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Research in Biophysics, Soft Materials and Pattern Formation

The soft matter and biophysics group started at LCE in September 2000. In general, the research is geared towards the interface between condensed matter physics, biology and material science. The great diversity of these systems, ranging, for instance, from complexes of DNA and cationic liposomes used in gene transfer to unexpected morphological evolution of polymers under shear flow and to pattern formation in biological processes, provides new challenges in both fundamental and applied research.

Typically, biological processes take place under non-equilibrium conditions. Modeling these processes provides many theoretical challenges since eventually the validity of equilibrium concepts, such as universality and scaling laws, breaks down. It is important to study their range of validity, and how the emergence of new time and length scales, and possibly a steady state, is manifested in dynamical systems. A good example of that is the shear flow behavior of complex fluids where the dynamics of order-disorder transition depends intimately on the application of shear. As vast number of industrial processes involve complex fluids and polymer mixtures under shear flow conditions, it is clear that a better theoretical understanding of these processes has immediate practical applications.

Another challenge arises from the interdisciplinary nature of these problems. A strong interaction between theory, computation, and experiments is essential in order to get insight of into the physical mechanisms producing these complex, often collective, phenomena. A clear example of this is the study of lipoplexes, i.e., the formation and behavior of DNA-cationic liposome complexes. There exists a large amount of experimental data, and in vivo experiments have shown that clinical application of lipoplexes is effective and safe. However, the processes and physical mechanisms, e.g., those involving interactions of electrostatic origin, that control the formation of these complex structures are not well established. Theoretical studies and, in particular, simulational studies, have the potential of helping to characterize better these complex processes.

The studies introduced below briefly describe our efforts in soft matter and biophysics. For details and up-to-date information, please see the corresponding project home page as given in connection of each project.

Modeling and computer simulation of DNA-cationic lipid complexes

Researchers: Mikko Karttunen, Antti Pakkanen, Paavo K.J. Kinnunen*, Ari Lukkarinen, and Kimmo Kaski
*Institute of Biomedicine, University of Helsinki

Project home page

The development in gene therapy has led to a need for new and more efficient transfection vectors. Viruses have been used in transfection several years. During the recent years, cationic liposomes have emerged as a potential rival for viruses. Cationic liposomes have several advantages over viruses, e.g., nonimmunogenity, low toxicity and a capability to carry large amount of DNA. However, the properties of cationic liposomes and their interaction with DNA is not known accurately.

  
Figures 25 and 26
Figure 25: Monte Carlo simulation of DNA (green) interacting with a lipid membrane. Figure 26: Top and side views of a Monte Carlo simulation of a monolayer consisting of zwitterionic lipids.

One of the major difficulties in determining the properties of liposomes and their interaction with DNA is the presence of many time and length scales. In addition, the collective nature of the complexation process makes the problem both theoretically and computationally very demanding. In addition to the van der Waals type interactions, the long-range electrostatic and dipolar interactions are crucial for the process - both lipids and DNA carry electric charge.

The current knowledge of DNA-cationic liposome complexes, also known as lipoplexes, is mainly based on experimental results. The aim of this study is to develop computationally effective theoretical models to study the nature of DNA-lipid interaction and complexation.

We have simulated small DNA-lipid membrane systems by using the Monte Carlo method. The electrostatic interactions were taken into account by using the direct Coulomb sum. To study larger systems the Ewald summation method for electrostatic interactions has been implemented. In addition, the Ewald summation method has been modified in such a way that it can be used to study systems having a finite extension in one of the directions, i.e., systems having a slab geometry. Currently, we are studying the properties of monolayers consisting of zwitterionic and cationic lipids using both Monte Carlo and molecular dynamics methods. These simulations are compared to experimental work in order to develop a better understanding of the relevant interactions and their exact nature in the lipoplex formation.

Mesoscopic simulation of self-assembly using dissipative particle dynamics

Researchers: Mikko Karttunen, Ilpo Vattulainen*,Gerhard Besold, James Polson+, Petri Nikunen
Max Planck Institute for Polymer Research, Mainz, Germany
*Technical Univ. of Denmark/Helsinki University of Technology
+University of Prince Edward Island, Charlottetown, Canada

Project home page

Dissipative Particle Dynamics (DPD) is a mesoscopic simulation technique which is particularly well suited for studies of soft condensed matter systems. It is characterized by coarse-graining in particle representation leading to a simplified description of interparticle interactions in terms of conservative, dissipative, and random forces. This formulation leads to momentum conservation, which implies that hydrodynamic flow effects are properly taken into account.

We use DPD to study the self-assembly of lipid bilayers and the formation of complex structures in polymer and lipid systems, see Figs. 27a and b. Self-assembly is cooperative process, and its many-particle nature together with the presence of many time and length scales poses many interesting challenges. Our main interest lies in lipid and polymeric systems containing charges. Practical applications include, for example, drug delivery by cationic liposomes, detergents and emulsions.

  
Figure 27
Figure 27: DPD simulation of symmetric 5-5 block co-polymer melt consisting of 40000 monomers. a) The initial state is completely disordered. b) During the simulation the system undergoes microphase separation. The snapshot is after 2000 time steps. c) It is important to choose a proper way to integrate the equations of motion. This is illustrated by plotting the ideal gas compressibility as a function of the time step for three different integration methods. Any deviations from one indicate artifacts.

The DPD method poses some practical problems, and during the first stage of this project we have studied the quality of various DPD integrators in terms of physical observables, such as response functions and transport coefficients. Due to the presence of stochastic and velocity-dependent dissipative forces, integration of the equations of motion may give rise to pronounced artifacts, see Fig. 27c. We have shown that artifacts can be sufficiently suppressed by using integrator schemes in which the velocity dependence of the dissipative forces is taken into account.

Shear induced morphological changes in complex fluids

Researchers: Markus Miettinen, Mikko Karttunen, Ilpo Vattulainen*, Ari Lukkarinen, Kimmo Kaski
*Laboratory of Physics, Helsinki University of Technology

Project home page

The effect of shear flow on rhelogical properties of polymer mixtures is of great interest from both practical and fundamental point of view. On the fundamental physics side, the problem is a nonequilibrium one making it theoretically and computationally difficult. It would be desirable to be able to test, e.g., to what extent scaling laws from the equilibrium theory are valid, what is the effect of shear on viscosity, how is the dynamics of order-disorder transition affected by shear, what is the effect of hydrodynamics, and so on. From the practical point of view, industrial processes often involve polymer mixtures under shear flow conditions. A better theoretical knowledge, for example, of how to control viscosity and phase separation would have immediate consequences in developing more efficient processes.

We use nonequilibrium molecular dynamics (NEMD) to study the morphological changes in polymer mixtures under shear flow. We use the so-called SLLOD algorithm and Lees-Edwards boundary conditions to implement shear. Changes in the morphological alignment as a function of the shear rate have been seen in many experiments but the theoretical explanation is still missing. Thus far, they have not been seen in computer simulations. During the first stage of this study we have implemented and tested a single processor NEMD code. The activities in the immediate future involve parallelization of the code. That is necessary since many of these changes are essentially due to collective effects.

 
Figure 28
Figure 28: Elongation of a single molecule under shear flow.

Turing systems in pattern formation

Researchers: T. Leppänen, K. Kaski, M. Karttunen and R.A. Barrio*
*Instituto de Fisica, Universidad Nacional Autonoma de Mexico

Project home page

Our goal is to study patterns generated by Turing systems, which are based on reaction-diffusion equations developed to describe some salient features of morphogenesis. In this study, we have solved these equations in two dimensions. Figure 29 shows one of these systems in the initial state and the result.

  
Figure 29
Figure 29: Evolution of a Turing pattern in 120x120 lattice. Left: the initial state with sources. Middle: the evolved pattern after 100000 iterations. Right: the grown network after 100000 iterations, which we propose to be reminiscent of neural network pattern.

Our main interest lies in Turing systems in the presence of morphogen sources and in the biological interpretation of the patterns formed. The particular question we are interested in is if Turing systems can produce an inductive signaling mechanism for neural patterning. Our model contains three morphogens, an inhibitor, an activator and a path finder. The patterns seem to bear remarkable likeness to patterns found in living creatures and organisms.

In addition to the studies about parameter dependence of these systems, we are developing a model that generates a three dimensional network that could be interpreted as a biological network, i.e, as a map of the dendrites between the neurons (see Figure 29). In other words, our model simulates the growth of dendrites between the neurons of an organism, i.e., the development of the nervous system or the brain (Figure 30).

  
Figure 30
Figure 30: 3D simulation of a Turing system. In the light of the results in two dimensions we may ask, whether it is possible to mathematically generate ``brain-like'' tissue in the future?

Atomic Diffusion in Disordered Many-particle Systems

Researchers: Leonel Perondi, Sir Roger Elliott*, and Kimmo Kaski
*Oxford University, UK

There has been a considerable interest in the development of new techniques for treating microscopic diffusion phenomena in ordered as well as disordered many-particle systems. As is well known many-particle effects may play a key role on the diffusion-related properties of a system. Applications range from ionic conduction in electronic insulators (ionic conductors) to electronic transport in semiconductors.

An isolated particle in contact with a heat reservoir undergoes a random walk montion (brownian motion), which may be characterized by a linear relation between the mean square displacement and time. The linear coefficient gives the free-particle diffusion constant D0. In an interacting many-particle system, the single-particle (tracer) diffusion constant is changed to fb fc D0, where fb and fc are termed the blocking and correlation factors, respectively. The blocking factor is a measure of the probability of a successful single-particle hop. Since the presence of other particles tends to hinder the movement of any given particle, fb is less than one. The correlation factor arises from the fact that interactions produce correlation among successive displacements. Such correlations slow down the diffusion process and fc is also less than one. The presence of static defects in the space in which the diffusion process takes place, further enhances both effects. Depending on the nature and concentration of such defects new diffusive regimes may settle in. In particular, when the mean square displacement increases with time to some power less than one, the diffusive regime is called anomalous.

One of the main objectives of the present project is the study of diffusion in many-particle systems in which the blocking and correlation effects may lead to an anomalous diffusive behaviour.

Electro- and Magneto-rheological Fluids

Researchers: Ari Lukkarinen and Kimmo Kaski

Electrorheological (ER) fluids are suspensions consisting of dielectric particles of size 0.1-100 microm and dielectric base fluid. Since the dielectric constant of suspensions particles differs from the dielectric constant of the base fluid, external electric field polarizes particles. These polarized particles interact and form chain-like or even lattice-like organized structures. Simultaneously the rheological properties of the suspension change effectively, e.g. the effective viscosity increases dramatically. ER-suspensions have also a magnetic analog consisting of ferromagnetic particles and the base liquid. As the viscosity of the electrorheological liquid can be controlled with the electric field strength, the viscosity of magnetorheological (MR) fluid is sensitive to the magnetic field.

  
Figure 31
Figure 31: Snapshots of the grown structure (on the left). The colour of the particle denotes its dielectric constant. On the right a system consisting of homogeneous particles is sheared in the direction that is almost normal to the surface of the paper. Particles form well-organized hexagonal shear-induced structures.

These fluids react rapidly to the applied field. The response time of electrorheological fluids is of the order of 1-10 ms, which in principle enables the use of these liquids in such applications as electrically controlled clutches, valves and active damping devices. Perhaps the most striking application utilizing electrorheological fluids is an artificial muscle made of polymer suspension particles in a polymer gel.

Recently we have studied structure formation and properties of mechnically stressed systems. For this study we deviced a model taking long range forces and many-particle interactions into account at the dipolar level. This model was also utilized in the study of a new kind of electrorheological fluid consisting of the base fluid and two kinds of suspension particles -- particles with larger and particles with smaller dielectric constant than that of the base fluid. It could be expected that some physical properties of such systems might differ from those observed in the systems where only one kind of particles were present. However, contrary to the static finite element studies, dynamic studies suggested that ER/MR systems get easily trapped to states of local energy minima corresponding to some kind of a polycrystalline structure. Moreover, there were some evidence that the ground state structure might be dependent on the volume fraction of the suspension particles such that only small volume fractions would favour the formation of isolated particle columns having a clear lattice symmetry.


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