Gene expression model inference from snapshot RNA data using Bayesian non-parametrics.

Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters. Here we propose a method to learn full distributions over gene states, state connectivities and associated rate parameters, simultaneously and self-consistently from single-molecule RNA counts. We propagate noise from fluctuating RNA counts over models by treating models themselves as random variables. We achieve this within a Bayesian non-parametric paradigm. We demonstrate our method on the Escherichia coli lacZ pathway and the Saccharomyces cerevisiae STL1 pathway, and verify its robustness on synthetic data.

Single-Molecule Reaction-Diffusion.

We propose to capture reaction-diffusion on a molecule-by-molecule basis from the fastest acquirable timescale, namely individual photon arrivals. We illustrate our method on intrinsically disordered human proteins, the linker histone H1.0 as well as its chaperone prothymosin α, as these diffuse through an illuminated confocal spot and interact forming larger ternary complexes on millisecond timescales. Most importantly, single-molecule reaction-diffusion, smRD, reveals single molecule properties without trapping or otherwise confining molecules to surfaces. We achieve smRD within a Bayesian paradigm and term our method Bayes-smRD. Bayes-smRD is further free of the average, bulk, results inherent to the analysis of long photon arrival traces by fluorescence correlation spectroscopy. In learning from thousands of photon arrivals continuous spatial positions and discrete conformational and photophysical state changes, Bayes-smRD estimates kinetic parameters on a molecule-by-molecule basis with two to three orders of magnitude less data than tools such as fluorescence correlation spectroscopy thereby also dramatically reducing sample photodamage.

Monte Carlo samplers for efficient network inference.

Accessing information on an underlying network driving a biological process often involves interrupting the process and collecting snapshot data. When snapshot data are stochastic, the data's structure necessitates a probabilistic description to infer underlying reaction networks. As an example, we may imagine wanting to learn gene state networks from the type of data collected in single molecule RNA fluorescence in situ hybridization (RNA-FISH). In the networks we consider, nodes represent network states, and edges represent biochemical reaction rates linking states. Simultaneously estimating the number of nodes and constituent parameters from snapshot data remains a challenging task in part on account of data uncertainty and timescale separations between kinetic parameters mediating the network. While parametric Bayesian methods learn parameters given a network structure (with known node numbers) with rigorously propagated measurement uncertainty, learning the number of nodes and parameters with potentially large timescale separations remain open questions. Here, we propose a Bayesian nonparametric framework and describe a hybrid Bayesian Markov Chain Monte Carlo (MCMC) sampler directly addressing these challenges. In particular, in our hybrid method, Hamiltonian Monte Carlo (HMC) leverages local posterior geometries in inference to explore the parameter space; Adaptive Metropolis Hastings (AMH) learns correlations between plausible parameter sets to efficiently propose probable models; and Parallel Tempering takes into account multiple models simultaneously with tempered information content to augment sampling efficiency. We apply our method to synthetic data mimicking single molecule RNA-FISH, a popular snapshot method in probing transcriptional networks to illustrate the identified challenges inherent to learning dynamical models from these snapshots and how our method addresses them.

Two-state swimming: Strategy and survival of a model bacterial predator in response to environmental cues.

Bdellovibrio bacteriovorus is a predatory bacterium preying upon Gram-negative bacteria. As such, B. bacteriovorus has the potential to control antibiotic-resistant pathogens and biofilm populations. To survive and reproduce, B. bacteriovorus must locate and infect a host cell. However, in the temporary absence of prey, it is largely unknown how B. bacteriovorus modulate their motility patterns in response to physical or chemical environmental cues to optimize their energy expenditure. To investigate B. bacteriovorus' predation strategy, we track and quantify their motion by measuring speed distributions as a function of starvation time. While an initial unimodal speed distribution relaxing to one for pure diffusion at long times may be expected, instead we observe a bimodal speed distribution with one mode centered around that expected from diffusion and the other centered at higher speeds. What is more, for an increasing amount of time over which B. bacteriovorus is starved, we observe a progressive reweighting from the active swimming state to an apparent diffusive state in the speed distribution. Distributions of trajectory-averaged speeds for B. bacteriovorus are largely unimodal, indicating switching between a faster swim speed and an apparent diffusive state within individual observed trajectories rather than there being distinct active swimming and apparent diffusive populations. We also find that B. bacteriovorus' apparent diffusive state is not merely caused by the diffusion of inviable bacteria as subsequent spiking experiments show that bacteria can be resuscitated and bimodality restored. Indeed, starved B. bacteriovorus may modulate the frequency and duration of active swimming as a means of balancing energy consumption and procurement. Our results thus point to a reweighting of the swimming frequency on a trajectory basis rather than a population level basis.

BNP-Track: A framework for multi-particle superresolved tracking.

When tracking fluorescently labeled molecules (termed "emitters") under widefield microscopes, point spread function overlap of neighboring molecules is inevitable in both dilute and especially crowded environments. In such cases, superresolution methods leveraging rare photophysical events to distinguish static targets nearby in space introduce temporal delays that compromise tracking. As we have shown in a companion manuscript, for dynamic targets, information on neighboring fluorescent molecules is encoded as spatial intensity correlations across pixels and temporal correlations in intensity patterns across time frames. We then demonstrated how we used all spatiotemporal correlations encoded in the data to achieve superresolved tracking. That is, we showed the results of full posterior inference over both the number of emitters and their associated tracks simultaneously and self-consistently through Bayesian nonparametrics. In this companion manuscript we focus on testing the robustness of our tracking tool, BNP-Track, across sets of parameter regimes and compare BNP-Track to competing tracking methods in the spirit of a prior Nature Methods tracking competition. We explore additional features of BNP-Track including how a stochastic treatment of background yields greater accuracy in emitter number determination and how BNP-Track corrects for point spread function blur (or "aliasing") introduced by intraframe motion in addition to propagating error originating from myriad sources (such as criss-crossing tracks, out-of-focus particles, pixelation, shot and camera artefact, stochastic background) in posterior inference over emitter numbers and their associated tracks. While head-to-head comparison with other tracking methods is not possible (as competitors cannot simultaneously learn molecule numbers and associated tracks), we can give competing methods some advantages in order to perform approximate head-to-head comparison. We show that even under such optimistic scenarios, BNP-Track is capable of tracking multiple diffraction-limited point emitters conventional tracking methods cannot resolve thereby extending the superresolution paradigm to dynamical targets.

CFTR function, pathology and pharmacology at single-molecule resolution.

The cystic fibrosis transmembrane conductance regulator (CFTR) is an anion channel that regulates salt and fluid homeostasis across epithelial membranes1. Alterations in CFTR cause cystic fibrosis, a fatal disease without a cure2,3. Electrophysiological properties of CFTR have been analysed for decades4-6. The structure of CFTR, determined in two globally distinct conformations, underscores its evolutionary relationship with other ATP-binding cassette transporters. However, direct correlations between the essential functions of CFTR and extant structures are lacking at present. Here we combine ensemble functional measurements, single-molecule fluorescence resonance energy transfer, electrophysiology and kinetic simulations to show that the two nucleotide-binding domains (NBDs) of human CFTR dimerize before channel opening. CFTR exhibits an allosteric gating mechanism in which conformational changes within the NBD-dimerized channel, governed by ATP hydrolysis, regulate chloride conductance. The potentiators ivacaftor and GLPG1837 enhance channel activity by increasing pore opening while NBDs are dimerized. Disease-causing substitutions proximal (G551D) or distal (L927P) to the ATPase site both reduce the efficiency of NBD dimerization. These findings collectively enable the framing of a gating mechanism that informs on the search for more efficacious clinical therapies.

Extraction of rapid kinetics from smFRET measurements using integrative detectors.

Hidden Markov models (HMMs) are used to learn single-molecule kinetics across a range of experimental techniques. By their construction, HMMs assume that single-molecule events occur on slower timescales than those of data acquisition. To move beyond that HMM limitation and allow for single-molecule events to occur on any timescale, we must treat single-molecule events in continuous time as they occur in nature. We propose a method to learn kinetic rates from single-molecule Förster resonance energy transfer (smFRET) data collected by integrative detectors, even if those rates exceed data acquisition rates. To achieve that, we exploit our recently proposed "hidden Markov jump process" (HMJP), with which we learn transition kinetics from parallel measurements in donor and acceptor channels. HMJPs generalize the HMM paradigm in two critical ways: (1) they deal with physical smFRET systems as they switch between conformational states in continuous time, and (2) they estimate transition rates between conformational states directly without having recourse to transition probabilities or assuming slow dynamics. Our continuous-time treatment learns the transition kinetics and photon emission rates for dynamic regimes that are inaccessible to HMMs, which treat system kinetics in discrete time. We validate our framework's robustness on simulated data and demonstrate its performance on experimental data from FRET-labeled Holliday junctions.

Residence time analysis of RNA polymerase transcription dynamics: A Bayesian sticky HMM approach.

The time spent by a single RNA polymerase (RNAP) at specific locations along the DNA, termed "residence time," reports on the initiation, elongation, and termination stages of transcription. At the single-molecule level, this information can be obtained from dual ultrastable optical trapping experiments, revealing a transcriptional elongation of RNAP interspersed with residence times of variable duration. Successfully discriminating between long and short residence times was used by previous approaches to learn about RNAP's transcription elongation dynamics. Here, we propose an approach based on the Bayesian sticky hidden Markov model that treats all residence times for an Escherichia coli RNAP on an equal footing without a priori discriminating between long and short residence times. Furthermore, our method has two additional advantages: we provide full distributions around key point statistics and directly treat the sequence dependence of RNAP's elongation rate. By applying our approach to experimental data, we find assigned relative probabilities on long versus short residence times, force-dependent average residence time transcription elongation dynamics, ∼10% drop in the average backtracking durations in the presence of GreB, and ∼20% drop in the average residence time as a function of applied force in the presence of RNaseA.

Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes.

The hidden Markov model (HMM) is a framework for time series analysis widely applied to single-molecule experiments. Although initially developed for applications outside the natural sciences, the HMM has traditionally been used to interpret signals generated by physical systems, such as single molecules, evolving in a discrete state space observed at discrete time levels dictated by the data acquisition rate. Within the HMM framework, transitions between states are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, whereas measurements are often performed at discrete time levels in the natural sciences, physical systems evolve in continuous time according to transition rates. It then follows that the modeling assumptions underlying the HMM are justified if the transition rates of a physical process from state to state are small as compared to the data acquisition rate. In other words, HMMs apply to slow kinetics. The problem is, because the transition rates are unknown in principle, it is unclear, a priori, whether the HMM applies to a particular system. For this reason, we must generalize HMMs for physical systems, such as single molecules, because these switch between discrete states in "continuous time". We do so by exploiting recent mathematical tools developed in the context of inferring Markov jump processes and propose the hidden Markov jump process. We explicitly show in what limit the hidden Markov jump process reduces to the HMM. Resolving the discrete time discrepancy of the HMM has clear implications: we no longer need to assume that processes, such as molecular events, must occur on timescales slower than data acquisition and can learn transition rates even if these are on the same timescale or otherwise exceed data acquisition rates.

The Epidemiological and Clinical Characteristics of 81 Children with COVID-19 in a Pandemic Hospital in Turkey: an Observational Cohort Study.

BACKGROUND: Coronavirus disease-2019 (COVID-19) pandemic has affected millions of people throughout the world since December 2019. However, there is a limited amount of data about pediatric patients infected with the disease agent, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). METHODS: The epidemiological, laboratory, radiological, and treatment features of the pediatric patients who were positive for SARS-CoV-2 based on the reverse-transcription polymerase chain reaction (RT-PCR) test, were investigated retrospectively. RESULTS: The median age of 81 children included in the study was 9.50 years (0-17.75 years). The most frequent symptoms at the time of admission were fever (58%), cough (52%), and fatigue or myalgia (19%). The abnormal laboratory findings in these cases were decreased lymphocytes (2.5%, n = 2), leucopenia (5%, n = 4), and increased lactate dehydrogenase (17.2%, n = 14), C-reactive protein (16%, n = 13), procalcitonin (3.7%, n = 3), and D-dimer (12.3%, n = 10). Three (4%) patients had consolidation in chest computed tomography, and three (4%) had ground-glass opacities. None of the patients needed intensive care except for the newborns. The median time to turn SARS-CoV-2 negative in the RT-PCR test was 5 (3-10) days. The median length of hospital stay was 5 (4-10) days. The time to turn SARS-CoV-2 negative in the RT-PCR test and the length of hospital stay were significantly longer for those aged five years or younger than others (P = 0.037, P = 0.01). CONCLUSION: Compared to adults, COVID-19 is milder and more distinctive in children. As a result, more conservative approaches might be preferred in children for the diagnostic, clinical, and even therapeutic applications.

A first-principle mechanism for particulate aggregation and self-assembly in stratified fluids.

An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Here, we observe and model mathematically an unexpected fundamental mechanism by which particles suspended within stratification may self-assemble and form large aggregates without adhesion. This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and aggregate geometry, which produces toroidal flows. We show that these flows yield attractive horizontal forces between particles at the same heights. We observe that many particles demonstrate a collective motion revealing a system which appears to solve jigsaw-like puzzles on its way to organizing into a large-scale disc-like shape, with the effective force increasing as the collective disc radius grows. Control experiments isolate the individual dynamics, which are quantitatively predicted by simulations. Numerical force calculations with two spheres are used to build many-body simulations which capture observed features of self-assembly.

[Investigation of Chlamydophila pneumoniae seropositivity and risk factors in patients with atherosclerotic vascular disease in Sivas, Turkey]. / Sivas Yöresinde Aterosklerotik Damar Hastaligi Olan Kisilerde Chlamydophila pneumoniae Seropozitifligi ve Risk Faktörleri ile Iliskisi.

The role of various microorganisms including Chlamydophila (formerly Chlamydia) pneumoniae, have been frequently investigated in the pathogenesis of atherosclerosis. In our study, the relationship between C.pneumoniae seropositivity and risk factors for atherosclerosis have been evaluated. A total of 90 atherosclerotic patients (71 of them were male; age range: 45-87 years; mean age: 65.3 ± 8.7 years) and 90 control subjects without coronary diseases (41 of them were male; age range: 42-84 years; mean age: 61.6 ± 9.6 years) were included in the study. Both groups were also evaluated for the presence of risk factors such as age, gender, smoking, hypertension, diabetes, obesity, dyslipidemia, familial history and the high levels of ferritin, cholesterol (total, HDL and LDL) and HS (high sensitive)-CRP. The presence of C.pneumoniae IgG, IgM and IgA antibodies were investigated by micro-immunofluorescence (MIF) and ELISA methods using commercial kits (Euroimmun, Germany). The total antibody seropositivity rate was found 100% (90/90) in patient group by both MIF and ELISA methods, while this rate in control group was 94% (85/90) by MIF and 92% (83/90) by ELISA. When MIF test results were taken into consideration (since it is accepted as the reference method for C.pneumoniae serology), IgG, IgM and IgA positivity rates in patient and control groups were found as 100% (90/90) and 89% (80/90); 70% (63/90) and 59% (53/90); 3% (3/90) and 2% (2/90), respectively. Statistically significant difference between patient and control groups was detected only for IgG positivity (p< 0.05) and for total antibody positivities (100% and 94%, respectively) (p< 0.05). The evaluation of the risk factors revealed that age, hypertension, dyslipidemia and HS-CRP levels exhibited statistically significant differences between patient and control groups (p< 0.05 for each parameter tested). Statistically significant relation was detected only between high HS-CRP levels and C.pneumoniae seropositivity (p< 0.05). It was concluded that in areas with high C.pneumoniae infection prevalence, early diagnosis and specific treatment of C.pneumoniae infections, may prevent establishment of chronic infection and eliminate a risk factor for the development of atherosclerosis.