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Leif Matsson

Associate professor

Contact address
Department of Physics
University of Gothenburg
SE-412 96 Göteborg, Sweden - Tel:+46 31 911252



Research areas:
Spindle assembly checkpoint and cell division – Condensation and higher order folding of chromatin by condensin - Tension and stretch in kinetochores and chromatin - Anaphase entry and chromosome segregation – Comparison of normal and cancerous cell division - Relationship between in vivo DNA dynamics and single DNA molecule stretching - Non-equilibrium statistical mechanics - Spontaneous symmetry breakdown in condensed matter (alive or inanimate) and particle physics.


Fig. 1. Mitotic spindle in late metaphase.                 

Fig. 2 Sister chromatid pair with
kinetochores stretched a
distance δ apart.


Spindle Assembly Checkpoint

Leif Matsson’s (LM) primary research in biological physics is focused on DNA replication [1-5, 8] and segregation of replicated chromosomes, in particular on the dynamics underlying the spindle assembly checkpoint (SAC) and the higher order folding of DNA, i.e., condensation of chromatin by consensin [11-12]. SAC is the mechanism by which a cell decides to inhibit or allow anaphase entry and separation of replicated chromosomes into two identical genomes. For the cell to enter anaphase the kinetochore protein complexes on all sister chromatid (SC) pairs must be first stably attached by microtubules (MT) from the two spindle poles (bi-orientated). Before anaphase entry can take place, in higher eukaryotes all SC pairs must then also line up on the metaphase plate. This indicates that strong spatial correlations between all SC pairs and position dependent forces are at work. However, segregation is well synchronized also in budding yeast cells, indicating that bi-oriented SC pairs are strongly correlated in space also in that case. Except for a general interest in how the living cell works, a deeper understanding of this process in normal cell division would almost certainly also lead to a better insight in cancerous cell division.
The currently asked question in molecular biology in this context is how events at the kinetochore complex, which contains some 80 proteins with different functions, are converted to inhibit the anaphase promoting complex (APC) and its co-activator Cdc20. However, at the same time it is clear that a cell’s decision to allow anaphase entry and divide is taken collectively by all stably attached kinetochores (or by all bioriented SC pairs). Similarly, this decision is collectively inhibited as long as there are unattached kinetochores, i.e., while the number of stably attached kinetochore complexes still increases. This non-equilibrium machinery works like a clock-work that counts the numbers of stably attached kinetochores. From a many-body physical aspect, except for the non-equilibrium dynamical conditions, the dividing cell is not different from any other condensed matter system with strong spatial correlations between the constituent particles. It is a well-known fact in physics that the collective effects of a system cannot be explained by the properties and functions of the individual constituent particle (the stably attached kinetochore complex). As described by LM [12], the SAC mechanism is controlled by a non-equilibrium collective dynamics of one variable only, i.e., the number of stably attached kinetochores (the order parameter). This is fortunate also because it reduces the number of things that can go wrong and thereby increases the fidelity of the segregation process.
The SAC problem thus boils down to formulating the non-equilibrium collective potential energy of the system. In contrast to inanimate condensed matter systems driven by temperature variations under chemical equilibrium conditions, the dynamics in a dividing cell is driven by the increase in the number of stably attached kinetochores, i.e., by the attachment rate equation, implying that the chemical potential increases, the temperature being constant. It was then demonstrated by LM that the position dependent integrated poleward and antipoleward forces and the in vivo integrated tension in kinetochores and chromatin can be derived from the collective potential energy as functions of the order parameter [12]. The second derivative of the collective potential energy yields the spectra of both metaphase and anaphase oscillations, which appear to be key to the synchronizations of anaphase entry and of chromosome separation.
It may look as if the last stable kinetochore attachment triggers anaphase entry. However, the relaxation time after each stable attachment, needed for the potential energy to be redistributed and shared equally between all previously stably attached kinetochores and SC pairs, shows that the transition into anaphase is a collective event. As was shown by LM [12], the collective binding energy for all SC pairs can attain its minimum, which is required for a synchronized and faithful (normal) proteolytic separation of all SC pairs, only after relaxation of the turmoil (redistribution of the collective energy) created by the last stable attachment.

Chromatin condensation

A faithful segregation of replicated chromosomes also requires reorganization and higher order folding of DNA into well compacted chromatids. This condensation process, which proceeds in different steps in the cell cycle, is in prophase mediated by condensin II and in prometaphase and metaphase by condensin I. However, it is also linked to the spindle assembly process and depends on the release of cohesin and a large turnover of histones. Different studies indicate that condensin forms pairwise topological links between different parts of the rod-like chromosomal fiber and that this can take place in a rather irregular manner. As was shown by LM [12], the compaction of chromatin becomes completed only after bi-orientation of all SC pairs and after a certain finite number of topological links. He also showed that the integrated MT mediated poleward forces, together with the chromatin compaction force induced by condensin I, yield the putative in-vivo tension in kinetochores and centromeric and peri-centromeric chromatin as functions of the order parameter.


Relationship to single DNA molecule studies

Stretching of a single DNA molecule in vitro by an external force has provided a wealth of information about DNA. However, in a living cell the chromatin becomes stretched by opposite microtubule mediated pulling forces which act pairwise on the two sister kinetochores, generating tension in kinetochores and centromeric and pericentromeric chromatin. As was demonstrated by LM [11, 12], the integrated (collective) force acting on kinetochores in a living cell can be related to the force-extension formula observed in laboratory. This relationship can in turn be employed to translate different results from single molecule force spectroscopy studies into the non-equilibrium conditions that prevail in a living cell. For instance, the putative in vivo tension in kinetochores and centromeric and peri-centromeric chromatin derived from the collective model could be validated indirectly [12]. Hopefully, alternative experimental methods can now be developed for more direct in vivo assessments.


Non-equilibrium statistical mechanics

Self-organization in non-equilibrium inanimate and biological systems can be described provided that these systems are void of strong spatial correlations between their respective constituent particles. Systems restricted by strong spatial correlations can be described too if the number of constituent particles is constant or fluctuates about a constant number. The long standing problem in physics has been to model systems with an increasing number of constituent particles (or molecules) that become strongly correlated in space. A dividing cell exhibits exactly this type of non-equilibrium dynamics that inhibits the APC in prometaphase and metaphase before the SAC control. To provide a solution to the SAC problem, LM thus first had to solve the non-equilibrium statistical physical problem [12].


Spontaneous symmetry breakdown

As was described by LM [12], the rate equation for attachment of microtubules to kinetochores and the strong spatial correlations between these kinetochores, combined with the initial boundary constraints, uniquely define the non-equilibrium dynamics underlying the SAC mechanism. This dynamics happens to be symmetric with respect to change of sign of the order parameter φ, which also represents the probability density for stable attachments. To make this probability density positive definite (a physical requirement), a constant number N must be added, φ + N = φ’ (or φ → −N + φ), implying that the actual symmetry becomes broken in living cells too. This operation allows the collective potential energy to also attain minimum in the absence of stable attachments (a second physical requirement). Compare a wine bottle with a hill shaped bottom on which a small ball is placed symmetrically on the top. The ball then spontaneously falls down to an asymmetric position at the circular lower level of the bottom. This is also what happens in a dividing cell once all kinetochores have been stably attached and the system has relaxed after redistribution of the collective potential energy [12]. More about the fundamental physical aspects can be found at http://www.leifmatsson.com/


Publications in Biological physics

1. L. Matsson, Soliton growth-signal transduction in topologically quantized T cells. Phys. Rev. E 48, 2217-2231 (1993). http://iopscience.iop.org/pre
2. L. Matsson, Response theory for nonstationary ligand-receptor interaction and a solution to the growth signal firing problem. J. Theor. Biol. 180, 93-104 (1996). http://www.sciencedirect.com/science/journal/00225193
3. L. Matsson, Long range interaction between protein complexes in DNA controls replication and cell cycle progression. J. Biol. Syst. 9 (No. 1), 41-65 (2001). http://www.worldscientific.com/worldscinet/jbs
4. L. Matsson, DNA replication and cell cycle progression regulated by long range interaction between protein complexes bound to DNA. J. Biol. Phys. 27, 329-359 (2001). https://www.ncbi.nlm.nih.gov/pmc/?term=L+Matsson
5. L. Matsson, Long range force between pre-replication complexes Pre-RC) in DNA controls replication and cell cycle progression. J. Biol. Phys. 28, 675-701 (2002). https://www.ncbi.nlm.nih.gov/pmc/?term=L+Matsson
6. L. Matsson, Virulh Sa-yakanit, and Santipong Boribarn, Ligand gated ion channel currents in nonstationary lyotropic model, Neurochemical Research 28, 377-384 (2003).
7. L. Matsson, and Adrian Parsegian, Completing our first decade of biological physics conferences. J. Biol. Phys. 31, 235-239 (2005). https://www.ncbi.nlm.nih.gov/pmc/?term=L+Matsson
8. L. Matsson, Model of DNA dynamics and replication. J. Biol. Phys. 31, 303-321 (2005). https://www.ncbi.nlm.nih.gov/pmc/?term=L+Matsson
9. L. Matsson, Virulh Sa-yakanit, and Santipong Boribarn, Lyotropic ion channel current model compared with Ising model. J. Biol. Phys. 31, 525-532 (2005). https://www.ncbi.nlm.nih.gov/pmc/?term=L+Matsson
10. Miljko V. Sataric, Leif Matsson and Jack A. Tuszynski, Complex movements of motor protein relay helices during the power stroke. Phys. Rev. E 74, 051902 (2006). http://iopscience.iop.org/pre
11. L. Matsson, Spindle checkpoint regulated by non-equilibrium collective spindle-chromosome interaction; Relationship to single DNA molecule force-extension formula. J. Phys. Cond. Matter 21, 502101 (2009). http://iopscience.iop.org/0953-8984/21/50/502101
12. L. Matsson, Chromatin compaction by condensin I, intra-kinetochore stretch and tension, and anaphase onset, in collective spindle assembly checkpoint interaction. J. Phys.: Cond. Matter 26, 155102 (2014). http://iopscience.iop.org/0953-8984/26/15/155102

Conference proceedings
1. “Nonlinear cooperative phenomena in biological systems”. Editor Leif Matsson, World Scientific, Singapore 1998. The conference was held 19-22 August 1977 at ICTP, Trieste. (Appendix A1) http://cds.cern.ch/record/391044/?ln=sv
2. “The first workshop on biological physics 2000”. Editors: Virulh Sayakanit, Leif Matsson and Hans Frauenfelder, World Scientific, Singapore 2001. The conference was held 18-22 September 2000 at Chulalongkorn University, Bangkok. (Appendix A2). http://www.bookdepository.com/Biological-Physics-2000/9789810246228
3. “The 5th international conference on biological physics”. J. Biol. Phys. (3/4) 31 (2005). Guest editor Leif Matsson. The conference was held 23-27 August 2004 at Gothenburg University and Chalmers University of Technology, Gothenburg. (Appendix A3). https://www.ncbi.nlm.nih.gov/pmc/?term=L+Matsson

Appendix A1
Appendix A2
Appendix A3


Condensed matter theory group

Gothenburg University, SE-412 96 Göteborg, Sweden

+46 (0)31- 772 1000

Sidansvarig: Evelyn Vilkman|Sidan uppdaterades: 2014-06-18

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