Liposomes are attractive vehicles for localized delivery of antibiotics. There exists, however, a gap in knowledge when it comes to achieving high liposomal loading efficiencies for antibiotics. To address this issue, we investigated three antibiotics of clinical relevance against staphylococcal infections with different hydrophilicity and chemical structure, namely, vancomycin hydrochloride, teicoplanin, and rifampin. We categorized the suitability of different encapsulation techniques on the basis of encapsulation efficiency, lipid requirement (important for avoiding lipid toxicity), and mass yield (percentage of mass retained during the preparation process). The moderately hydrophobic (teicoplanin) and highly hydrophobic (rifampin) antibiotics varied significantly in their encapsulation load (max 23.4 and 15.5%, respectively) and mass yield (max 74.1 and 71.8%, respectively), favoring techniques that maximized partition between the aqueous core and the lipid bilayer or those that produce oligolamellar vesicles, whereas vancomycin hydrochloride, a highly hydrophilic molecule, showed little preference to any of the protocols. In addition, we report significant bias introduced by the choice of analytical method adopted to quantify the encapsulation efficiency (underestimation of up to 24% or overestimation by up to 57.9% for vancomycin and underestimation of up to 61.1% for rifampin) and further propose ultrafiltration and bursting by methanol as the method with minimal bias for quantification of encapsulation efficiency in liposomes. The knowledge generated in this work provides critical insight into the more practical, albeit less investigated, aspects of designing vesicles for localized antibiotic delivery and can be extended to other nanovehicles that may suffer from the same biases in analytical protocols.

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions.They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space.We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes.We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution π with a density L with respect to a reference distribution 0 and compute the normalizing constant ∫ L d 0 . A typical use case is when 0 is a prior distribution, L a likelihood function and π the corresponding posterior distribution.

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Sampling from complex target distributions is a challenging task fundamental to Bayesian inference. Parallel tempering (PT) addresses this problem by constructing a Markov chain on the expanded state space of a sequence of distributions interpolating between the posterior distribution and a fixed reference distribution, which is typically chosen to be the prior. However, in the typical case where the prior and posterior are nearly mutually singular, PT methods are computationally prohibitive. In this work we address this challenge by constructing a generalized annealing path connecting the posterior to an adaptively tuned variational reference. The reference distribution is tuned to minimize the forward (inclusive) KL divergence to the posterior distribution using a simple, gradient-free moment-matching procedure. We show that our adaptive procedure converges to the forward KL minimizer, and that the forward KL divergence serves as a good proxy to a previously developed measure of PT performance. We also show that in the large-data limit in typical Bayesian models, the proposed method improves in performance, while traditional PT deteriorates arbitrarily. Finally, we introduce PT with two references-one fixed, one variational-with a novel split annealing path that ensures stable variational reference adaptation. The paper concludes with experiments that demonstrate the large empirical gains achieved by our method in a wide range of realistic Bayesian inference scenarios.