Bio-economic modeling of bovine intramammary infections

The aim of this study was to make accurate predictions on the interaction of biologically relevant molecules with lipid bilayer membranes. We emphasised on the partitioning of these molecules between the membrane phase, and the aqueous phase quantified by the partition coefficient. To make detailed predictions a theory had to be set up along the lines of the self-consistent-field theory developed by Scheutjens and Fleer and extended by Evers, Leermakers, Van Lent, Böhmer, Barneveld, Israëls, Wijmans, Van der Linden, and others for (chain) molecules in inhomogeneous systems.As a first step towards this goal we have investigated bare membranes in chapter 1. A membrane of dimyristoylphosphatidylcholine (DMPC) has been used as a model for biological membranes, existing in plant and animals, in which this molecule is a major component. For comparison, membranes consisting of the anionic dimyristoylphosphatidylserine (DMPS) were also modelled. It was found that the zwitterionic phosphatidylcholine (PC) head group was laying on average flat on the membrane surface. This result is in line with experiments and in accordance with other theoretical calculations. At high salt concentrations however, two preferred conformations had to be distinguished, both about equally populated, one with the choline moiety closer to the water phase than the phosphate moiety and one the other way around. Due to the out of plane tilting of the head group, an electrostatic potential profile develops. The electrostatic potential is positive in the membrane centre and on the membrane surface, but negative in the middle of the head group region at the average position of the phosphate groups.The ionic head groups of DMPS are found tilted towards the aqueous solution. Counterions interpenetrate the head group region and compensate the charge to a large extent even at low ionic strength. At high salt concentrations ions are depleted from the head group space but, due to asymmetric depletion of anions and cations, charge compensation is still achieved.The variability of the PC head group orientation was investigated theoretically by attaching a hydrophilic chain to the choline moiety of DMPC. Varying the chain length had two effects: First, due to the interchain steric repulsion the head group area increased and therefore the dimension of the hydrophobic core decreased which eventually destabilised the membranes. Second, the head group orientation changed non-monotonously. Short chains attached to the choline moiety 'drag' it towards the water phase, while longer chains attached to it do not affect the average orientation of the dipole, which is parallel to the membrane surface. This is caused by the fact that, for longer hydrophilic chains, the most bulky part of the head group is located further from the hydrophobic core in the centre of the polymeric coil. This relaxes the packing constraints at the position of the choline. Hence the phosphate moieties and the electrostatics forces, that favour a flat conformation, meet less opposition.In the second chapter we concentrate on the interplay of the electrostatic potential profile across the membrane and the valence of the ions present in solution. From the calculations it can be concluded that the electrostatic interactions can explain the accumulation of charges in the head group area without introduction of specific chemical interactions between e.g. a divalent ion like calcium and the phosphate group.An important issue in the modelling of non-interacting, free-standing membranes is the proof that the modelled bilayers are thermodynamically the most stable structures. From thermodynamic arguments, it can be shown that the surface tension of these layers should vanish. This is a necessary, but not sufficient condition. For isolated, free-standing bilayers to be stable, the membranes should be mutually repulsive. The interaction between bilayers is the topic of chapter 3. In this chapter a thermodynamic derivation is presented of the various ways the interaction curve can be calculated from the self-consistent-anisotropic-field (SCAF) theory. The results show that three force-distance regimes can be distinguished for a DMPC bilayer in a moderate salt concentration: two repulsive regimes, one of electrostatic and one of steric origin flank an attractive one that was shown to be of entropic origin. The entropic attraction is caused by an increase in the number of head group conformations. At large separation the head groups are oriented mostly parallel to the membrane surface. Upon closer approach of two bilayers the head group conformation is allowed to change. The head group can now cross the gap between the bilayers without an electrostatic penalty. As a function of the screening of the electrostatic interactions we observe various changes in the interaction curves. At high salt concentration both the electrostatic repulsion and the entropic attraction become negligible. At low salt concentration the entropic attraction increases whereas, at the same time, the electrostatic repulsion vanishes. This last effect is caused by the perfect alignment of the head group parallel to the membrane surface so that virtually no charge separation occurs.Stretching the membranes increases the entropic attraction but decreases the electrostatic repulsion. We did not incorporate undulations in our theory so the decrease of undulations was not the phenomenon that caused the stress-induced tendency to adhere. In our model stretched membranes have a larger head group area which relaxes the head group packing constraints. This allows these groups to assume a position more parallel to the bilayer surface, leading to a reduced electrostatic repulsion and a stronger entropic attraction.Addition of non-ionic surfactants (dodecanol) to DMPC bilayers caused the membranes to grow thicker without changing the interaction curve. Ionic surfactants (e.g. dodecylammonium and dodecylsulphide) did not change the overall membrane thickness but made, due to a modification of the electrostatic interactions, the interaction profile completely repulsive. Cationic surfactants had a more pronounced effect than anionics. Cationics push the choline moieties outwards while the anionics pull these more inwards towards the membrane centre.Finally in chapter 4 the SCAF theory for molecules containing rigid structures is given. The coupling of the segment potential {u(z)} to the volume fraction profile {(p(z)} is in principle accomplished according to the following simple, basic method. First, all conformations of the molecules are generated and then the statistical weights of these conformations in the potential field are added and normalised. For flexible molecules, that can assume very many conformations, an efficient technique exists that is just doing this in one single operation, it generate the conformations, calculate the statistical weight, and add the results to obtain the densities (the propagator method). For rigid structures, that can assume relatively few conformations, the basic methods is already effective. A hybrid scheme was developed for partly rigid molecules, where the basic method for the rigid parts was combined with the propagator method for the flexible parts.Partition coefficients calculated for a number of linear and branched alcohols as well as for phenols were compared with measurements. Good quantitative comparison was found for these molecules. Trends known from literature, like the exponential dependence of the partition coefficient on the chain length in homologue series, were reproduced.To illustrate the possibilities of the theory some results were presented of calculations on three groups of molecules having the same zwitterionic isomer (C _{<font size="-1">22N</font>}<font size="-2">+</font>S <sup>-</SUP>, containing a benzene-like structure). The calculations showed that in DMPC membranes the partition coefficient can change by a factor of ten depending on the molecular architecture. The positional and orientational data revealed that negatively charged units partition much more readily into the membrane core than positively charged segments do. This can be rationalised by the electrostatic potential profile which, as told above, is positive both in the centre and on the outskirts of the membrane while being negative at the average position of the phosphate segments.Calculations on a number of substituted tetrahydroxynaphthalenes showed that, with only small changes in the partition coefficient, large orientational and positional variations can be realised, changing from spanning the membrane for 2,3,6,7- tetrahydroxy naphthalene to parallel to the membrane surface positioned at the head group-hydrophobic core interface for 1,3,5,7-tetrahydroxy naphthalene. This kind of large orientational changes, while keeping the partition coefficient virtually constant, can be of great importance in the development and the improvement of new drugs, or in elucidating the working mechanism of existing ones.Our model has provided a detailed insight into the nature of model lipid membranes and will hopefully advance the development of products and contribute to the optimisation and interpretation of experiments in which lipid bilayers play a role. At present reasonable (semi) quantitative agreement with many experimental results have already been achieved. There are however cases where the present theory does not yet give good enough predictions. For this it is good to know that the theory can be readily extended to incorporate more details in the calculations