Research

   The Theoretical Biological Physics group does teaching and research in mainly computational biological physics. Below is a partial listing of the current research projects.

Modeling of biological membranes

Research leader(s)
Olle Edholm, Professor, Tel +46 (0)8 5537 8168, e-mail:
oed@kth.se

Scientist(s)
Erik Brandt, Qaiser Waheed 

Keywords
Molecular Dynamics Simulation, Monte Carlo Simulation, Simulated Annealing 

Project period
2000- 

Project description
This research takes its starting point in the application of computational statistical mechanics to problems in biological physics. The main part of the efforts fall into the area soft condensed matter physics with its main applications to biological membranes. Model membranes, lipid bilayers, are studied at atomic resolution with molecular dynamics simulations using parallel computing. Simulations contain the order of hundred thousand to a million atoms and span times up to a micro second. This requires huge super computing efforts and we are one of the groups in the world that have been pushing the limits for large scale molecular dynamics simulations. Emphasis is put on validating the basic atomistic models against experimental data and on interpreting the simulation results in terms of simplified models. We can since some years reach the time and spatial scales of mesoscopic undulations and thickness fluctuations. This enables us to calculate quantities that are parameters of the continuum models and test the validity of such models. Stress profiles across the bilayers can be calculated which gives an understanding for why different lipids form different aggregates like bilayers, micelles or hexagonal phases. lipid bilayer folding , i.e. the formation of lipid bilayers from a random mixture of water and lipids in computer simulations has been solved. This is easier and less time consuming than the protein folding problem but shows that this problem might be solved with similar techniques in the future. More detailed properties of the bilayers, like the complicated dynamics that gives rise to frequency dependent NMR relaxation can be reproduced and understood from time correlation functions that can be calculated from the simulations and shown to be stretched over 5-6 orders of magnitude in time. Density autocorrelation functions in space and time has been calculated and present simulation results are much more accurate that those obtained from inelastic x-ray or neutron scattering. From this the regions of validity and parameters of generalized molecular hydrodynamics are probed. The applications also involve studies of pore formation in membranes. Experimentally, this is performed by applying strong electrostatic fields or adding chemical substances. In simulations we may calculate the free energy cost of pore formation and growth and show that one goes from a fluctuation driven regime at small radius at which the free energy is quadratic in the radius into a regime at large radius at which the free energy is linear and can be characterized by a line tension. More realistic membranes consisting of mixtures of different lipids (e.g. cholesterol containing ones) and systems containing membrane proteins are also studied with simulation techniques. Further problems that have been and will be studied include the gel/liquid crystalline phase transition, the origin of the membrane dipole potential, simplified models for the hydrocarbon chain dynamics and the water structure at the lipid/water interface.

Source of funding
VR (Swedish Science Research Council)

Modeling of membrane proteins

Research leader(s)
Olle Edholm, Professor, Tel +46 (0)8 5537 8168, e-mail:
oed@kth.se

Keywords
Bacteriorhodopsin, Helix/Helix Packing, Molecular Dynamics Simulation, Monte Carlo Simulation, Simulated Annealing 

Project period
1986-1995 - 

Project description
Many membrane proteins consist of a small number of secondary structural elements such as membrane spanning alpha-helices. The objective is to study the packing of these aiming at a prediction of the three dimensional structure of such membrane proteins. Computer simulation methods like molecular dynamics simulations and Monte Carlo simulations are used to investigate the structure and functioning of membrane proteins like bacteriorhodopsin. The general idea is that secondary structure to a large extent can be predicted independently of the detailed three-dimensional structure. In this way model structures can be constructed that may be taken as starting points for the computer simulations. We have found Monte Carlo simulations at elevated temperatures a specially powerful method to overcome energy barriers and predict low energy helix/helix packing. The problem of getting trapped in metastable states may be overcome by running ensembles of simulations using different seeds to the random number generators in the different runs. References: Jähnig, F and Edholm O., Modeling of the structure of bacteriorhodopsin; A molecular dynamics study, J. Mol. Biol. 226 (1992) 837-850. Edholm O., Berger O. and Jähnig. F., S Structure and fluctuations of bacteriorhodopsin in the purple membrane; A molecular dynamics study, J. Mol. Biol. 250(1995) 94-111.

Free energy of pore nucleation in lipid membranes

Research leader(s)
Olle Edholm, Professor, Tel +46 (0)8 5537 8168, e-mail: oed@kth.se

Scientist(s)
Jakob Wohlert

Collaborators
W.J. Briels and W.K. den Otter, University of Twente, The Netherlands

Keywords
Molecular Dynamics Simulation, Lipid Bilayers, Pore Nucleation

Project period
2004-2006

Project description
It has long been known that pores of sizes from a few nanometer up to the micrometer range can be formed and closed reversibly in lipid bilayers. Usually they are formed under very special circumstances, such as applied strong electric fields (electroporation) or mechanical stress, but they also form spontanuosly. This is however a very rare event suggesting a free energy barrier which is large compared to thermal energies. The free energy profile of growing (or shrinking) an already existing pore is well described by existing theories which states that the free energy is directly proportional to the diameter of the pore. This theory does not however describe the nucleation process itself. We are studying this process by means of molecular dynamics simulations of an atomistic model of a lipid bilayer. To get an free energy profile we use the Potentials of Mean Constraint Force (PMCF) method, along a reaction coordinate invented by T.V. Tolpekina et al. for a simplified (coarse grained) model (J. Chem. Phys., 121:12060-12066). While this reaction coordinate is easily related to the size of a pore, it is also perfectly well defined for an intact bilayer and intermediate conformations during nucleation.

Dynamic calculation of protonation states of proteins

Research leader(s)
Olle Edholm, Professor, Tel +46 (0)8 5537 8168, e-mail:
oed@kth.se

Scientist(s)
Lars Sandberg, now at Astra Zenecca 

Keywords
Grand Canonical Monte Carlo, pKa-Calculation, Poisson-Boltzmann Equation, Polyelectrolyte, Titration Curve 

Project period
1994-2002  

Project description
Proteins have several sites that may be protonated and deprotonated. The objective is to develop methods to calculate how the protonation state of these sites changes due to small structural changes that occur with the protein. Calculations of protonation states in proteins have been performed since a couple of years and are usually performed on a fixed protein structure while the solvent and counter ions are represented in a continuum approximation. This means that the Poisson-Boltzmann equation is solved numerically. However, the results seem to be very sensitive to small changes in the protein structure. Our aim is to go beyond these approximations, treat everything at the atomic level and take fluctuations and structural changes in the protein into account. This is important for the study of the photocycle in bacteriorhodopsin. This protein pumps protons across a cell membrane and is driven by light. It is known that this process is coupled to small structural changes and the protonation and deprotonation of a handful of sites in the middle of the protein. References: Sandberg L. and Edholm O., Biophys Chemistry, 65 (1997) 189-204 and Nagel J. et. al., Biochem. 36( 1997) 2875-2883. 

Modelling of biological network processes. Aspects of stability and random influence

Research leader(s)
Clas Blomberg, Professor, Tel +46 (0)8 5537 8166, e-mail: cob@theophys.kth.se

Project period
-2001 

Keywords
Biological control mechanisms, Chaos, Nerve impulses, Noise 

Project description
Chemical reactions in living cells comprise complex networks with important control (feedback) mechanisms. It is also suggested that cells by the possibilities of evolution can reach optimal levels for essential processes. To analyse this properly, mathematical modelling is essential. Because of the complexity, an influence of a foreign substance is seldom straight-forward. Further, a proper function can be destroyed by random influences, but sometimes random influences are essential for creating a necessary activity. Possibilities to reach optimal results may also depend on such effects. 
We have previously investigated the accuracy of synthesis processes and factors that may influence it. A project under this title is going with an aim to understand the response to free radicals in the cells. In another project we investigate what can be achieved by spontaneous generation of nerve impulses by random influences. One question here is whether living systems and, in particular, the neural system can systematically use random processes and even generate chaotic behaviour for an optimal performance. In connection with these problems, we also investigate the effect of noise in simpler model systems, governed by non-linear dynamics. 

Source of funding
NFR (Swedish Natural Science Research Council), TFR (Swedish Research Council for Engineering Sciences)

Physical problems concerning diversity and the occurrence of function in the Origin of Life

Research leader(s)
Clas Blomberg, Professor, Tel +46 (0)8 5537 8166, e-mail: cob@theophys.kth.se

Scientist(s)
Mikael Cronhjort 

Project period
-2001 

Keywords
Artificial life, Complexity, Origins of life, Self-Organization 

Project description
Mathematical modelling and physical reasoning provide valuable information about the occurrence of organisation and stages in the origin of life which are otherwise not amenable to experimental studies. In that way, we get an understanding of the steps that must have preceeded the occurrence of life and, with that, a wider understanding of Life itself.
In particular, we are interested in questions about how stability and also a rich diversity could be reached. Life as today shows a very high stability, but this is accomplished by a rich biochemical controlling machinery. A big question is how this was achieved at the onset. Also, even the first cell that occurred must have had a large number of functions. Still, models for understanding these steps do not easily explain how such a diversity could have arisen. 
These studies are closely related to the field of "Artificial Life", which aims to understand features of life by studying artificial, mainly abstract systems with many of the features of real life. Again, stability questions are crucial for these systems. 

Source of funding
NFR (Swedish Natural Science Research Council) 


Responsible for this page: Olle Edholm <oed@kth.se>