A comparison of numerical approaches for statistical inference with stochastic models.

Due to our limited knowledge about complex environmental systems, our predictions of their behavior under different scenarios or decision alternatives are subject to considerable uncertainty. As this uncertainty can often be relevant for societal decisions, the consideration, quantification and communication of it is very important. Due to internal stochasticity, often poorly known influence factors, and only partly known mechanisms, in many cases, a stochastic model is needed to get an adequate description of uncertainty. As this implies the need to infer constant parameters, as well as the time-course of stochastic model states, a very high-dimensional inference problem for model calibration has to be solved. This is very challenging from a methodological and a numerical perspective. To illustrate aspects of this problem and show options to successfully tackle it, we compare three numerical approaches: Hamiltonian Monte Carlo, Particle Markov Chain Monte Carlo, and Conditional Ornstein-Uhlenbeck Sampling. As a case study, we select the analysis of hydrological data with a stochastic hydrological model. We conclude that the performance of the investigated techniques is comparable for the analyzed system, and that also generality and practical considerations may be taken into account to guide the choice of which technique is more appropriate for a particular application. Supplementary Information: The online version contains supplementary material available at 10.1007/s00477-023-02434-z.

High-density EEG power topography and connectivity during confusional arousal.

Confusional arousal is the milder expression of a family of disorders known as Disorders of Arousal (DOA) from non-REM sleep. These disorders are characterized by recurrent abnormal behaviors that occur in a state of reduced awareness for the external environment. Despite frequent amnesia for the nocturnal events, when actively probed, patients are able to report vivid hallucinatory/dream-like mental imagery. Traditional (low-density) scalp and stereo-electroencephalographic (EEG) recordings previously showed a pathological admixture of slow oscillations typical of NREM sleep and wake-like fast-mixed frequencies during these phenomena. However, our knowledge about the specific neural EEG dynamics over the entire brain is limited. We collected 2 consecutive in-laboratory sleep recordings using high-density (hd)-EEG (256 vertex-referenced geodesic system) coupled with standard video-polysomnography (v-PSG) from a 12-year-old drug-naïve and otherwise healthy child with a long-lasting history of sleepwalking. Source power topography and functional connectivity were computed during 20 selected confusional arousal episodes (from -6 to +18 sec after motor onset), and during baseline slow wave sleep preceding each episode (from - 3 to -2 min before onset). We found a widespread increase in slow wave activity (SWA) theta, alpha, beta, gamma power, associated with a parallel decrease in the sigma range during behavioral episodes compared to baseline sleep. Bilateral Broadman area 7 and right Broadman areas 39 and 40 were relatively spared by the massive increase in SWA power. Functional SWA connectivity analysis revealed a drastic increase in the number and complexity of connections from baseline sleep to full-blown episodes, that mainly involved an increased out-flow from bilateral fronto-medial prefrontal cortex and left temporal lobe to other cortical regions. These effects could be appreciated in the 6 sec window preceding behavioral onset. Overall, our results support the idea that DOA are the expression of peculiar brain states, compatible with a partial re-emergence of consciousness.

Holistic View on Cell Survival and DNA Damage: How Model-Based Data Analysis Supports Exploration of Dynamics in Biological Systems.

In this work, a method is established to calibrate a model that describes the basic dynamics of DNA damage and repair. The model can be used to extend planning for radiotherapy and hyperthermia in order to include the biological effects. In contrast to "syntactic" models (e.g., describing molecular kinetics), the model used here describes radiobiological semantics, resulting in a more powerful model but also in a far more challenging calibration. Model calibration is attempted from clonogenic assay data (doses of 0-6 Gy) and from time-resolved comet assay data obtained within 6 h after irradiation with 6 Gy. It is demonstrated that either of those two sources of information alone is insufficient for successful model calibration, and that both sources of information combined in a holistic approach are necessary to find viable model parameters. Approximate Bayesian computation (ABC) with simulated annealing is used for parameter search, revealing two aspects that are beneficial to resolving the calibration problem: (1) assessing posterior parameter distributions instead of point-estimates and (2) combining calibration runs from different assays by joining posterior distributions instead of running a single calibration run with a combined, computationally very expensive objective function.

Accelerating phylogeny-aware alignment with indel evolution using short time Fourier transform.

Recently we presented a frequentist dynamic programming (DP) approach for multiple sequence alignment based on the explicit model of indel evolution Poisson Indel Process (PIP). This phylogeny-aware approach produces evolutionary meaningful gap patterns and is robust to the 'over-alignment' bias. Despite linear time complexity for the computation of marginal likelihoods, the overall method's complexity is cubic in sequence length. Inspired by the popular aligner MAFFT, we propose a new technique to accelerate the evolutionary indel based alignment. Amino acid sequences are converted to sequences representing their physicochemical properties, and homologous blocks are identified by multi-scale short-time Fourier transform. Three three-dimensional DP matrices are then created under PIP, with homologous blocks defining sparse structures where most cells are excluded from the calculations. The homologous blocks are connected through intermediate 'linking blocks'. The homologous and linking blocks are aligned under PIP as independent DP sub-matrices and their tracebacks merged to yield the final alignment. The new algorithm can largely profit from parallel computing, yielding a theoretical speed-up estimated to be proportional to the cubic power of the number of sub-blocks in the DP matrices. We compare the new method to the original PIP approach and demonstrate it on real data.

High-resolution two-field nuclear magnetic resonance spectroscopy.

Nuclear magnetic resonance (NMR) is a ubiquitous branch of spectroscopy that can explore matter at the scale of an atom. Significant improvements in sensitivity and resolution have been driven by a steady increase of static magnetic field strengths. However, some properties of nuclei may be more favourable at low magnetic fields. For example, transverse relaxation due to chemical shift anisotropy increases sharply at higher magnetic fields leading to line-broadening and inefficient coherence transfers. Here, we present a two-field NMR spectrometer that permits the application of rf-pulses and acquisition of NMR signals in two magnetic centres. Our prototype operates at 14.1 T and 0.33 T. The main features of this system are demonstrated by novel NMR experiments, in particular a proof-of-concept correlation between zero-quantum coherences at low magnetic field and single quantum coherences at high magnetic field, so that high resolution can be achieved in both dimensions, despite a ca. 10 ppm inhomogeneity of the low-field centre. Two-field NMR spectroscopy offers the possibility to circumvent the limits of high magnetic fields, while benefiting from their exceptional sensitivity and resolution. This approach opens new avenues for NMR above 1 GHz.

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

Broadband excitation in solid-state NMR using interleaved DANTE pulse trains with N pulses per rotor period.

We analyze the direct excitation of wide one-dimensional spectra of nuclei with spin I=1/2 or 1 in rotating solids submitted to pulse trains in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE), either with one short rotor-synchronized pulse of duration τp in each of K rotor periods (D1(K)) or with N interleaved equally spaced pulses τp in each rotor period, globally also extending over K rotor periods (D(N)(K)). The excitation profile of D(N)(K) scheme is a comb of rf-spikelets with Nν(R)=N/T(R) spacing from the carrier frequency, and a width of each spikelet inversely proportional to the length, KT(R), of D(N)(K) scheme. Since the individual pulse lengths, τp, are typically of a few hundreds of ns, D(N)(K) scheme can readily excite spinning sidebands families covering several MHz, provided the rf carrier frequency is close enough to the resonance frequency of one the spinning sidebands. If the difference of isotropic chemical shifts between distinct chemical sites is less than about 1.35/(KT(R)), D(N)(K) scheme can excite the spinning sidebands families of several sites. For nuclei with I=1/2, if the homogeneous and inhomogeneous decays of coherences during the DANTE sequence are neglected, the K pulses of a D1(K) train have a linearly cumulative effect, so that the total nutation angle is θ(tot)=K2πν1τp, where ν1 is the rf-field amplitude. This allows obtaining nearly ideal 90° pulses for excitation or 180° rotations for inversion and refocusing across wide MAS spectra comprising many spinning sidebands. If one uses interleaved DANTE trains D(N)(K) with N>1, only spinning sidebands separated by intervals of Nν(R) with respect to the carrier frequency are observed as if the effective spinning speed was Nν(R). The other sidebands have vanishing intensities because of the cancellation of the N contributions with opposite signs. However, the intensities of the remaining sidebands obey the same rules as in spectra obtained with νR. With increasing N, the intensities of the non-vanishing sidebands increase, but the total intensity integrated over all sidebands decreases. Furthermore, the NK pulses in a D(N)(K) train do not have a simple cumulative effect and the optimal cumulated flip angle for optimal excitation, θ(tot)(opt)=NK2πν1τp, exceeds 90°. Such D(N)(K) pulse trains allow achieving efficient broadband excitation, but they are not recommended for broadband inversion or refocusing as they cannot provide proper 180° rotations. Since D(N)(K) pulse trains with N>1 are shorter than basic D1(K) sequences, they are useful for broadband excitation in samples with rapid homogeneous or inhomogeneous decay. For nuclei with I=1 (e.g., for (14)N), the response to basic D1(K) pulse train is moreover affected by inhomogeneous decay due to 2nd-order quadrupole interactions, since these are not of rank 2 and therefore cannot be eliminated by spinning about the magic angle. For large quadrupole interactions, the signal decay produced by second-order quadrupole interaction can be minimized by (i) reducing the length of D(N)(K) pulse trains using N>1, (ii) fast spinning, (iii) large rf-field, and (iv) using high magnetic fields to reduce the 2nd-order quadrupole interaction.

Dynamic Nuclear Polarization and other magnetic ideas at EPFL.

Although nuclear magnetic resonance (NMR) can provide a wealth of information, it often suffers from a lack of sensitivity. Dynamic Nuclear Polarization (DNP) provides a way to increase the polarization and hence the signal intensities in NMR spectra by transferring the favourable electron spin polarization of paramagnetic centres to the surrounding nuclear spins through appropriate microwave irradiation. In our group at EPFL, two complementary DNP techniques are under investigation: the combination of DNP with magic angle spinning at temperatures near 100 K ('MAS-DNP'), and the combination of DNP at 1.2 K with rapid heating followed by the transfer of the sample to a high-resolution magnet ('dissolution DNP'). Recent applications of MAS-DNP to surfaces, as well as new developments of magnetization transfer of (1)H to (13)C at 1.2 K prior to dissolution will illustrate the work performed in our group. A second part of the paper will give an overview of some 'non-enhanced' activities of our laboratory in liquid- and solid-state NMR.

Uniform broadband excitation of crystallites in rotating solids using interleaved sequences of delays alternating with nutation.

In solids that are spinning about the magic angle, trains of short pulses in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE) allow one to improve the efficiency of the excitation of magnetization compared to rectangular pulses. By interleaving N pulse trains with N>1, one obtains 'DANTE-N' sequences comprising N pulses per rotor period that extend over K rotor periods. Optimized interleaved DANTE schemes with N>1 are shorter than basic DANTE-1 sequences with N=1. Therefore, they are less affected by coherent or incoherent decays, thus leading to higher signal intensities than can be obtained with basic DANTE-1 or with rectangular pulses. Furthermore, the shorter length of DANTE-N with N>1 increases the width of the spikelets in the excitation profile, allowing one to cover the range of isotropic chemical shifts and second-order quadrupolar effects typical for side-chain and backbone amide (14)N sites in peptides at B(0)=18.8 T. In DANTE-N, spinning sidebands only appear at multiples of the spinning frequency ν(rot), as if the samples were rotating at Nν(rot). We show applications to direct detection of nitrogen-14 nuclei with spin I=1 subject to large quadrupole interactions, using fast magic angle spinning (typically ν(rot)≥60 kHz), backed up by simulations that provide insight into the properties of basic and interleaved DANTE sequences. When used for indirect detection, we show by numerical simulations that even basic DANTE-1 sequences can lead to a four-fold boost of efficiency compared to standard rectangular pulses.

Boosting the sensitivity of ligand-protein screening by NMR of long-lived states.

A new NMR method for the study of ligand-protein interactions exploits the unusual lifetimes of long-lived states (LLSs). The new method provides better contrast between bound and free ligands and requires a protein-ligand ratio ca. 25 times lower than for established T(1ρ) methods, thus saving on costly proteins. The new LLS method was applied to the screening of inhibitors of urokinase-type plasminogen activator (uPA), which is a prototypical target of cancer research. With only 10 µM protein, a dissociation constant (K(D)) of 180 ± 20 nM was determined for the strong ligand (inhibitor) UK-18, which can be compared with K(D) = 157 ± 39 nM determined by the established surface plasmon resonance method.

Time scales of slow motions in ubiquitin explored by heteronuclear double resonance.

Understanding how proteins function at the atomic level relies in part on a detailed characterization of their dynamics. Ubiquitin, a small single-domain protein, displays rich dynamic properties over a wide range of time scales. In particular, several regions of ubiquitin show the signature of chemical exchange, including the hydrophobic patch and the ß4-α2 loop, which are both involved in many interactions. Here, we use multiple-quantum relaxation techniques to identify the extent of chemical exchange in ubiquitin. We employ our recently developed heteronuclear double resonance method to determine the time scales of motions that give rise to chemical exchange. Dispersion profiles are obtained for the backbone NH(N) pairs of several residues in the hydrophobic patch and the ß4-α2 loop, as well as the C-terminus of helix α1. We show that a single time scale (ca. 50 µs) can be used to fit the data for most residues. Potential mechanisms for the propagation of motions and the possible extent of correlation of these motions are discussed.

Extending timescales and narrowing linewidths in NMR.

Among the different fields of research in nuclear magnetic resonance (NMR) which are currently investigated in the Laboratory of Biomolecular Magnetic Resonance (LRMB), two subjects that are closely related to each other are presented in this article. On the one hand, we show how to populate long-lived states (LLS) that have long lifetimes T(LLS) which allow one to go beyond the usual limits imposed by the longitudinal relaxation time T1. This makes it possible to extend NMR experiments to longer time-scales. As an application, we demonstrate the extension of the timescale of diffusion measurements by NMR spectroscopy. On the other hand, we review our work on long-lived coherences (LLC), a particular type of coherence between two spin states that oscillates with the frequency of the scalar coupling constant J(IS) and decays with a time constant T(LLC). Again, this time constant T(LLC) can be much longer than the transverse relaxation time T2. By extending the coherence lifetimes, we can narrow the linewidths to an unprecedented extent. J-couplings and residual dipolar couplings (RDCs) in weakly-oriented phases can be measured with the highest precision.

Broadband excitation and indirect detection of nitrogen-14 in rotating solids using Delays Alternating with Nutation (DANTE).

A train of short rotor-synchronized pulses in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE) applied to nitrogen-14 nuclei (I=1) in samples spinning at the magic angle at high frequencies (typically νrot=62.5 kHz so that τrot=16 µs) allows one to achieve uniform excitation of a great number of spinning sidebands that arise from large first-order quadrupole interactions, as occur for aromatic nitrogen-14 nuclei in histidine. With routine rf amplitudes ω1(14N)/(2π)=60 kHz and very short pulses of a typical duration 0.5<τp<2 µs, efficient excitation can be achieved with 13 rotor-synchronized pulses in 13 τrot=208 µs. Alternatively, with 'overtone' DANTE sequences using 2, 4, or 8 pulses per rotor period one can achieve efficient broadband excitation in fewer rotor periods, typically 2-4 τrot. These principles can be combined with the indirect detection of 14N nuclei via spy nuclei with S=½ such as 1H or 13C in the manner of Dipolar Heteronuclear Multiple-Quantum Correlation (D-HMQC).

Control of cross relaxation of multiple-quantum coherences induced by fast chemical exchange under heteronuclear double-resonance irradiation.

A fully analytical description of the control of the cross-correlated cross relaxation of multiple-quantum coherences in the presence of local dynamics under heteronuclear double-resonance radio-frequency (RF) irradiation is presented. The contribution of chemical exchange to relaxation can be partly or fully quenched by RF fields. We assume a correlated two-site chemical exchange model with arbitrary populations, and show that in the limit of fast exchange the dependence of the effective multiple-quantum cross-relaxation rate on the applied RF amplitude can be described by a compact analytical expression. Numerical simulations and preliminary experiments support our theoretical results. The relaxation dispersion as a function of RF amplitude can provide accurate information on the kinetics of correlated processes.

New tools in bio-NMR: indirect detection of nitrogen-14 in solids.

This paper presents an overview of recently developed methods for the indirect detection of 14N nuclei (spin l = 1) in spinning solids by nuclear magnetic resonance spectroscopy. These methods exploit the transfer of coherence from a neighboring 'spy' nucleus with spin S = 1/2, such as 13C or 1H, to single- or double-quantum transitions of 14N nuclei. The two-dimensional correlation methods presented here are closely related to the well-known heteronuclear single- and multiple-quantum correlation (HSQC and HMQC, respectively) experiments, already widely used for the investigation of molecules in liquids. Nitrogen-14 NMR spectra exhibit powder patterns characterized by second- and third-order quadrupolar couplings which can provide important information about structure and dynamics of molecules in powder samples.

Line-narrowing in proton-detected nitrogen-14 NMR.

In solids spinning at the magic angle, the indirect detection of single-quantum (SQ) and double-quantum (DQ) (14)N spectra (I=1) via spy nuclei S=1/2 such as protons can be achieved in the manner of heteronuclear single- or multiple-quantum correlation (HSQC or HMQC) spectroscopy. The HMQC method relies on the excitation of two-spin coherences of the type T(11)(I)T(11)(S) and T(21)(I)T(11)(S) at the beginning of the evolution interval t(1). The spectra obtained by Fourier transformation from t(1) to omega(1) may be broadened by the homogenous decay of the transverse terms of the spy nuclei S. This broadening is mostly due to homonuclear dipolar S-S' interactions between the proton spy nuclei. In this work we have investigated the possibility of inserting rotor-synchronized symmetry-based C or R sequences and decoupling schemes such as Phase-Modulated Lee-Goldburg (PMLG) sequences in the evolution period. These schemes reduce the homonuclear proton-proton interactions and lead to an enhancement of the resolution of both SQ and DQ proton-detected (14)N HMQC spectra. In addition, we have investigated the combination of HSQC with symmetry-based sequences and PMLG and shown that the highest resolution in the (14)N dimension is achieved by using HSQC in combination with symmetry-based sequences of the R-type. We show improvements in resolution in samples of l-alanine and the tripeptide ala-ala-gly (AAG). In particular, for l-alanine the width of the (14)N SQ peak is reduced from 2 to 1.2 kHz, in agreement with simulations. We report accurate measurements of quadrupolar coupling constants and asymmetry parameters for amide (14)N in AAG peptide bonds.

Heteronuclear double resonance in nuclear magnetic resonance spectroscopy: Relaxation of multiple-quantum coherences.

Theoretical and experimental investigations of the relaxation rates of multiple-quantum coherences during heteronuclear double resonance (HDR) pulse sequences are presented. Average Liouvillian theory yields analytical expressions to describe the effective relaxation rates of multiple-quantum coherences during HDR irradiation. Experiments were carried out on a (13)C-(1)H pair in glycerol to measure the effective auto- and cross-relaxation rates of multiple-quantum coherences during HDR schemes. The experimental results exhibit a very good agreement with theoretical predictions, even when the average Liouvillian expansion is truncated to zeroth order.

Preservation of heteronuclear multiple-quantum coherences in NMR by double-resonance irradiation.

A heteronuclear double-resonance (HDR) method based on MLEV-32 or WALTZ-32 pulse sequences has been designed for the investigation of relaxation of heteronuclear multiple-quantum (MQ) coherences. The theoretical analysis of this technique uses average Hamiltonian theory (AHT) to treat the effects of coherent evolution associated with scalar couplings, offsets, and inhomogeneous radiofrequency (rf) fields during the pulse sequence. Under most conditions, the dynamics of the MQ coherences during the HDR sequence is not affected by rf inhomogeneities and scalar couplings for offsets as large as the nutation frequency. The predictions drawn from AHT are supported by numerical simulations and experiments.

Evidence for dynamics on a 100 ns time scale from single- and double-quantum nitrogen-14 NMR in solid peptides.

The indirect detection of 14N spectra via protons in the manner of heteronuclear multiple-quantum correlation (HMQC) allows one to obtain single- (SQ) and double-quantum (DQ) 14N spectra in solids. A comparison of the SQ and DQ line widths as a function of temperature with simulations reveals motions in the tripeptide AAG with rates on the order of 107 s(-1) at 49 degrees C.