Adaptive multilevel splitting: Historical perspective and recent results

Validation studies and multiomics analysis of Zhx2 as a candidate quantitative trait gene underlying brain oxycodone metabolite (oxymorphone) levels and behavior

Sensitivity to the subjective reinforcing properties of opioids has a genetic component and can predict addiction liability of opioid compounds. We previously identified Zhx2 as a candidate gene underlying increased brain concentration of the oxycodone (OXY) metabolite oxymorphone (OMOR) in BALB/cJ (J) versus BALB/cByJ (By) females that could increase OXY state-dependent reward. A large structural intronic variant is associated with a robust reduction of Zhx2 expression in J mice, which we hypothesized enhances OMOR levels and OXY addiction-like behaviors. We tested this hypothesis by restoring the Zhx2 loss-of-function in J mice (mouse endogenous retroviral element knockout) and modeling the loss-of-function variant through knocking out the Zhx2 coding exon (exon 3 knockout [E3KO]) in By mice and assessing brain OXY metabolite levels and behavior. Consistent with our hypothesis, Zhx2 E3KO females showed an increase in brain OMOR levels and OXY-induced locomotor activity. However, contrary to our hypothesis, state-dependent expression of OXY conditioned place preference decreased in E3KO females and increased in E3KO males. We also overexpressed Zhx2 in the livers and brains of J mice and observed Zhx2 overexpression in select brain regions that was associated with reduced OXY state-dependent learning. Integrative transcriptomic and proteomic analysis of E3KO mice identified astrocyte function, cell adhesion, extracellular matrix properties, and endothelial cell functions as pathways influencing brain OXY metabolite concentration and behavior. These results support Zhx2 as a quantitative trait gene underlying brain OMOR concentration that is associated with changes in OXY behavior and implicate potential quantitative trait mechanisms that together inform our overall understanding of Zhx2 in brain function. SIGNIFICANCE STATEMENT: This study validated Zhx2 as a gene whose dysfunction increases brain levels of a highly potent and addictive metabolite of oxycodone, oxymorphone, in a female-specific manner. This result has broad implications for understanding the role of oxycodone metabolism and brain oxymorphone levels in the addiction liability of oxycodone (the active ingredient in OxyContin) and highlights the need for the study of sex differences in opioid metabolism as it relates to the addiction liability of opioids and opioid use disorder.

The ultrasonic vocalization (USV) syllable profile during neonatal opioid withdrawal and a kappa opioid receptor component to increased USV emissions in female mice

RATIONALE

Opioid use during pregnancy can lead to negative infant health outcomes, including neonatal opioid withdrawal syndrome (NOWS). NOWS comprises gastrointestinal, autonomic nervous system, and neurological dysfunction that manifest during spontaneous withdrawal. Variability in NOWS severity necessitates a more individualized treatment approach. Ultrasonic vocalizations (USVs) in neonatal mice are emitted in isolation as a stress response and are increased during opioid withdrawal, thus modeling a negative affective state that can be utilized to test new treatments.

OBJECTIVES

We sought to identify the behavioral and USV profile, brainstem transcriptomic adaptations, and role of kappa opioid receptors in USVs during neonatal opioid withdrawal.

METHODS

We employed a third trimester-approximate opioid exposure model, where neonatal inbred FVB/NJ pups were injected twice-daily with morphine (10mg/kg, s.c.) or saline (0.9%, 20 ul/g, s.c.) from postnatal day(P) 1 to P14. This protocol induces reduced weight gain, hypothermia, thermal hyperalgesia, and increased USVs during spontaneous morphine withdrawal.

RESULTS

On P14, there were increased USV emissions and altered USV syllables during withdrawal, including an increase in Complex 3 syllables in FVB/NJ females (but not males). Brainstem bulk mRNA sequencing revealed an upregulation of the kappa opioid receptor (Oprk1), which contributes to withdrawal-induced dysphoria. The kappa opioid receptor (KOR) antagonist, nor-BNI (30 mg/kg, s.c.), significantly reduced USVs in FVB/NJ females, but not males during spontaneous morphine withdrawal. Furthermore, the KOR agonist, U50,488h (0.625 mg/kg, s.c.), was sufficient to increase USVs on P10 (both sexes) and P14 (females only) in FVB/NJ mice.

CONCLUSIONS

We identified an elevated USV syllable, Complex 3, and a female-specific recruitment of the dynorphin/KOR system in increased USVs associated with neonatal opioid withdrawal severity.

Resilience of the Atlantic meridional overturning circulation

We address the issue of resilience of the Atlantic Meridional Overturning Circulation (AMOC) given the many indications that this dynamical system is in a multi-stable regime. A novel approach to resilience based on rare event techniques is presented, which leads to a measure capturing "resistance to change" and "ability to return" aspects in a probabilistic way. The application of this measure to a conceptual model demonstrates its suitability for assessing AMOC resilience but also shows its potential use in many other non-autonomous dynamical systems. This framework is then extended to compute the probability that the AMOC undergoes a transition conditioned on an external forcing. Such conditional probability can be estimated by exploiting the information available when computing the resilience of this system. This allows us to provide a probabilistic view on safe operating spaces by defining a conditional safe operating space as a subset of the parameter space of the (possibly transient) imposed forcing.

Adaptive power method for estimating large deviations in Markov chains

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model nonequilibrium systems. This algorithm was introduced in the context of risk-sensitive control of Markov chains and was recently adapted to diffusions evolving continuously in time. Here we provide an in-depth study of the convergence of this algorithm close to dynamical phase transitions, exploring the speed of convergence as a function of the learning rate and the effect of including transfer learning. We use as a test example the mean degree of a random walk on an Erdős-Rényi random graph, which shows a transition between high-degree trajectories of the random walk evolving in the bulk of the graph and low-degree trajectories evolving in dangling edges of the graph. The results show that the adaptive power method is efficient close to dynamical phase transitions, while having many advantages in terms of performance and complexity compared to other algorithms used to compute large deviation functions.

Extreme events in transitional turbulence

Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier-Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD

The Collective Variables Dashboard is a software tool for real-time, seamless exploration of molecular structures and trajectories in a customizable space of collective variables. The Dashboard arises from the integration of the Collective Variables Module (also known as Colvars) with the visualization software VMD, augmented with a fully discoverable graphical interface offering interactive workflows for the design and analysis of collective variables. Typical use cases include a priori design of collective variables for enhanced sampling and free energy simulations as well as analysis of any type of simulation or collection of structures in a collective variable space. A combination of those cases commonly occurs when preliminary simulations, biased or unbiased, reveal that an optimized set of collective variables is necessary to improve sampling in further simulations. Then the Dashboard provides an efficient way to intuitively explore the space of likely collective variables, validate them on existing data, and use the resulting collective variable definitions directly in further biased simulations using the Collective Variables Module. Visualization of biasing energies and forces is proposed to help analyze or plan biased simulations. We illustrate the use of the Dashboard on two applications: discovering coordinates to describe ligand unbinding from a protein binding site and designing volume-based variables to bias the hydration of a transmembrane pore.

Optimal sampling of dynamical large deviations via matrix product states

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions.

The RED scheme: Rate-constant estimation from pre-steady state weighted ensemble simulations

We present the Rate from Event Durations (RED) scheme, a new scheme that more efficiently calculates rate constants using the weighted ensemble path sampling strategy. This scheme enables rate-constant estimation from shorter trajectories by incorporating the probability distribution of event durations, or barrier-crossing times, from a simulation. We have applied the RED scheme to weighted ensemble simulations of a variety of rare-event processes that range in complexity: residue-level simulations of protein conformational switching, atomistic simulations of Na+/Cl- association in explicit solvent, and atomistic simulations of protein-protein association in explicit solvent. Rate constants were estimated with up to 50% greater efficiency than the original weighted ensemble scheme. Importantly, our scheme accounts for the systematic error that results from statistical bias toward the observation of events with short durations and reweights the event duration distribution accordingly. The RED scheme is relevant to any simulation strategy that involves unbiased trajectories of similar length to the most probable event duration, including weighted ensemble, milestoning, and standard simulations as well as the construction of Markov state models.

Taming Rugged Free Energy Landscapes Using an Average Force

The observation of complex structural transitions in biological and abiological molecular objects within time scales amenable to molecular dynamics (MD) simulations is often hampered by significant free energy barriers associated with entangled movements. Importance-sampling algorithms, a powerful class of numerical schemes for the investigation of rare events, have been widely used to extend simulations beyond the time scale common to MD. However, probing processes spanning milliseconds through microsecond molecular simulations still constitutes in practice a daunting challenge because of the difficulty of taming the ruggedness of multidimensional free energy surfaces by means of naive transition coordinates. To address this limitation, in recent years we have elaborated importance-sampling methods relying on an adaptive biasing force (ABF). In this Account, we review recent developments of algorithms aimed at mapping rugged free energy landscapes that correspond to complex processes of physical, chemical, and biological relevance. Through these developments, we have broadened the spectrum of applications of the popular ABF algorithm while improving its computational efficiency, notably for multidimensional free energy calculations. One major algorithmic advance, coined meta-eABF, merges the key features of metadynamics and an extended Lagrangian variant of ABF (eABF) by simultaneously shaving the barriers and flooding the valleys of the free energy landscape, and it possesses a convergence rate up to 5-fold greater than those of other importance-sampling algorithms. Through faster convergence and enhanced ergodic properties, meta-eABF represents a significant step forward in the simulation of millisecond-time-scale events. Here we introduce extensions of the algorithm, notably its well-tempered and replica-exchange variants, which further boost the sampling efficiency while gaining in numerical stability, thus allowing quantum-mechanical/molecular-mechanical free energy calculations to be performed at a lower cost. As a paradigm to bridge microsecond simulations to millisecond events by means of free energy calculations, we have applied the ABF family of algorithms to decompose complex movements in molecular objects of biological and abiological nature. We show here how water lubricates the shuttling of an amide-based rotaxane by altering the mechanism that underlies the concerted translation and isomerization of the macrocycle. Introducing novel collective variables in a computational workflow for the rigorous determination of standard binding free energies, we predict with utmost accuracy the thermodynamics of protein-ligand reversible association. Because of their simplicity, versatility, and robust mathematical foundations, the algorithms of the ABF family represent an appealing option for the theoretical investigation of a broad range of problems relevant to physics, chemistry, and biology.