Active systems

Molecular machines are responsible for a variety of non-equilibrium actions. They can make cells themselves move about, and perhaps exhibit fascinating collective motion, and the are responsible, amongst other things, for the transportation of cargo, or play a role in the tightening of the contractile ring during cells division.

A range of molecular motors move along the filamentous structures, microtubules and actin filaments, in the cell.  It is interesting and challenging to ask and understand how molecular motors when connected in different ways start modifying the properties of the networks of filaments, or how their functioning alters the mechanical and conformational, and other dynamical properties of a variety of structures.

There is a wide range of interesting introductory articles by various authors, for example, check out this one

Motility assays

A system with a relatively simple set-up is an array of filaments that move on top of a flat bed of molecular motors, a so-called motility assay. When a large number of motor heads grabs, moves, detaches to a filament, they cause it to move, but also to respond to an applied force.  Under certain conditions, we found that an instability occurs [Banerjee, et al.].  Current work is related to dealing with interactions of filaments.

Above: A single filament moving on a surface with tethered motors.   Cartoon for physical content of Banerjee paper.  (Copyright Kristian Müller-Nedebock)

Stepping mechanism formalism

In the project with Janusz Meylahn we introduced novel ways to formulate the stepping action of motor heads using ideas from dynamical networking theories.  We hope to present these results very soon.

Contractile rings

Can we think about the tension in contractile rings, given the latest, fascinating experiment on filament orientation and the motors linking the rings?  This is part of the project Stanard Mebwe Pachong is investigating in her research.

Contractile rings are formed of actin filaments and molecular machines (and possible other components) to actively pinch of the cell membrane after the division of genetic material. A ring of these filaments forms and then contracts ever more tightly.

We are currently studying these systems using analytical dynamical approaches. These are complemented by some simple Langevin dynamics simulations.


Above: A simulations of the motions of actin filaments (some oriented clockwise and others counter-clockwise) under the action of networking and active forces. Two filaments with opposite orientations have been highlighted. (Copyright Kristian Müller-Nedebock)

Active gels

When networks of filaments are formed (which is typical of the cytoskeleton) pairs of molecular motor heads, for example, can link different strands in addition (perhaps) to other crosslinks, forming an active gel.  In past years two MSc theses on these topics have been completed in the group:  a general network formalism (using ideas from equilibrium networks in polymer physics) and a dynamical perspective.  The work was done by former members Mohau Mateyisi and Karl Möller.

Collaborator: Ben Loos

Dr Ben Loos (Dept of Physiological Sciences at Stellenbosch University) has a long-standing interest in the molecular mechanisms that control cell death susceptibility. His research centres around protein degradative mechanisms and their dynamics, transport and function of mitochondria along tubulin networks and their role in neuronal degeneration and migration.  His research group utilizes in vitro models for neuronal protein aggregation storage disorders such as Alzheimer’s disease, to unravel and to direct the complex molecular interplay towards an environment that favours cellular function and survival. He has an equally long-standing interest in high resolution fluorescence-based microscopy techniques, and has managed the Cell Imaging Unit ( for many years. Integral part of his research in physiological sciences is the application of powerful microscopy techniques such as SR-SIM.


The organisation and dynamics of intracellular structures that maintain a cell’s form, shape, function and viability are rather complex. An emerging central theme which addresses this complexity deals with ATP-driven intracellular transport mechanisms along the tubulin network or the ability of mitochondria to rapidly undergo fission and fusion, and thereby creating a network that is adapted to the required ATP demands of the cell. In many physiological disorders, such as neuronal degeneration, these processes are disturbed, leading to increased cellular susceptibility to undergo cell death.

Physics modelling can add meaningful insight into the above processes. For example, semi-microscopic theories for membrane energetics and fluctuations can be utilised to understand the fusion between organelles. Descriptions including simple and driven – or active – dynamics of fusion and separation processes are possible. Predictions on transport processes and collective activity are accessible through nonequilibrium statistical physical treatments. On a slightly larger scale the insights from the fusion can be applied to network modalities. Here theoretical physical and mathematical characterisation of network properties would certainly assist in the analysis of experimental data.

For example the phenomena associated with autophagy can be studied through a variety of approaches.  We recently published a chapter “Autophagic Flux, Fusion Dynamics, and Cell Death” that shows how physics modelling can be added to the understanding of this process, understanding of which might ultimately help science to understand a variety of disorders.

The Nanobiophysics-SU group is particularly interested in the emerging field of organelle network analysis related to properties such as elasticity, connectivity and efficiency that report on molecular interactions and cellular function. A unique approach lies in the nested approach of theory and experimentally derived data on the nano-scale. By plugging into the power of molecular imaging technologies such as structured illumination superresolution microscopy (SR-SIM), this group addresses questions that arise only at the interface of nanotechnology and biology. SR-SIM allows to resolve specifically labelled structures down to 80 nm. Current projects address fusion dynamics between autophagosomes and lysosomes, mitochondrial network connectivity and actin-cyctoskeletal stiffness. For example, microscopy data together with physics models for networking and organelle structure can help to cast light on the dynamics inherent to mitochondrial networks numerically. The predictive power that this interdisciplinary approach allows to generate, is highly valuable for both biology and theoretical statistical physics alike.

The principal investigators are Dr Ben Loos (Dept of Physiological Sciences, Stellenbosch University) and Kristian Müller-Nedebock (Dept of Physics, Stellenbosch University)

Kristian Müller-Nedebock

Kristian Müller-Nedebock is a physicist, employed as Professor in the Department of Physics at Stellenbosch University.  His route to the current position in Stellenbosch included a PhD at the Cavendish Laboratory from the University of Cambridge and several years as a post-doctoral researcher at the Max Planck Institute for Polymer Research in Mainz.

Kristian Müller-Nedebock

Kristian Müller-Nedebock

This site shows some of the scientific work members of the group and he do at Stellenbosch.

Alumnus: Mohau Mateyisi

Jacob Mohau Mateyisi graduated with a PhD in December 2014.  The work in his dissertation covered the diffusion of particles in narrow, laterally coupled channels.  Previously he worked on active networks, using a reversible formalism and the replica method to compute the network elasticity.

Mohau has worked at the African Institute for Mathematical Sciences in Muizenberg, Cape Town, South Africa, and at the Leibniz Institute for Polymer Research in Dresden, Germany.

Alumnus: Christian Rohwer

Dr Christian Rohwer completed a PhD on entanglements in 2013/2014 and continued as a postdoctoral research fellow under the supervision of Kristian Müller-Nedebock and Frederik Scholtz.  He is currently a postdoctoral research associate in Stuttgart.

See the pages related the Christian Rohwer.

Dealing with entanglements

Our recent paper (See post here; CM Rohwer, KK Müller-Nedebock “Operator Formalism for Topology-Conserving Crossing Dynamics in Planar Knot Diagrams”, Journal of Statistical Physics 159, 120-157 (2015), introduces a dynamical perspective to the venerable polymer physics problem of conserving the state of entanglement in polymer loops.

To understand what this means we show the example of a single strand (polymer) that forms a closed loop, but, as in the accompanying figure of the so-called trefoil knot, trefoilcannot be manipulated into a simple circular form without cutting and re-glueing the strand.  We can now ask how one can characterise the strand as it is subjected to continuous changes of its configurations due to the environment in which it finds itself. (Think of a polymer loop in a fluid.)  As it reconfigures its shape changes, but the topology of the knot must remain invariant.  The statistical physics entails computing the sum over all possible configurations maintaining the topology.  Great papers by Edwards and Frisch and Wasserman have done this elegantly.  Yet many severe and interesting mathematical challenges still face the enumeration of conformations, but also just in checking whether two knots are equivalent in a way that can be suitably implemented in statistical physics.

Our dynamical formalism is one possible approach in which one can start thinking about a dynamical route to exploring the possible permissible configurations (albeit in the reduced two-dimensional crossings in the projection of the knot only) without needing to compute and compare knot invariants.

Previously, we also published an alternative enumeration scheme to knots in which the winding number is preserved (See the related post; CM Rohwer, KK Müller-Nedebock, F-E Mpiana Mulamba “Conservation of polymer winding states: a combinatoric approach” J Phys A-Math Theor 47, 065001 (2014) DOI: