couple of years. Here we will describe quantitative optical measurements of single molecules and organelles in a living cell. This is a process which requires many steps, among those the attachment of a well-defined “handle” to the biological molecule or organelle whose mechanical properties one wants to study, and the determination of the spring constant of the optical tweezers in the cytoplasm of the living cell.
A single cell biological organism
In the laboratory we culture cells, where different organelles express a protein, which can be seen in fluorescence microscopy, the so-called Green Fluorescent Protein (GFP), see Fig. 1, top.
This figure also shows a cell where naturally occurring droplets of fat, also known as granules, can be seen as dark areas. The induced dipole moment in granules is so strong that the granules can be manipulated by the optical tweezers, and in the group we have already applied those lipid droplets for the investigation of viscoelastic properties of the cytoplasm [7].
Since granules are not attached to a certain organelle, they cannot be used as a “handle” for quantitative measurements and manipulation, however. Therefore our strategy is to insert particles into the cell, which can be attached to, e.g., the nuclear membrane and applied as a handle for optical manipulation and quantitative determination of the forces which are exerted on the cell nucleus, e.g., during cell division.
It is important to choose the particles to be inserted in a way that they are on the one hand not reactive and on the other hand very small. With this choice one minimizes the risk that the particles would change natural processes within the cell. Since gold or silver particles of nm size have a relatively large induced dipole moment and are further relatively inert, they are a reasonable choice for a “handle” [4].
Gold particles as handles
For the application of gold particles as “handles” inside the cell, it is necessary to get them into the cell and to bind them to the desired molecule. Unfortunately, the S. pombe cell has a very stiff cell wall and it is not trivial to insert the gold beads. We have developed a method which involves as a first step the enzymatic degradation of the outmost layer of the cell and thereafter the injection of the gold particles with a very thin glass pipette, and in the final step the regeneration of the outer wall of the cell [8]. The method is visualized in Fig. 3.
Quantitative force determination in a living cell
We want to perform quantitative measurements within the living cell. For this purpose the optical tweezers are used as a “force-scope”. In this section we outline some of the processes which are necessary to go through in order to characterize the optical tweezers and to use it as a device for force measurements in the inner of a living cell, i.e., within the cytoplasm. The cytoplasm exhibits both viscous and elastic properties.
We consider a particle which is moving in a viscoelastic medium while it is simultaneously held in the trap potential of the optical tweezers. By envisaging a sequence of measurements on such a particle, theoretical and numerical considerations show that it is possible to determine the characteristics of the optical tweezers and of the medium [9]. The proposed experimental protocol consists of measurements of two types of time series for positions of particles. In type I one measures positions only “passively”, i.e., one determines time series of the particle’s position while it is performing Brownian motion due to thermal noise in the viscoelastic medium. In type II one measures “actively”: Here one determines the response of the particle when the trap potential is translated periodically with respect to the particle, as sketched in Fig. 4. This is done again by measuring a time series for the particle position.
Information about the characteristics of the trap and the medium is obtained by spectral analysis and a combination of power and relaxation spectra for experiments of type I and II. In this way one obtains first of all a frequency-dependent estimate of the trap potential’s spring constant kK, where the index K refers to the frequency value. The values for kK can be averaged which yields the average value k(av). Since the cell contains active processes which typically occur at low frequencies it is necessary to omit those low frequencies when averaging. Correspondingly it is necessary to omit frequencies which are affected by others forms of experimental noise. Thereafter the spectra obtained can be used for estimates of the viscoelastic properties of the cytoplasm.
The mechanics of cell division
The state of the art is that we can optically trap gold particles and we can perform a microinjection into the yeast cell S. pombe. Further, we have theoretical tools to characterize the optical trap within the complex cytoplasm. In future, we intend to perform experiments like the one drafted in Fig. 6. Here, a gold bead is connected to the membrane of the cell nucleus and we envisage that the gold bead could act as a handle on the cell nucleus which we could hold and manipulate in this way. We could measure the forces which are exerted on the nucleus during the process of cell division.
If one succeeds in performing quantitative measurements in the cytoplasm of living cells, e.g., of the force exerted by microtubules on the cell nucleus, there will be an abundance of cellular processes whose nano-mechanics can be revealed by corresponding investigations. Ultimately, we want to investigate the control mechanisms of the cell connected with cell division, i.e., among other things also the interplay between biochemical and mechanical processes within the cell.
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