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Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these uncertain inverse problems. Standard methods used to identify uncertain parameters are Markov Chain Monte Carlo (MCMC) methods with explicit evaluation of a likelihood function. However, if the likelihood is very complex, such that its evaluation is computationally expensive, or even unknown in its explicit form, Approximate Bayesian Computation (ABC) methods provide a promising alternative. In this work both methods are first applied to artificially generated data and second on a real world problem, by using data of an electric motor test bench. We show that both methods are able to infer the distribution of varying parameters with a Bayesian hierarchical approach. But the proposed ABC method is computationally much more efficient in order to achieve results with similar accuracy. We suggest to use summary statistics in order to reduce the dimension of the data which significantly increases the efficiency of the algorithm. Further the simulation model is replaced by a Polynomial Chaos Expansion (PCE) surrogate to speed up model evaluations. We proof consistency for the proposed surrogate-based ABC method with summary statistics under mild conditions on the (approximated) forward model.

In the mammalian plasma membrane, cholesterol can translocate rapidly between the exoplasmic and cytoplasmic leaves, so that its distribution between them should be given by the equality of its chemical potential in the leaves. Due to its favorable interaction with sphingomyelin, which is almost entirely in the outer leaf, one expects the great majority of cholesterol to be there also. Experimental results do not support this, implying that there is some mechanism which attracts cholesterol to the inner leaf. We hypothesize that it is drawn there to reduce the bending free energy of the membrane caused by the presence of phosphatidylethanolamine (PE). It does this in two ways: first by simply diluting the amount of PE in the inner leaf, and second by ordering the tails of the PE so as to reduce its spontaneous curvature. Incorporating this mechanism into a model free energy for the bilayer, we find that between 50 and 60% of the total cholesterol should be in the inner leaf of human erythrocytes.

We consider the effect of mobile ions on the applied potential needed to reorient a lamellar system of two different materials placed between two planar electrodes. The reorientation occurs from a configuration parallel to the electrodes favored by surface interactions to an orientation perpendicular to the electrodes favored by the electric field. The system consists of alternating A and B layers with different dielectric constants. The mobile ions are assumed to be insoluble in the B layers and hence confined to the A layers. We find that the ions reduce the needed voltage most strongly when they are constrained such that each A lamella is electrically neutral. In this case, a macroscopic separation of charge and its concomitant lowering of free energy, is attained only in the perpendicular orientation. When the ions are free to move between different A layers, such that charge neutrality is only required globally, their effect is smaller and depends upon the preferred surface interaction of the two materials. Under some conditions, the addition of ions can actually stabilize the parallel configuration. Our predictions are relevant to recent experiments conducted on lamellar phases of diblock copolymer films with ionic selective impurities., Comment: To be published in the Journal of Chemical Physics

We present a phenomenological theory for the phase behavior of ternary mixtures of cholesterol and saturated and unsaturated lipids, one which describes both liquid and gel phases, and illuminates the mechanism of the behavior. In a binary system of the lipids, the two phase separate when the saturated chains are well ordered, as in the gel phase, simply due to packing effects. In the liquid phase the saturated ones are not sufficiently well ordered for separation to occur. The addition of cholesterol, however, increases the saturated lipid order to the point that phase separation is once again favorable. For the system above the main chain transition of the saturated lipid, we can obtain phase diagrams in which there is liquid-liquid phase separation in the ternary system but not in any of the binary ones, while below that temperature we obtain the more common phase diagram in which a gel phase, rich in saturated lipid, appears in addition to the two liquid phases., Comment: 16 pages, 2 figures

We extend previous work on homogeneous bilayers to calculate the barriers to fusion of planar bilayers which contain two different amphiphiles, a lamellae-former and a hexagonal former, with different compositions of the twoin each leaf. Self-consistent field theory is employed, and both standard and alternative pathways are explored. We first calculate these barriers as the amount of hexagonal former is increased equally in both leaves to levels appropriate to the plasma membrane of human red blood cells. We follow these barriers as the composition of hexagonal-formers is then increased in the cis layer and decreased in the trans layer, again to an extent comparable to the biological system. We find that, while the fusion pathway exhibits two barriers in both the standard and alternative pathways, in both cases the magnitudes of these barriers are comparable to one another, and small, on the order of 13 kT. As a consequence, one expects that once the bilayers are brought sufficiently close to one another to initiate the process, fusion should occur rapidly., Comment: 9 figures

We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ simple and soft effective potentials, coarse-grained models can provide rather direct insight into collective phenomena in membranes on large time and length scales. We present a summary of recent progress in this rapidly evolving field, and pay special attention to model development and computational techniques. Applications of coarse-grained models to changes of the membrane topology are illustrated with studies of membrane fusion utilizing simulations and self-consistent field theory., Comment: 88 pages, 39 figures, accepted to Physics Reports, version with higher resolution figures available at http://www.mrl.ucsb.edu/~katsov/pubs/pub024.pdf

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first paper of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with system architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few $k_BT$ over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway.

We study the phase behavior of diblock copolymers in presence of an external electric field. We employ self-consistent field theory and treat the relevant Maxwell equation as an additional self-consistent equation. Because we do not treat the electric field perturbatively, we can examine its effects even when its magnitude is large. The electric field couples to the system's morphology only through the difference between the dielectric constants of the two blocks. We find that an external field aligns a body-centered cubic phase along the (111) direction, reducing its symmetry group to $R{\bar 3}m$. Transitions between this phase and the disordered or hexagonal phases can occur for external electric fields ranging from a minimum to a maximum value beyond which the $R{\bar 3m}$ phase disappears completely. This electric-field range depends on diblock architecture and temperature. We present several cuts through the phase diagram in the space of temperature, architecture and applied field, including one applicable to a system recently studied., Comment: 23 pages, 6 figures, submitted to Macromolecules on February 25,2005

Self-consistent field theory is used to determine structural and energetic properties of metastable intermediates and unstable transition states involved in the standard stalk mechanism of bilayer membrane fusion. A microscopic model of flexible amphiphilic chains dissolved in hydrophilic solvent is employed to describe these self-assembled structures. We find that the barrier to formation of the initial stalk is much smaller than previously estimated by phenomenological theories. Therefore its creation it is not the rate limiting process. The barrier which is relevant is associated with the rather limited radial expansion of the stalk into a hemifusion diaphragm. It is strongly affected by the architecture of the amphiphile, decreasing as the effective spontaneous curvature of the amphiphile is made more negative. It is also reduced when the tension is increased. At high tension the fusion pore, created when a hole forms in the hemifusion diaphragm, expands without bound. At very low membrane tension, small fusion pores can be trapped in a flickering metastable state. Successful fusion is severely limited by the architecture of the lipids. If the effective spontaneous curvature is not sufficiently negative, fusion does not occur because metastable stalks, whose existence is a seemingly necessary prerequisite, do not form at all. However if the spontaneous curvature is too negative, stalks are so stable that fusion does not occur because the system is unstable either to a phase of stable radial stalks, or to an inverted-hexagonal phase induced by stable linear stalks. Our results on the architecture and tension needed for successful fusion are summarized in a phase diagram., Comment: in press, Biophys.J. accepted version

Effects of the mismatch between the hydrophobic length, d, of transmembrane alpha helices of integral proteins and the hydrophobic thickness, D_h, of the membranes they span are studied theoretically utilizing a microscopic model of lipids. In particular, we examine the dependence of the period of a lamellar phase on the hydrophobic length and volume fraction of a rigid, integral, peptide. We find that the period decreases when a short peptide, such that dD_h, is inserted. The effect is due to the replacement of extensible lipid tails by rigid peptide. As the peptide length is increased, the lamellar period continues to increase, but at a slower rate, and can eventually decrease. The amount of peptide which fails to incorporate and span the membrane increases with the magnitude of the hydrophobic mismatch |d-D_h|. We explicate these behaviors which are all in accord with experiment. Predictions are made for the dependence of the tilt of a single trans-membrane alpha helix on hydrophobic mismatch and helix density., Comment: 14 pages, 5 figures

We apply self consistent field theory to twist grain boundaries of block copolymer melts. The distribution of monomers throughout the grain boundary is obtained as well as the grain boundary free energy per unit area as a function of twist angle. We define an intermaterial dividing surface in order to compare it with minimal surfaces which have been proposed. Our calculation shows that the dividing surface is not a minimal one, but the linear stack of dislocations seems to be a better representation of it for most angles than is Scherck's first surface., Comment: 10 pages, 6 figures, submitted for publication

We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains strongly depends on the angle $\theta$, between the normals of the grains. When this angle is small, the lamellae transform smoothly from one orientation to the other, creating the chevron morphology. As $\theta$ increases, a gradual transition is observed to an omega morphology characterized by a protrusion of the lamellae along the interface between the two phases. We present a theoretical approach to find these tilt boundaries in two-dimensional systems, based on a Ginzburg-Landau expansion of the free energy. Calculated order parameter profiles and energies agree well with transmission electron microscope experiments, and with full numerical solution of the same problem., Comment: 11 pages, 10 gzipped postscript and jpeg figures, published in PRE Vol. 61, March 2000

Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak segregation limit, leading to density profiles which can extend over many wavelengths of the lamellar phase. The latter are studied numerically and exactly. We find a change from smooth chevron configurations typical of small tilt angles to distorted omega configurations at large tilt angles in agreement with experiment., Comment: 9 pages, 6 figures 9 pages, 6 figures