Modeling active matter systems with applications to cell dynamics
Update: 2016-02-02 13:41:32      Author: yangjuan@csrc.ac.cn

Active matter is a class of materials that are driven out of equilibrium by energy input at the microscopic scale via biochemical or catalytic activities. As a result,   emergent dynamical structures may emerge such as long-range order, anomalous fluctuations, dynamical spatial-temporal structures and patterns, and dynamical phase transitions [1,2]. When coupled with regulatory signaling pathways, active matter systems are seen in living systems such as the cortical layer or the microtubule ensemble in the cytoskeleton of live cells and bacteria colonies [1,2].

Active particles in the active matter are generally anisotropic and can form ordered states at a sufficiently high concentration. The nature of the ordered state depends on both the configuration of the individual particles and the interactions among the particles. A class of active matter of these features is also known as the active liquid crystal, which may form liquid crystalline phases at sufficiently high particle concentrations or under strong particle-particle interaction. 

A useful theoretical framework for describing the collective behavior of active matter systems is a continuum model that generalizes liquid crystal hydrodynamics to include new activities due to the microscopic energy input. We have developed a general framework for deriving models for complex fluids based on the generalized Onsager’s principle [4]. This approach has been extended to include models for active matter.

Using the continuum hydrodynamic models, we have investigated systematically hydrodynamics of a polar active liquid crystal system and identified important roles played by the active viscosity and self-propelling speed on hydrodynamics of the active matter system. This study leads to the discovery of a rich set of emergent dynamical patterns in 2-D channel and cavity flows, including traveling waves as well as irregular oscillatory patterns (see Fig 1).

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Fig 1. Irregular pattern (a)(left) and out-of-plan travel wave (b)(right).

In cells, two types of active matter systems coexist. One is the F-actin coupled with myosin motors and the other is the microtubule coupled with myosin motors. In a region adjacent to the cell membrane, known as the cell cortical layer, F-actin+myosins form the cytoskeleton to provide the mechanical support for the membrane and to regulate cell motion. In order to develop a whole cell model at the continuum level, active matter model is an ideal choice.

As a major application of the active matter modeling, we have developed a set of multiphase field models to describe cell motion on a substratum as well as cell mitosis, especially, cytokinesis. The basic ingredient in the multiphase models is depicted in Fig 2.

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Fig 2. Portrait of a simple 3-phase cell model, where the cortical layer is modeled as an active liquid crystal phase.

Using this model, we can simulate cytokinesis of an eukaryotic cell with a very good precision. Fig 3a depicts the 3-D simulation and Fig 3b shows a comparison with the experiment on the radius of the neck. This model has been extended to study cell migration on substrate, cell oscillation and cell rounding.

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Fig 3. 3D simulations of cytokinesis and comparison with experiment. A. (Left) 3D simulations. B. (Right) Radis predicted by the model and the experimentally measured radius at various time.

Cell modeling using active matter models is a promising direction with a great potential to produce accurate and versatile models to study various mecho-chemical mechanisms inherent in cells and explain various transporting phenomena including signaling through mechanical sensing.

References:

1. S. Ramaswamy. The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys.,1:323, 2010.

2. M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha.

3. Hydrodynamics of soft active matter. Rev. Mod. Phys., 85:1143, 2013.Jia Zhao and Qi Wang, Modeling  and Simulations of Cytokinesis of  Eukaryotic Cells, International Journal for Numerical Methods in Biomedical Engineering, 2015.

4.Xiaogang Yang and Qi Wang, Structures and basic patterns in cavity flows of active liquid crystals:  Computers and Fluids, 2015.

 


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