The effect of hydrostatic pressure on lipid membrane lateral structure.

High pressure is both an environmental challenge to which deep sea biology has to adapt, and a highly sensitive thermodynamic tool that can be used to trigger structural changes in biological molecules and assemblies. Lipid membranes are amongst the most pressure sensitive biological assemblies and pressure can have a large influence on their structure and properties. In this chapter, we will explore the use of high pressure small angle X-ray diffraction and high pressure microscopy to measure and quantify changes in the lateral structure of lipid membranes under both equilibrium high pressure conditions and in response to pressure jumps.

n-Alcohol Length Governs Shift in Lo-Ld Mixing Temperatures in Synthetic and Cell-Derived Membranes.

A persistent challenge in membrane biophysics has been to quantitatively predict how membrane physical properties change upon addition of new amphiphiles (e.g., lipids, alcohols, peptides, or proteins) in order to assess whether the changes are large enough to plausibly result in biological ramifications. Because of their roles as general anesthetics, n-alcohols are perhaps the best-studied amphiphiles of this class. When n-alcohols are added to model and cell membranes, changes in membrane parameters tend to be modest. One striking exception is found in the large decrease in liquid-liquid miscibility transition temperatures (Tmix) observed when short-chain n-alcohols are incorporated into giant plasma membrane vesicles (GPMVs). Coexisting liquid-ordered and liquid-disordered phases are observed at temperatures below Tmix in GPMVs as well as in giant unilamellar vesicles (GUVs) composed of ternary mixtures of a lipid with a low melting temperature, a lipid with a high melting temperature, and cholesterol. Here, we find that when GUVs of canonical ternary mixtures are formed in aqueous solutions of short-chain n-alcohols (n ≤ 10), Tmix increases relative to GUVs in water. This shift is in the opposite direction from that reported for cell-derived GPMVs. The increase in Tmix is robust across GUVs of several types of lipids, ratios of lipids, types of short-chain n-alcohols, and concentrations of n-alcohols. However, as chain lengths of n-alcohols increase, nonmonotonic shifts in Tmix are observed. Alcohols with chain lengths of 10-14 carbons decrease Tmix in ternary GUVs of dioleoyl-PC/dipalmitoyl-PC/cholesterol, whereas 16 carbons increase Tmix again. Gray et al. observed a similar influence of the length of n-alcohols on the direction of the shift in Tmix. These results are consistent with a scenario in which the relative partitioning of n-alcohols between liquid-ordered and liquid-disordered phases evolves as the chain length of the n-alcohol increases.

Conditions that Stabilize Membrane Domains Also Antagonize n-Alcohol Anesthesia.

Diverse molecules induce general anesthesia with potency strongly correlated with both their hydrophobicity and their effects on certain ion channels. We recently observed that several n-alcohol anesthetics inhibit heterogeneity in plasma-membrane-derived vesicles by lowering the critical temperature (Tc) for phase separation. Here, we exploit conditions that stabilize membrane heterogeneity to further test the correlation between the anesthetic potency of n-alcohols and effects on Tc. First, we show that hexadecanol acts oppositely to n-alcohol anesthetics on membrane mixing and antagonizes ethanol-induced anesthesia in a tadpole behavioral assay. Second, we show that two previously described "intoxication reversers" raise Tc and counter ethanol's effects in vesicles, mimicking the findings of previous electrophysiological and behavioral measurements. Third, we find that elevated hydrostatic pressure, long known to reverse anesthesia, also raises Tc in vesicles with a magnitude that counters the effect of butanol at relevant concentrations and pressures. Taken together, these results demonstrate that ΔTc predicts anesthetic potency for n-alcohols better than hydrophobicity in a range of contexts, supporting a mechanistic role for membrane heterogeneity in general anesthesia.

Separation of liquid domains in model membranes induced with high hydrostatic pressure.

We have imaged the formation of membrane microdomains immediately after their induction using a novel technology platform coupling high hydrostatic pressure to fluorescence microscopy. After formation, the ordered domains are small and highly dynamic. This will enhance links between model lipid assemblies and dynamic processes in cellular membranes.

Pressure-temperature phase behavior of mixtures of natural sphingomyelin and ceramide extracts.

Ceramides are a group of sphingolipids that act as highly important signaling molecules in a variety of cellular processes including differentiation and apoptosis. The predominant in vivo synthetic pathway for ceramide formation is via sphingomyelinase catalyzed hydrolysis of sphingomyelin. The biochemistry of this essential pathway has been studied in detail; however, there is currently a lack of information on the structural behavior of sphingomyelin- and ceramide-rich model membrane systems, which is essential for developing a bottom-up understanding of ceramide signaling and platform formation. We have studied the lyotropic phase behavior of sphingomyelin-ceramide mixtures in excess water as a function of temperature (30-70 °C) and pressure (1-200 MPa) by small- and wide-angle X-ray scattering. At low ceramide concentrations the mixtures form the ripple gel phase (P(ß)') below the gel transition temperature for sphingomyelin, and this observation has been confirmed by atomic force microscopy. Formation of the ripple gel phase can also be induced at higher temperatures via the application of hydrostatic pressure. At high ceramide concentration an inverse hexagonal phase (HII) is formed coexisting with a cubic phase.

Electrostatic swelling of bicontinuous cubic lipid phases.

Lipid bicontinuous cubic phases have attracted enormous interest as bio-compatible scaffolds for use in a wide range of applications including membrane protein crystallisation, drug delivery and biosensing. One of the major bottlenecks that has hindered exploitation of these structures is an inability to create targeted highly swollen bicontinuous cubic structures with large and tunable pore sizes. In contrast, cubic structures found in vivo have periodicities approaching the micron scale. We have been able to engineer and control highly swollen bicontinuous cubic phases of spacegroup Im3m containing only lipids by (a) increasing the bilayer stiffness by adding cholesterol and (b) inducing electrostatic repulsion across the water channels by addition of anionic lipids to monoolein. By controlling the composition of the ternary mixtures we have been able to achieve lattice parameters up to 470 Å, which is 5 times that observed in pure monoolein and nearly twice the size of any lipidic cubic phase reported previously. These lattice parameters significantly exceed the predicted maximum swelling for bicontinuous cubic lipid structures, which suggest that thermal fluctuations should destroy such phases for lattice parameters larger than 300 Å.

Kernel learning at the first level of inference.

Kernel learning methods, whether Bayesian or frequentist, typically involve multiple levels of inference, with the coefficients of the kernel expansion being determined at the first level and the kernel and regularisation parameters carefully tuned at the second level, a process known as model selection. Model selection for kernel machines is commonly performed via optimisation of a suitable model selection criterion, often based on cross-validation or theoretical performance bounds. However, if there are a large number of kernel parameters, as for instance in the case of automatic relevance determination (ARD), there is a substantial risk of over-fitting the model selection criterion, resulting in poor generalisation performance. In this paper we investigate the possibility of learning the kernel, for the Least-Squares Support Vector Machine (LS-SVM) classifier, at the first level of inference, i.e. parameter optimisation. The kernel parameters and the coefficients of the kernel expansion are jointly optimised at the first level of inference, minimising a training criterion with an additional regularisation term acting on the kernel parameters. The key advantage of this approach is that the values of only two regularisation parameters need be determined in model selection, substantially alleviating the problem of over-fitting the model selection criterion. The benefits of this approach are demonstrated using a suite of synthetic and real-world binary classification benchmark problems, where kernel learning at the first level of inference is shown to be statistically superior to the conventional approach, improves on our previous work (Cawley and Talbot, 2007) and is competitive with Multiple Kernel Learning approaches, but with reduced computational expense.

Optimally regularised kernel Fisher discriminant classification.

Mika, Rätsch, Weston, Schölkopf and Müller [Mika, S., Rätsch, G., Weston, J., Schölkopf, B., & Müller, K.-R. (1999). Fisher discriminant analysis with kernels. In Neural networks for signal processing: Vol. IX (pp. 41-48). New York: IEEE Press] introduce a non-linear formulation of Fisher's linear discriminant, based on the now familiar "kernel trick", demonstrating state-of-the-art performance on a wide range of real-world benchmark datasets. In this paper, we extend an existing analytical expression for the leave-one-out cross-validation error [Cawley, G. C., & Talbot, N. L. C. (2003b). Efficient leave-one-out cross-validation of kernel Fisher discriminant classifiers. Pattern Recognition, 36(11), 2585-2592] such that the leave-one-out error can be re-estimated following a change in the value of the regularisation parameter with a computational complexity of only O(l(2)) operations, which is substantially less than the O(l(3)) operations required for the basic training algorithm. This allows the regularisation parameter to be tuned at an essentially negligible computational cost. This is achieved by performing the discriminant analysis in canonical form. The proposed method is therefore a useful component of a model selection strategy for this class of kernel machines that alternates between updates of the kernel and regularisation parameters. Results obtained on real-world and synthetic benchmark datasets indicate that the proposed method is competitive with model selection based on k-fold cross-validation in terms of generalisation, whilst being considerably faster.

Gene selection in cancer classification using sparse logistic regression with Bayesian regularization.

MOTIVATION: Gene selection algorithms for cancer classification, based on the expression of a small number of biomarker genes, have been the subject of considerable research in recent years. Shevade and Keerthi propose a gene selection algorithm based on sparse logistic regression (SLogReg) incorporating a Laplace prior to promote sparsity in the model parameters, and provide a simple but efficient training procedure. The degree of sparsity obtained is determined by the value of a regularization parameter, which must be carefully tuned in order to optimize performance. This normally involves a model selection stage, based on a computationally intensive search for the minimizer of the cross-validation error. In this paper, we demonstrate that a simple Bayesian approach can be taken to eliminate this regularization parameter entirely, by integrating it out analytically using an uninformative Jeffrey's prior. The improved algorithm (BLogReg) is then typically two or three orders of magnitude faster than the original algorithm, as there is no longer a need for a model selection step. The BLogReg algorithm is also free from selection bias in performance estimation, a common pitfall in the application of machine learning algorithms in cancer classification. RESULTS: The SLogReg, BLogReg and Relevance Vector Machine (RVM) gene selection algorithms are evaluated over the well-studied colon cancer and leukaemia benchmark datasets. The leave-one-out estimates of the probability of test error and cross-entropy of the BLogReg and SLogReg algorithms are very similar, however the BlogReg algorithm is found to be considerably faster than the original SLogReg algorithm. Using nested cross-validation to avoid selection bias, performance estimation for SLogReg on the leukaemia dataset takes almost 48 h, whereas the corresponding result for BLogReg is obtained in only 1 min 24 s, making BLogReg by far the more practical algorithm. BLogReg also demonstrates better estimates of conditional probability than the RVM, which are of great importance in medical applications, with similar computational expense. AVAILABILITY: A MATLAB implementation of the sparse logistic regression algorithm with Bayesian regularization (BLogReg) is available from http://theoval.cmp.uea.ac.uk/~gcc/cbl/blogreg/

Sparse Bayesian kernel survival analysis for modeling the growth domain of microbial pathogens.

Survival analysis is a branch of statistics concerned with the time elapsing before "failure," with diverse applications in medical statistics and the analysis of the reliability of electrical or mechanical components. We introduce a parametric accelerated life survival analysis model based on kernel learning methods that, at least in principal, is able to learn arbitrary dependencies between a vector of explanatory variables and the scale of the distribution of survival times. The proposed kernel survival analysis method is then used to model the growth domain of Clostridium botulinum, the food processing and storage conditions permitting the growth of this foodborne microbial pathogen, leading to the production of the neurotoxin responsible for botulism. A Bayesian training procedure, based on the evidence framework, is used for model selection and to provide a credible interval on model predictions. The kernel survival analysis models are found to be more accurate than models based on more traditional survival analysis techniques but also suggest a risk assessment of the foodborne botulism hazard would benefit from the collection of additional data.

Constructing Bayesian formulations of sparse kernel learning methods.

We present here a simple technique that simplifies the construction of Bayesian treatments of a variety of sparse kernel learning algorithms. An incomplete Cholesky factorisation is employed to modify the dual parameter space, such that the Gaussian prior over the dual model parameters is whitened. The regularisation term then corresponds to the usual weight-decay regulariser, allowing the Bayesian analysis to proceed via the evidence framework of MacKay. There is in addition a useful by-product associated with the incomplete Cholesky factorisation algorithm, it also identifies a subset of the training data forming an approximate basis for the entire dataset in the kernel-induced feature space, resulting in a sparse model. Bayesian treatments of the kernel ridge regression (KRR) algorithm, with both constant and heteroscedastic (input dependent) variance structures, and kernel logistic regression (KLR) are provided as illustrative examples of the proposed method, which we hope will be more widely applicable.

Fast exact leave-one-out cross-validation of sparse least-squares support vector machines.

Leave-one-out cross-validation has been shown to give an almost unbiased estimator of the generalisation properties of statistical models, and therefore provides a sensible criterion for model selection and comparison. In this paper we show that exact leave-one-out cross-validation of sparse Least-Squares Support Vector Machines (LS-SVMs) can be implemented with a computational complexity of only O(ln2) floating point operations, rather than the O(l2n2) operations of a naïve implementation, where l is the number of training patterns and n is the number of basis vectors. As a result, leave-one-out cross-validation becomes a practical proposition for model selection in large scale applications. For clarity the exposition concentrates on sparse least-squares support vector machines in the context of non-linear regression, but is equally applicable in a pattern recognition setting.

Potassium channels from normal and denervated mouse skeletal muscle fibers.

The properties of singles K+ channels in normal and denervated muscles were compared using the "patch-clamp" technique. Single channels were recorded from vesicles obtained by stretching bundles of normal and denervated extensor digitorium longus (EDL) muscles. The most frequently observed channel in normal muscles was a high conductance (266 pS) Ca++ activated K+ channel. Although channel density, as estimated by patch recording, showed a significant decrease in denervated muscles, no differences were found in conductance and gating properties. Another voltage-dependent K+ channel (81 pS) was only recorded from normal muscles, but never from denervated ones. In addition, a 35 pS conductance was recorded from both normal and denervated fibers. This channel displayed neither voltage dependence nor sensitivity to tetraethylammonium (TEA). In contrast, another TEA-insensitive (16 pS) channel was recorded only from denervated muscles. We conclude that denervation induces significant changes in the distribution and expression of K+ channels in mammalian skeletal muscles.