The intention is to provide a broad overview of the role of noise and basic methods to describe noise effects in biological systems. It starts from a brief discussion of the statistical mechanical basis, and Brownian motion which is generalised to calculations of randomly induced transitions over energy barriers, and stochastic resonance. The description of discrete step processes provides another approach, which also is a basis of a stochastic description of chemical reactions. Macromolecular structure changes are considered as triggered by the background fluctuations. A strong emphasis is put on "fluctuation-dissipation" relations, relations between the irregular fluctuations and the dissipative spreading of energy towards a most probable distribution. We also take up some applications to non-linear systems, noise effects together with oscillations and signal transmission as well as models on unidirectional motion of various kinds with Brownian ratchets and active transport as examples.

The purpose of the book is to give a survey of the physics that is relevant for biological applications, and also to discuss what kind of biology needs physics. The book gives a broad account of basic physics, relevant for the applications and various applications from properties of proteins to processes in the cell to wider themes such as the brain, the origin of life and evolution. It also considers general questions of common interest such as reductionism, determinism and randomness, where the physics view often is misunderstood. The subtle balance between order and disorder is a repeated theme appearing in many contexts. There are descriptive parts which shall be sufficient for the comprehension of general ideas, and more detailed, formalistic parts for those who want to go deeper, and see the ideas expressed in terms of mathematical formulas. - Describes how physics is needed for understanding basic principles of biology - Discusses the delicate balance between order and disorder in living systems - Explores how physics play a role high biological functions, such as learning and thinking.

Lipid molecules form thin biological membranes that envelop all living cells, and behave as two-dimensional liquid sheets immersed in bulk water. The interactions of such biomembranes with their environment lay the foundation of a plethora of biological processes rooted in the mesoscopic domain - length scales of 1-1000 nm and time scales of 1-1000 ns. Research in this intermediate regime has for a long time been out of reach for conventional experiments, but breakthroughs in computer simulation methods and scattering experimental techniques have made it possible to directly probe static and dynamic properties of biomembranes on these scales.

Biomembranes are soft, with a relatively low energy cost of bending, and are thereby influenced by random, thermal fluctuations of individual molecules. Molecular dynamics simulations show how in-plane (density fluctuations) and out-of-plane (undulations) motions are intertwined in the bilayer in the mesoscopic domain. By novel methods, the fluctuation spectra of lipid bilayers can be calculated withdirect Fourier analysis. The interpretation of the fluctuation spectra reveals a picture where density fluctuations and undulations are most pronounced on different length scales, but coalesce in the mesoscopic regime. This analysis has significant consequences for comparison of simulation data to experiments. These new methods merge the molecular fluctuations on small wavelengths, with continuum fluctuations of the elastic membrane sheet on large wavelengths, allowing electron density profiles (EDP) and area per lipid to be extracted from simulations with high accuracy.

Molecular dynamics simulations also provide insight on the small-wavelength dynamics of lipid membranes. Rapidly decaying density fluctuations can be described as propagating sound waves in the framework of linearized hydrodynamics, but there is a slow, dispersive, contribution that needs to be described by a stretched exponential over a broad range of length- and time scales - recent experiments suggest that this behavior can prevail even on micrometer length scales. The origin of this behavior is discussed in the context of fluctuations of the bilayer interface and the molecular structure of the bilayer itself. Connections to recent neutron scattering experiments are highlighted.

Atomic resolution and coarse-grained simulations of dimyristoylphosphatidylcholine lipid bilayers were analyzed for fluctuations perpendicular to the bilayer using a completely Fourier-based method. We find that the fluctuation spectrum of motions perpendicular to the bilayer can be decomposed into just two parts: 1), a pure undulation spectrum proportional to q(-4) that dominates in the small-q regime; and 2), a molecular density structure factor contribution that dominates in the large-q regime. There is no need for a term proportional to q(-2) that has been postulated for protrusion fluctuations and that appeared to have been necessary to fit the spectrum for intermediate q. We suggest that earlier reports of such a term were due to the artifact of binning and smoothing in real space before obtaining the Fourier spectrum. The observability of an intermediate protrusion regime from the fluctuation spectrum is discussed based on measured and calculated material constants.

The decay of fluctuations in fluid biomembranes is strongly stretched and nonexponential on nanometer lengthscales. We report on calculations of structural correlation functions for lipid bilayer membranes from atomistic and coarse-grained molecular dynamics simulations. The time scales extend up to microseconds, whereas the linear size of the largest systems is around 50 nm. Thus, we can cover the equilibrium dynamics of wave vectors over two orders of magnitude (0.2-20 nm(-1)). The time correlations observed in the simulations are best described by stretched exponential functions, with exponents of 0.45 for the atomistic and 0.60 for the coarse-grained model. Area number density fluctuations, thickness fluctuations, and undulations behave dynamically in a similar way and have almost exactly the same dynamics for wavelengths below 3 nm, indicating that in this regime undulations and thickness fluctuations are governed by in-plane density fluctuations. The out-of-plane height fluctuations are apparent only at the longest wavelengths accessible in the simulations (above 6 nm). The effective correlation times of the stretched exponentials vary strongly with the wave vector. The variation fits inverse power-laws that change with wavelength. The exponent is 3 for wavelengths smaller than about 1.25 nm and switches to 1 above this. There are indications for a switch to still another exponent, 2, for wavelengths above 20 nm. Compared to neutron spin-echo (NSE) experiments, the simulation data indicate a faster relaxation in the hydrodynamic limit, although an extrapolation of NSE data, as well as inelastic neutron scattering data, is in agreement with our data at larger wave vectors.

The traditional method for extracting electron density and other transmembrane profiles from molecular dynamics simulations of lipid bilayers fails for large bilayer systems, because it assumes a flat reference surface that does not take into account long wavelength undulations. We have developed what we believe to be a novel set of methods to characterize these undulations and extract the underlying profiles in the large systems. Our approach first obtains an undulation reference surface for each frame in the simulation and subsequently isolates the long-wavelength undulations by filtering out the intrinsic short wavelength modes. We then describe two methods to obtain the appropriate profiles from the undulating reference surface. Most combinations of methods give similar results for the electron density profiles of our simulations of 1024 DMPC lipids. From simulations of smaller systems, we also characterize the finite size effect related to the boundary conditions of the simulation box. In addition, we have developed a set of methods that use the undulation reference surface to determine the true area per lipid which, due to undulations, is larger than the projected area commonly reported from simulations.

Background: Much research in epidemiology has been focused on evaluating conventional methods of control strategies in the event of an epidemic or pandemic. Travel restrictions are often suggested as an efficient way to reduce the spread of a contagious disease that threatens public health, but few papers have studied in depth the effects of travel restrictions. In this study, we investigated what effect different levels of travel restrictions might have on the speed and geographical spread of an outbreak of a disease similar to severe acute respiratory syndrome (SARS). Methods: We used a stochastic simulation model incorporating survey data of travel patterns between municipalities in Sweden collected over 3 years. We tested scenarios of travel restrictions in which travel over distances > 50 km and 20 km would be banned, taking into account different levels of compliance. Results: We found that a ban on journeys > 50 km would drastically reduce the speed and geographical spread of outbreaks, even when compliance is < 100%. The result was found to be robust for different rates of intermunicipality transmission intensities. Conclusion: This study supports travel restrictions as an effective way to mitigate the effect of a future disease outbreak.

The present study analyzes the effect of the simulation conditions on the results of molecular dynamics simulations of G-protein coupled receptors (GPCRs) performed with an explicit lipid bilayer. Accordingly, the present work reports the analysis of different simulations of bovine rhodopsin embedded in a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer using two different sampling conditions and two different approaches for the treatment of long-range electrostatic interactions. Specifically, sampling was carried out either by using the statistical ensembles NVT or NPT (constant number of atoms, a pressure of 1 arm in all directions and fixed temperature), and the electrostatic interactions were treated either by using a twin-cutoff, or the particle mesh Ewald summation method (PME). The results of the present study suggest that the use of the NPT ensemble in combination with the PME method provide more realistic simulations. The use of NPT during the equilibration avoids the need of an a priori estimation of the box dimensions, giving the correct area per lipid. However, once the system is equilibrated, the simulations are irrespective of the sampling conditions used. The use of an electrostatic cutoff induces artifacts on both lipid thickness and the ion distribution, but has no direct effect on the protein and water molecules.

The behavior of electrolytes in molecular dynamics simulations of zwitterionic phospholipid bilayers; is very sensitive to the force field parameters used. Here, several 200 ns molecular dynamics of simulations of dipalmitoyl phosphotidylcholine (PC) bilayers in 0.2 M sodium or potassium chloride using various common force field parameters for the cations are presented. All employed parameter sets give a larger number of Na+ ions than K+ ions that bind to the lipid heads, but depending on the parameter choice quite different results are seen. A wide range of coordination numbers for the Na+ and K+ ions is also observed. These findings have been analyzed and compared to published experimental data. Some simulations produce aggregates of potassium chloride, indicating (in accordance with published simulations) that these force fields do not reproduce the delicate balance between salt and solvated ions. The differences between the force fields can be characterized by one single parameter, the electrostatic radius of the ion, which is correlated to sigma(MO) (M represents Na+/K+), the Lennard-Jones radius. When this parameter exceeds a certain threshold, binding to the lipid heads is no longer observed. One would, however, need more accurate experimental data to judge or rank the different force fields precisely. Still, reasons for the poor performance of some of the parameter sets are clearly demonstrated, and a quality control. procedure is provided.

The effect of physiological concentrations of different chlorides on the structure of a dipalmitoyl phosphatidylcholine (DPPC) bilayer has been investigated through atomistic molecular dynamics simulations. These calculations provide support to the concept that Li+, Na+, Ca2+, Mg2+, Sr2+, Ba2+, and Ac3+, but not K+, bind to the lipid-head oxygens. Ion binding exhibits an influence on lipid order, area per lipid, orientation of the lipid head dipole, the charge distribution in the system, and therefore the electrostatic potential across the head-group region of the bilayer. These structural effects are sensitive to the specific characteristics of each cation, i.e., radius, charge, and coordination properties. These results provide evidence aimed at shedding some light into the apparent contradictions among different studies reported recently regarding the ordering effect of ions on zwitterionic phosphatidylcholine lipid bilayers.

The question has arisen in recent literature: how to partition the total area in simulations of membranes consisting of more than one kind of molecule into average areas for each kind of molecule. Several definitions have been proposed, each of which has arbitrary features. When applied to mixtures of cholesterol and DPPC, these definitions give different results. This note recalls that physical chemistry provides a canonical way to de. ne molecular area, in analogy to the definition of partial-specific volume. Results for partial-specific area are obtained from simulations of DPPC/cholesterol bilayers and compared to the results from the other recent definitions. The partial-specific-area formalism dramatically demonstrates the condensing effect of cholesterol and this leads to the introduction of a specific model that accounts for the area of mixtures of cholesterol and lipid over the entire range of cholesterol concentrations.

The two potassium ion channels KirBac1.1 and KcsA are compared in a Molecular Dynamics (MD) simulation study. The location and motion of the potassium ions observed in the simulations are compared to those in the X-ray structures and previous simulations. In our simulations several of the crystallography resolved ion sites in KirBac1.1 are occupied by ions. In addition to this, two in KirBac1.1 unresolved sites where occupied by ions at sites that are in close correspondence to sites found in KcsA. There is every reason to believe that the conserved alignment of the selectivity filter in the potassium ion channel family corresponds to a very similar mechanism for ion transport across the filter. The gate residues, Phe146 in KirBac1.1 and Ala111 in KcsA acted in the simulations as effective barriers which never were passed by ions nor water molecules.

The effect of the inhomogeneous environment upon solvent molecules close to a macromolecular surface is evaluated from a molecular-dynamics simulation of a protein, myoglobin, in water solution. The simulation is analyzed in terms of a mean-field potential from the protein upon the water molecules and spatially varying translational diffusion coefficients for solvent molecules in directions parallel and perpendicular to the protein surface. The diffusion coefficients can be obtained from the slope of the average-square displacements vs time, as well as from the integral of the velocity autocorrelation functions. It is shown that the former procedure gives a lot of ambiguities due to the variation of the slope of the curve with time. The latter, however, after analytic correction for the contribution from algebraic long-time tails, furnish a much more reliable alternative.

When simulating a molecular system, a cutoff distance for interactions is often used to speed up the simulations. This is made at the cost of neglecting some interactions which will lead to inaccurate results for energy, pressure components and surface tension (for systems with surfaces). To compensate for the neglected long-range interactions, continuum corrections can be added to the surface tension, system energies and pressures. For a homogenous isotropic system this is straight-forward but for a system with a surface it is more complicated. In this work we have derived expressions for the corrections to the surface tension, system energies and pressures that are more general than previous results. When these corrections are added to multi-component systems with a surface (or single-component systems with vacuum) they compensate for the change in surface tension, system energy and pressures due to the finite cutoff. When simulating systems with no Coulomb-interactions, the structure of the system may change significantly if the cutoffs are too short. If this is the case then these corrections alone will not be enough. The solution is to add corrections to the force acting on each molecule added during the simulation, which we derive in this work. This solves the structural problem at low cutoffs and makes it possible to calculate an accurate surface tension independent of cutoff. 

It is known that a cutoff on the van der Waals interactions in molecular dy- namics simulations of systems containing a surface (gas/liquid for instance) may cause substantial changes in the densities of the different parts of the system. In order to make the density independent of the cutoff, we have calculated forces from continuum integrations and added them to the forces calculated in a molecular dynamics program. These corrections compensate for the lack of long range interactions and exert a pressure on the system that may be several hundred bars. We show here that inclusion of such corrections makes the density profile independent of the cutoff. This makes it possible to calculate a surface tension that is independent of the cutoff. 

Molecular dynamics simulations are usually performed using cutoffs (r_c) for the short-ranged dispersion interactions (r⁻⁶). For isotropic systems, long-range interactions are often added in a continuum approximation. This usually leads to excellent results that are independent of the cutoff length down to about 1 nm. For systems with interfaces or other anisotropic systems the situation is more complicated. We study here planar interfaces, focusing on the surface tension, which is sensitive to cutoffs. Previous analytic results giving the long-range correction to the surface tension of a liquid-vapor interface as a two- or three-dimensional integral are revisited. They are generalized by introducing a dispersion density profile which makes it possible to handle multi-component systems. For the simple but common hyperbolic tangent profile the integral may be Taylor-expanded in the dimensionless parameter obtained by dividing the profile width with the cutoff length. This parameter is usually small and excellent agreement with numerical calculations of the integral is obtained by keeping two terms in the expansion. The results are compared to simulations with different lengths of the cutoff for some simple systems. The surface tension in the simulations varies linearly in r_c⁻², although a small r_c⁻⁴-term may be added to improve the agreement. The slope of the r_c⁻²-line could in several cases be predicted from the change in dispersion density at the interface. The disagreements observed in some cases when comparing to theory, occur when the finite cutoff used in the simulations causes structural differences compared to long-range cutoffs or Ewald summation for the r⁻⁶-interactions. 

Molecular dynamics simulations are usually performed using cutoffs (r(c)) for the short-ranged dispersion interactions (r(-6)). For isotropic systems, long-range interactions are often added in a continuum approximation. This usually leads to excellent results that are independent of the cutoff length down to about 1 nm. For systems with interfaces or other anisotropic systems the situation is more complicated. We study here planar interfaces, focusing on the surface tension, which is sensitive to cutoffs. Previous analytic results giving the long-range correction to the surface tension of a liquid-vapor interface as a two- or three-dimensional integral are revisited. They are generalized by introducing a dispersion density profile which makes it possible to handle multicomponent systems. For the simple but common hyperbolic tangent profile the integral may be Taylor-expanded in the dimensionless parameter obtained by dividing the profile width with the cutoff length. This parameter is usually small, and excellent agreement with numerical calculations of the integral is obtained by keeping two terms in the expansion. The results are compared to simulations with different lengths of the cutoff for some simple systems. The surface tension in the simulations varies linearly in r(c)(-2), although a small r(c)(-4)-term may be added to improve the agreement. The slope of the r(c)(-2)-line could in several cases be predicted from the change in dispersion density at the interface. The disagreements observed in some cases when comparing to theory occur when the finite cutoff used in the simulations causes structural differences compared to long-range cutoffs or Ewald summation for the r(-6)-interactions.

2,6-lutidine molecules mix with water at high and low temperatures but in a wide intermediate temperature range a 2,6-lutidine/water mixture exhibits a miscibility gap. We constructed and validated an atomistic model for 2,6-lutidine and performed molecular dynamics simulations of 2,6-lutidine/water mixture at different temperatures. We determined the part of demixing curve with the lower critical point. The lower critical point extracted from our data is located close to the experimental one. The estimates for critical exponents obtained from our simulations are in a good agreement with the values corresponding to the 3D Ising universality class.

A systematic density functional theory (DFT) study has been performed to investigate the electronicand magnetic properties of one-dimensional sandwich polymers constructed with benzene (Bz) and thesecond-row transition metal (TM = Y, Zr, Nb, Mo, and Tc). Within the framework of generalized gra-dient approximation (GGA), [Tc(Bz)]∞ is a ferromagnetic half-metal, and [Nb(Bz)]∞ is a ferromagneticmetal. With the on-site Coulomb interaction for 4d TM atoms being taken into account, [Tc(Bz)]∞keeps a robust half-metallic behavior, while [Nb(Bz)]∞ becomes a spin-selective semiconductor. Thestability of the half-metallic [Tc(Bz)]∞ polymer is discussed based on magnetic anisotropy energy(MAE). Compared with 0.1 meV per metal atom in [Mn(Bz)]∞ , the calculated MAE for [Tc(Bz)]∞ is2.3 meV per metal atom. Such a significantly larger MAE suggests that Tc(Bz)]∞ is practically morepromising than its first-row TM equivalent.

In this thesis the properties of proteins and membranes are studied by molecular dynamics simulations. The subject is decomposed into parts addressing free energy calculations in proteins, mechanical inclusion models for lipid bilayers, phase transitions and structural correlations in lipid bilayers and atomistic lipid bilayer models. The work is based on results from large scale computer simulations, quantum mechanical and continuum models. Efficient statistical sampling and the coarseness of the models needed to describe the ordered and disordered states are of central concern.

Classical free energy calculations of zinc binding, in metalloproteins, require a quantum mechanical correction in order to obtain realistic binding energies. Classical electrostatic polarisation will influence the binding energy in a large region surrounding the ion and produce reasonable equilibrium structures in the bound state, when compared to experimental evidence.

The free energy for inserting a protein into a membrane is calculated with continuum theory. The free energy is assumed quadratic in the mismatch and depend on two elastic constants of the membrane. Under these circumstances, the free energy can then be written as a line tension multiplied by the circumference of the membrane inclusion. The inclusion model and coarse grained particle simulations of the membranes show that the thickness profile around the protein will be an exponentially damped oscillation.

Coarse-grained particle simulations of model membranes containing mixtures of phospholipid and cholesterol molecules at different conditions were performed. The gel-to-liquid crystalline phase transition is successively weakened with increasing amounts of cholesterol without disappearing even at a concentration of cholesterol as high as 60%.

A united atom parameterization of diacyl lipids was constructed. The aim was to construct a new force field that retains and improves the good agreement for the fluid phase and at the same time produces a gel phase at low temperatures, with properties coherent with experimental findings. The global bilayer tilt obtains an azimuthal value of 31^◦ and is aligned between lattice vectors in the bilayer plane. It is also shown that the model yield a correct heat of melting as well as heat capacities in the fluid and gel phase of DPPC.

A systematic molecular dynamics (MD) study of zinc binding to a peptide that mimics the structural binding site of horse liver alcohol dehydrogenase (HLADH) has been conducted. The four zinc binding cysteines were successively mutated into alanines to study the stability, zinc coordination, and free energy of binding. The zinc ion is coordinated to four sulfurs in the native peptide as in x-ray structures of HLADH. When the cysteines are replaced by alanines, the zinc coordinating sulfurs are replaced by waters and/or polypeptide backbone carbonyl oxygens. With two or fewer cysteines, the coordination number increases from four to six, while the coordination number varies between four and six with three cysteines depending on which of the cysteines that is replaced by an alanine. The binding free energies of zinc to the proteins were calculated from MD free energy integration runs to which corrections from quantum mechanical cluster calculations were added. There is a reasonable correlation with experimental binding free energies [T. Bergman , Cell. Mol. Life Sci. 65, 4019 (2008)]. For the chains with the lowest structural fluctuations and highest free energies lower coordination numbers for zinc are obtained. Finally, x-ray absorption fine structure spectra were calculated from the MD structures.

A new united atom parametrization of diacyl lipids like dipalmitoylphosphatidylcholine (DPPC) and the dimyristoylphosphatidylcholine (DMPC) has been constructed based on ab initio calculations to obtain fractional charges and the dihedral potential of the hydrocarbon chains, while the Lennard-Jones parameters of the acyl chains were fitted to reproduce the properties of liquid hydrocarbons. The results have been validated against published experimental X-ray and neutron scattering data for fluid and gel phase DPPC. The derived charges of the lipid phosphatidylcholine (PC) headgroup are shown to yield dipole components in the range suggested by experiments. The aim has been to construct a new force field that retains and improves the good agreement for the fluid phase and at the same time produces a gel phase at low temperatures, with properties coherent with experimental findings. The gel phase of diacyl-PC lipids forms a regular triangular lattice in the hydrocarbon region. The global bilayer tilt obtains an azimuthal value of 31 degrees and is aligned between lattice vectors in the bilayer plane. We also show that the model yields a correct heat of melting as well as decent heat capacities in the fluid and gel phase of DPPC.

Membrane inclusion interactions are studied within the scope of continuum theory. We show that the free energy functional for the membrane thickness can be rewritten as a constant times a dimensionless integral. For cylindrical inclusions, the resulting differential equation gives a thickness profile that depends on the radius of the cylinder and one single lipid property, a correlation length that is determined by the ratio of the thickness compressibility and bending moduli. The solutions decay in a non-monotonic fashion with one single observable minimum. A solution for planar geometry may either be explicitly constructed or obtained by letting the radius of the cylinder go to infinity. In dimensionless units the initial derivative of the thickness profile is universal and equal to -1/root 2 In physical units, the derivative depends on the size of the hydrophobic mismatch as well as the membrane correlation length and will usually be fairly small but clearly non-zero. The line tension between the protein inclusion and a fluid phase membrane will depend on the hydrophobic mismatch and be of the order of 10 pN (larger for the gel phase). This results in free energy costs for the inclusion that will be up to tens of kJ/mol (in the fluid phase).

Biological membranes mainly constituent lipid molecules along with some proteins and steroles. The properties of the pure lipid bilayers as well as in the presence of other constituents (in case of two or three component systems) are very important to be studied carefully to model these systems and compare them with the realistic systems. Molecular dynamic simulations provide a good opportunity to model such systems and to study them at microscopic level where experiments fail to do. In this thesis we study the structural and dynamic properties of the pure phospholipid bilayers and the phase behavior of phospholipid bilayers when other constituents are present in them. Material and structural properties like area per lipid and area compressibility of the phospholipids show a big scatter in experiments. These properties are studied for different system sizes and it was found that the increasing undulations in large systems effect these properties. A correction was applied to area per lipid and area compressibility using the Helfrich theory in Fourier space. Other structural properties like order of the lipid chains, electron density and radial distribution functions are calculated which give the structure of the lipid bilayer along the normal and in the lateral direction. These properties are compared to the X-ray and neutron scattering experiments after Fourier transform. Thermodynamic properties like heat capacity and heat of melting are also calculated from derivatives of energies available in molecular dynamics. Heat capacity on the other hand include quantum effect and are corrected for that by applying quantum correction using normal mode analysis for a simple as well as ambiguous system like water. Here it is done for SPC/E water model. The purpose of this study is to further apply the quantum corrections on macromolecules like lipids by using this technique. Furthermore the phase behavior of two component systems (phospholipids/cholesterol) is also studied. Phase transition in these systems is observed at different cholesterol concentrations as a function of temperature by looking at different quantities (as an order parameter) like the order of chains, area per molecule and partial specific area. Radial distribution functions are used to look at the in plane structure for different phases having a different lateral or positional order. Adding more cholesterol orders the lipid chains changing a liquid disordered system into a liquid ordered one and turning a solid ordered system into a liquid ordered one. Further more the free energy of domain formation is calculated to investigate the two phasecoexistence in binary systems. Free energy contains two terms. One is bulk freeenergy which was calculated by the chemical potential of cholesterol moleculein a homogeneous system which is favorable for segregation. Second is thefree energy of having an interface which is calculated from the line tension of the interface of two systems with different cholesterol concentration which in unfavorable for domain formation. The size of the domains calculated from these two contributions to the free energy gives the domains of a few nm in size. Though we could not find any such domains by directly looking at our simulations.

Lipid bilayers consisting of binary mixtures of phospholipids and cholesterol are studied above and below the main phase transition temperature using coarse grained (CG) and united atom (UA) models by molecular dynamics simulations. The purpose is to explore whether phase segregation into cholesterol-rich and cholesterol-poor domains is favorable from a free energy point of view and what the required size of these domains would be. We observe directly in simulations that phase separated fluid phase systems mix in less than 200 ns. Since, the dynamics is about 2 orders of magnitude slower in the gel phase mixing was not observed in such system. The chemical potential for cholesterol insertion was calculated from simulations. This resulted in a small bulk free energy of about 0.3kBT per lipid that favors phase separation while a small line tension (a couple of pN) between cholesterol-rich and -poor regions favors mixing. Although a simple continuum theory would indicate stabilization of domains as small as 1-2 nm in size, this was not observed in direct simulations.

Classical simulations of simple water models reproduce many properties of the liquid and ice but overestimate the heat capacity by about 65% at ordinary temperatures and much more for low temperature ice. This is due to the fact that the atomic vibrations are quantum mechanical. The application of harmonic quantum corrections to the molecular motion results in good heat capacities for the liquid and for ice at low temperatures but a successively growing positive deviation from experimental results for ice above 200 K that reaches 15% just below melting. We suggest that this deviation is due to the lack of quantum corrections to the anharmonic motions. For the liquid, the anharmonicities are even larger but also softer and thus in less need of quantum correction. Therefore, harmonic quantum corrections to the classically calculated liquid heat capacities result in agreement with the experimental values. The classical model underestimates the heat of melting by 15%, while the application of quantum corrections produces fair agreement. On the other hand, the heat of vaporization is overestimated by 10% in the harmonically corrected classical model.

It is here shown that there is a considerable system size-dependence in the area compressibility calculated from area fluctuations in lipid bilayers. This is caused by the contributions to the area fluctuations from undulations. This is also the case in experiments. At present, such a contribution, in most cases, is subtracted from the experimental values to obtain a true area compressibility. This should also be done with the simulation values. Here, this is done by extrapolating area compressibility versus system size, down to very small (zero) system size, where undulations no longer exist. The area compressibility moduli obtained from such simulations do not agree with experimental true area compressibility moduli as well as the uncorrected ones from contemporary or earlier simulations, but tend, instead, to be similar to 50% too large. As a byproduct, the bending modulus can be calculated from the slope of the compressibility modulus versus system-size. The values obtained in this way for the bending modulus are then in good agreement with experiment.

Coarse-grained simulations of model membranes containing mixtures of phospholipid and cholesterol molecules at different concentrations and temperatures have been performed. A random mixing without tendencies for segregation or formation of domains was observed on spatial scales corresponding to a few thousand lipids and timescales up to several micro-seconds. The gel-to-liquid crystalline phase transition is successively weakened with increasing amounts of cholesterol without disappearing completely even at a concentration of cholesterol as high as 60%. The phase transition temperature increases slightly depending on the cholesterol concentration. The gel phase system undergoes a transition with increasing amounts of cholesterol from a solid-ordered phase into a liquid-ordered one. In the solid phase, the amplitude of the oscillations in the radial distribution function decays algebraically with a prefactor that goes to zero at the solid-liquid transition.

One of the most important aspects for all life on this planet is the act to keep their biological processes in a state where they do not reach equilibrium. One part in the upholding of this imbalanced state is the barrier between the cells and their surroundings, created by the cell membrane. Additionally, terrestrial animal life often requires a barrier that protects the organism's body from external hazards and water loss. As an alternative to experiments, the investigation of the processes occurring at these barriers can be performed by using molecular dynamics simulations. Through this method we can obtain an atomistic description of the dynamics associated with events that are not accessible to experimental setups.

 In this thesis the first paper presents an improved particle-mesh Ewald method for the calculation of long-range Lennard-Jones interactions in molecular dynamics simulations, which solves the historical performance problem of the method. The second paper demonstrate an improved implementation, with a higher accuracy, that only incurs a performance loss of roughly 15% compared to conventional simulations using the Gromacs simulation package. Furthermore, the third paper presents a study of cholesterol's effect on the permeation of six different solutes across a variety of lipid bilayers. A laterally inhomogeneous permeability in cholesterol-containing membranes is proposed as an explanation for the large differences between experimental permeabilities and calculated partition coefficients in simulations. The fourth paper contains a coarse-grained simulation study of a proposed structural transformation in ceramide bilayer structures, during the formation of the stratum corneum. The simulations show that glycosylceramides are able to stabilize a three-dimensionally folded bilayer structure, while simulations with ceramides collapse into a lamellar bilayer structure.

One of the most important aspects for all life on this planet is theact to keep their cellular processes in a state where they do notreach equilibrium. One part in the upholding of this imbalanced stateis the barrier between the cells and their surroundings, created bythe cell membrane. In addition to experiments, the investigation ofprocesses occuring in the cell membrane can be performed by usingmolecular dynamics simulations. Through this method we can obtain anatomistic description of the dynamics associated with events that arenot accessible to experimental setups. Molecular dynamics relies onthe integration of Newton's equations of motion in order to sample therelevant parts of phase-space for the system, and therefore it isdependent on a correct description of the interactions between all thesimulated particles. In this thesis I first present an improved methodfor the calculation of long-range interactions in molecular dynamicssimulations, followed by a study of cholesterol's impact on thepermeation of small solutes across a lipid bilayer.

The first paper presents a previously derived modification to theparticle-mesh Ewald method, which makes it possible to apply thisto long-range Lennard-Jones interactions. Old implementations of themethod have been haunted by an extreme performance degradation andhere I propose a solution to this problem by applying a modifiedinteraction potential. I further show that the historical treatmentof long-range interactions in simulations of lipid bilayers hasnon-negligible effects on their structural properties.In the second paper, this modification is improved such that the smallerrors introduced by the modified interaction potential becomenegligible. Furthermore, I demonstrate that I have also improved theimplementation of the method so that it now only incurs a performanceloss of roughly 15% compared to conventional simulations using theGromacs simulation package.The third paper presents a simulation study of cholesterol's effect onthe permeation of six different solutes across a variety of lipidbilayers. I analyze the effect of different head groups, tail lengths,and tail saturation by performing simulations of the solutes in fourdifferent bilayers, with cholesterol contents between 0% and50%. Analysis of the simulations shows that the impact of the surfacearea per lipid on the partitioning of the solute could be lower thanpreviously thought. Furthermore, a model with a laterallyinhomogeneous permeability in cholesterol-containing membranes isproposed, which could explain the large differences betweenpermeabilities from experiments and calculated partition coefficientsin simulations.

The stratum corneum is the outer-most layer of the human skin, and constitutes the primary barrier to penetration of external substances. The barrier function of the stratum corneum is primarily located to its extracellular space, which consists of long-chain ceramides, free fatty acids and cholesterol organised into a stacked lamellar bilayer structure. Recent experimental studies have shown that these lamellar structures are formed through a structural reorganization of glycosylceramide-based bilayers, folded in three dimensions with a cubic-like symmetry. Here we present coarse-grained molecular dynamics simulations of human ceramide- and glycosylceramide bilayer structures with gyroid cubic symmetry. The bilayer structures with glycosylceramides are able to maintain the cubic symmetry, while the bilayer structures with ceramides collapse into a stacked lamellar bilayer structure as the water content is reduced.

Computer simulation has become an important tool for the study of biomolecular systems. This thesis deals with molecular dynamics simulations of one-component lipid bilayers, which may serve as models for biological membranes.

The main scientific contributions are:

• It is possible to analyze the electrostatic contribution to the surface tension at a lipid-water interface in terms of dipole-dipole interactions between lipid headgroup shielded by a dielectric medium (water). The interaction can be divided into two parts. The in-plane components of the dipoles give rise to a positive, i.e. contractive

contribution to the surface tension, albeit rather short ranged due to them being fluctuating dipoles. The normal components give rise to a negative, i.e. expansive contribution that will dominate the interaction at large distances.

• Simulated membrane areas are extremely sensitive to details, especially the treatment of long-range electrostatic interactions. When cut-offs are used for the electrostatics, the exact definition of charge groups play an important role. Furthermore, using Ewald summation for the long-range interactions seems to have an overall stabilizing effect, and the area becomes less sensitive to other factors, such as system size and hydration.

• Using atomistic simulations it is possible to study formation and evolution of a hydrophilic trans-membrane pore in detail. Free energy of pore nucleation and expansion can be calculated using potentials of mean constraint force. The resulting free energy profile shows no local maximum between the intact and pre-pore states, contrary to what is suggested by experiments.

• The present force field reproduces even the slowest dynamics in the lipid chains, as reflected in NMR relaxation rates. Furthermore, since the simulated system was relatively small, the experimentally observed variation of relaxation rates with Larmor frequency cannot be explained by large scale collective dynamics, or it would not have shown up in the simulation.

• Lipid lateral diffusion can be studied in detail on all relevant time scales by molecular dynamics. Using simple assumptions, the different diffusion coefficients measured on short and long times respectively can be connected in an analytic expression that fit calculated mean square displacements on timescales ranging from picoseconds to hundreds of nanoseconds.

In molecular dynamics simulations of lipid bilayers, the structure is sensitive to the precise treatment of electrostatics. The dipole-dipole interactions between headgroup dipoles are not long-ranged, but the area per lipid and, through it, other properties of the bilayer are very sensitive to the detailed balance between the perpendicular and in-plane components of the headgroup dipoles. This is affected by the detailed properties of the cutoff scheme or if long-range interactions are included by Ewald or particle-mesh Ewald techniques. Interaction between the in-plane components of the headgroup dipoles is attractive and decays as the inverse sixth power of distance. The interaction is screened by the square of a dielectric permittivity close to the value for water. Interaction between the components perpendicular to the membrane plane is repulsive and decays as the inverse third power of distance. These interactions are screened by a dielectric permittivity of the order 10. Thus, despite the perpendicular components being much smaller in magnitude than the in-plane components, they will dominate the interaction energies at large distances.

Cys-loop receptors are membrane proteins that are key players for the fast synaptic neurotransmission. Their ion transport initiates new nerve signals after activation by small agonist molecules, but this function is also highly sensitive to allosteric modulation by a number of compounds such as anesthetics, alcohol or anti-parasitic agents. For a long time, these modulators were believed to act primarily on the membrane, but the availability of high- resolution structures has made it possible to identify several binding sites in the transmembrane domains of the ion channels. It is known that ligand binding in the extracellular domain causes a conformational earthquake that interacts with the transmembrane domain, which leads to channel opening. The investigations carried out in this thesis aim at understanding the connection between ligand binding and channel opening.

I present new models of the mammalian GABA_A receptor based on the eukaryotic structure GluCl co-crystallized with an anti-parasitic agent, and show how these models can be used to study receptor-modulator interactions. I also show how removal of the bound modulator leads to gradual closing of the channel in molecular dynamics simulations. In contrast, simulations of the receptor with both the agonist and the modulator remain stable in an open-like conformation. This makes it possible to extract several key interactions, and I propose mechanisms for how the extracellular domain motion is initiated. The rapid increase in the number of cys-loop receptor structures the last few years has further made it possible to use principal component analysis (PCA) to create low-dimensional descriptions of the conformational landscape. By performing PCA on the crystal structure ensemble, I have been able to divide the structures into functional clusters and sample the transitions between them using various sampling methods.

The studies presented in this thesis contribute to our understanding of the gating mechanism and the functional clustering of the cys-loop receptor structures, which both are important to design new allosteric modulator drugs that influence the channel function, in particular to treat neurological disorders.

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-I-stim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-I-stim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane.

Modifying the density and distribution of ion channels in a neuron (by natural up- and downregulation or by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In this investigation we analyzed how the impulse patterns are regulated by the density of voltage-gated channels in a neuron model based on voltage-clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf-bifurcation threshold dynamics, respectively. Single, strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive. ring over a considerable range of channel densities. The relationship found here between channel densities and oscillatory behavior may partly explain the difference between the principal spiking patterns previously described for crab axons (class 1 and 2) and cortical neurons ( regular. ring and fast spiking).

Modifying the density and distribution of ion channels in a neuron (by natural up- and down-regulation, by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In the present investigation, we analyze how the impulse patterns are regulated by the density of voltage-gated channels in a model neuron, based on voltage clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf bifurcation threshold dynamics, respectively. Single strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The presently found relationship between channel densities and oscillatory behavior may be relevance for understanding principal spiking patterns of cortical neurons (regular firing and fast spiking). It may also be of relevance for understanding the action of pharmacological compounds on brain oscillatory activity.