Serotonin synthesis, release and reuptake in terminals: a mathematical model.

BACKGROUND: Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system. METHODS: We construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data. RESULTS: We compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct in silico experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine. CONCLUSIONS: Serotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.

Myosin VIIA, important for human auditory function, is necessary for Drosophila auditory organ development.

BACKGROUND: Myosin VIIA (MyoVIIA) is an unconventional myosin necessary for vertebrate audition [1]-[5]. Human auditory transduction occurs in sensory hair cells with a staircase-like arrangement of apical protrusions called stereocilia. In these hair cells, MyoVIIA maintains stereocilia organization [6]. Severe mutations in the Drosophila MyoVIIA orthologue, crinkled (ck), are semi-lethal [7] and lead to deafness by disrupting antennal auditory organ (Johnston's Organ, JO) organization [8]. ck/MyoVIIA mutations result in apical detachment of auditory transduction units (scolopidia) from the cuticle that transmits antennal vibrations as mechanical stimuli to JO. PRINCIPAL FINDINGS: Using flies expressing GFP-tagged NompA, a protein required for auditory organ organization in Drosophila, we examined the role of ck/MyoVIIA in JO development and maintenance through confocal microscopy and extracellular electrophysiology. Here we show that ck/MyoVIIA is necessary early in the developing antenna for initial apical attachment of the scolopidia to the articulating joint. ck/MyoVIIA is also necessary to maintain scolopidial attachment throughout adulthood. Moreover, in the adult JO, ck/MyoVIIA genetically interacts with the non-muscle myosin II (through its regulatory light chain protein and the myosin binding subunit of myosin II phosphatase). Such genetic interactions have not previously been observed in scolopidia. These factors are therefore candidates for modulating MyoVIIA activity in vertebrates. CONCLUSIONS: Our findings indicate that MyoVIIA plays evolutionarily conserved roles in auditory organ development and maintenance in invertebrates and vertebrates, enhancing our understanding of auditory organ development and function, as well as providing significant clues for future research.

The kinase Grk2 regulates Nedd4/Nedd4-2-dependent control of epithelial Na+ channels.

Epithelial Na(+) channels mediate the transport of Na across epithelia in the kidney, gut, and lungs and are required for blood pressure regulation. They are inhibited by ubiquitin protein ligases, such as Nedd4 and Nedd4-2, with loss of this inhibition leading to hypertension. Here, we report that these channels are maintained in the active state by the G protein-coupled receptor kinase, Grk2, which has been previously implicated in the development of essential hypertension. We also show that Grk2 phosphorylates the C terminus of the channel beta subunit and renders the channels insensitive to inhibition by Nedd4-2. This mechanism has not been previously reported to regulate epithelial Na(+) channels and provides a potential explanation for the observed association of Grk2 overactivity with hypertension. Here, we report a G protein-coupled receptor kinase regulating a membrane protein other than a receptor and provide a paradigm for understanding how the interaction between membrane proteins and ubiquitin protein ligases is controlled.

Computational inference of neural information flow networks.

Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal such neural information flow have been made using linear computational methods, but neural interactions are known to be nonlinear. Here, we demonstrate that a dynamic Bayesian network (DBN) inference algorithm we originally developed to infer nonlinear transcriptional regulatory networks from gene expression data collected with microarrays is also successful at inferring nonlinear neural information flow networks from electrophysiology data collected with microelectrode arrays. The inferred networks we recover from the songbird auditory pathway are correctly restricted to a subset of known anatomical paths, are consistent with timing of the system, and reveal both the importance of reciprocal feedback in auditory processing and greater information flow to higher-order auditory areas when birds hear natural as opposed to synthetic sounds. A linear method applied to the same data incorrectly produces networks with information flow to non-neural tissue and over paths known not to exist. To our knowledge, this study represents the first biologically validated demonstration of an algorithm to successfully infer neural information flow networks.

Less wiring, more firing: low-performing older adults compensate for impaired white matter with greater neural activity.

The reliable neuroimaging finding that older adults often show greater activity (over-recruitment) than younger adults is typically attributed to compensation. Yet, the neural mechanisms of over-recruitment in older adults (OAs) are largely unknown. Rodent electrophysiology studies have shown that as number of afferent fibers within a circuit decreases with age, the fibers that remain show higher synaptic field potentials (less wiring, more firing). Extrapolating to system-level measures in humans, we proposed and tested the hypothesis that greater activity in OAs compensates for impaired white-matter connectivity. Using a neuropsychological test battery, we measured individual differences in executive functions associated with the prefrontal cortex (PFC) and memory functions associated with the medial temporal lobes (MTLs). Using event-related functional magnetic resonance imaging, we compared activity for successful versus unsuccessful trials during a source memory task. Finally, we measured white-matter integrity using diffusion tensor imaging. The study yielded 3 main findings. First, low-executive OAs showed greater success-related activity in the PFC, whereas low-memory OAs showed greater success-related activity in the MTLs. Second, low-executive OAs displayed white-matter deficits in the PFC, whereas low-memory OAs displayed white-matter deficits in the MTLs. Finally, in both prefrontal and MTL regions, white-matter decline and success-related activations occurred in close proximity and were negatively correlated. This finding supports the less-wiring-more-firing hypothesis, which provides a testable account of compensatory over-recruitment in OAs.

Neuronal correlates of metacognition in primate frontal cortex.

Humans are metacognitive: they monitor and control their cognition. Our hypothesis was that neuronal correlates of metacognition reside in the same brain areas responsible for cognition, including frontal cortex. Recent work demonstrated that nonhuman primates are capable of metacognition, so we recorded from single neurons in the frontal eye field, dorsolateral prefrontal cortex, and supplementary eye field of monkeys (Macaca mulatta) that performed a metacognitive visual-oculomotor task. The animals made a decision and reported it with a saccade, but received no immediate reward or feedback. Instead, they had to monitor their decision and bet whether it was correct. Activity was correlated with decisions and bets in all three brain areas, but putative metacognitive activity that linked decisions to appropriate bets occurred exclusively in the SEF. Our results offer a survey of neuronal correlates of metacognition and implicate the SEF in linking cognitive functions over short periods of time.

Metacognition in monkeys during an oculomotor task.

This study investigated whether rhesus monkeys show evidence of metacognition in a reduced, visual oculomotor task that is particularly suitable for use in fMRI and electrophysiology. The 2-stage task involved punctate visual stimulation and saccadic eye movement responses. In each trial, monkeys made a decision and then made a bet. To earn maximum reward, they had to monitor their decision and use that information to bet advantageously. Two monkeys learned to base their bets on their decisions within a few weeks. We implemented an operational definition of metacognitive behavior that relied on trial-by-trial analyses and signal detection theory. Both monkeys exhibited metacognition according to these quantitative criteria. Neither external visual cues nor potential reaction time cues explained the betting behavior; the animals seemed to rely exclusively on internal traces of their decisions. We documented the learning process of one monkey. During a 10-session transition phase, betting switched from random to a decision-based strategy. The results reinforce previous findings of metacognitive ability in monkeys and may facilitate the neurophysiological investigation of metacognitive functions.

Lack of evidence for ectopic sprouting of genetically labeled Aβ touch afferents in inflammatory and neuropathic trigeminal pain.

BACKGROUND: Mechanical and in particular tactile allodynia is a hallmark of chronic pain in which innocuous touch becomes painful. Previous cholera toxin B (CTB)-based neural tracing experiments and electrophysiology studies had suggested that aberrant axon sprouting from touch sensory afferents into pain-processing laminae after injury is a possible anatomical substrate underlying mechanical allodynia. This hypothesis was later challenged by experiments using intra-axonal labeling of A-fiber neurons, as well as single-neuron labeling of electrophysiologically identified sensory neurons. However, no studies have used genetically labeled neurons to examine this issue, and most studies were performed on spinal but not trigeminal sensory neurons which are the relevant neurons for orofacial pain, where allodynia oftentimes plays a dominant clinical role. FINDINGS: We recently discovered that parvalbumin::Cre (Pv::Cre) labels two types of Aβ touch neurons in trigeminal ganglion. Using a Pv::CreER driver and a Cre-dependent reporter mouse, we specifically labeled these Aβ trigeminal touch afferents by timed taxomifen injection prior to inflammation or infraorbital nerve injury (ION transection). We then examined the peripheral and central projections of labeled axons into the brainstem caudalis nucleus after injuries vs controls. We found no evidence for ectopic sprouting of Pv::CreER labeled trigeminal Aβ axons into the superficial trigeminal noci-receptive laminae. Furthermore, there was also no evidence for peripheral sprouting. CONCLUSIONS: CreER-based labeling prior to injury precluded the issue of phenotypic changes of neurons after injury. Our results suggest that touch allodynia in chronic orofacial pain is unlikely caused by ectopic sprouting of Aβ trigeminal afferents.

Activity in descending dopaminergic neurons represents but is not required for leg movements in the fruit fly Drosophila.

Modulatory descending neurons (DNs) that link the brain to body motor circuits, including dopaminergic DNs (DA-DNs), are thought to contribute to the flexible control of behavior. Dopamine elicits locomotor-like outputs and influences neuronal excitability in isolated body motor circuits over tens of seconds to minutes, but it remains unknown how and over what time scale DA-DN activity relates to movement in behaving animals. To address this question, we identified DA-DNs in the Drosophila brain and developed an electrophysiological preparation to record and manipulate the activity of these cells during behavior. We find that DA-DN spike rates are rapidly modulated during a subset of leg movements and scale with the total speed of ongoing leg movements, whether occurring spontaneously or in response to stimuli. However, activating DA-DNs does not elicit leg movements in intact flies, nor do acute bidirectional manipulations of DA-DN activity affect the probability or speed of leg movements over a time scale of seconds to minutes. Our findings indicate that in the context of intact descending control, changes in DA-DN activity are not sufficient to influence ongoing leg movements and open the door to studies investigating how these cells interact with other descending and local neuromodulatory inputs to influence body motor output.

A whole-cell and single-channel study of the voltage-dependent outward potassium current in avian hepatocytes.

Voltage-dependent membrane currents were studied in dissociated hepatocytes from chick, using the patch-clamp technique. All cells had voltage-dependent outward K+ currents; in 10% of the cells, a fast, transient, tetrodotoxin-sensitive Na+ current was identified. None of the cells had voltage-dependent inward Ca2+ currents. The K+ current activated at a membrane potential of about -10 mV, had a sigmoidal time course, and did not inactivate in 500 ms. The maximum outward conductance was 6.6 +/- 2.4 nS in 18 cells. The reversal potential, estimated from tail current measurements, shifted by 50 mV per 10-fold increase in the external K+ concentration. The current traces were fitted by n2 kinetics with voltage-dependent time constants. Omitting Ca2+ from the external bath or buffering the internal Ca2+ with EGTA did not alter the outward current, which shows that Ca2+-activated K+ currents were not present. 1-5 mM 4-aminopyridine, 0.5-2 mM BaCl2, and 0.1-1 mM CdCl2 reversibly inhibited the current. The block caused by Ba was voltage dependent. Single-channel currents were recorded in cell-attached and outside-out patches. The mean unitary conductance was 7 pS, and the channels displayed bursting kinetics. Thus, avian hepatocytes have a single type of K+ channel belonging to the delayed rectifier class of K+ channels.

Evaluating functional network inference using simulations of complex biological systems.

MOTIVATION: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to recover a complex functional network from biologically reasonable simulated data. RESULTS: We designed a simulator to generate data representing a complex biological system at multiple levels of organization: behaviour, neural anatomy, brain electrophysiology, and gene expression of songbirds. About 90% of the simulated variables are unregulated by other variables in the system and are included simply as distracters. We sampled the simulated data at intervals as one would sample from a biological system in practice, and then used the sampled data to evaluate the effectiveness of an algorithm we developed for functional network inference. We found that our algorithm is highly effective at recovering the functional network structure of the simulated system-including the irrelevance of unregulated variables-from sampled data alone. To assess the reproducibility of these results, we tested our inference algorithm on 50 separately simulated sets of data and it consistently recovered almost perfectly the complex functional network structure underlying the simulated data. To our knowledge, this is the first approach for evaluating the effectiveness of functional network inference algorithms at recovering models from limited data. Our simulation approach also enables researchers a priori to design experiments and data-collection protocols that are amenable to functional network inference.

Practice-Level Variation in Outpatient Cardiac Care and Association With Outcomes.

BACKGROUND: Utilization of cardiac services varies across regions and hospitals, yet little is known regarding variation in the intensity of outpatient cardiac care across cardiology physician practices or the association with clinical endpoints, an area of potential importance to promote efficient care. METHODS AND RESULTS: We included 7 160 732 Medicare beneficiaries who received services from 5635 cardiology practices in 2012. Beneficiaries were assigned to practices providing the plurality of office visits, and practices were ranked and assigned to quartiles using the ratio of observed to predicted annual payments per beneficiary for common cardiac services (outpatient intensity index). The median (interquartile range) outpatient intensity index was 1.00 (0.81-1.24). Mean payments for beneficiaries attributed to practices in the highest (Q4) and lowest (Q1) quartile of outpatient intensity were: all cardiac payments (Q4 $1272 vs Q1 $581; ratio, 2.2); cardiac catheterization (Q4 $215 vs Q1 $64; ratio, 3.4); myocardial perfusion imaging (Q4 $253 vs Q1 $83; ratio, 3.0); and electrophysiology device procedures (Q4 $353 vs Q1 $142; ratio, 2.5). The adjusted odds ratios (95% CI) for 1 incremental quartile of outpatient intensity for each outcome was: cardiac surgical/procedural hospitalization (1.09 [1.09, 1.10]); cardiac medical hospitalization (1.00 [0.99, 1.00]); noncardiac hospitalization (0.99 [0.99, 0.99]); and death at 1 year (1.00 [0.99, 1.00]). CONCLUSION: Substantial variation in the intensity of outpatient care exists at the cardiology practice level, and higher intensity is not associated with reduced mortality or hospitalizations. Outpatient cardiac care is a potentially important target for efforts to improve efficiency in the Medicare population.

A screw microdrive for adjustable chronic unit recording in monkeys.

A screw microdrive is described that attaches to the grid system used for recording single neurons from brains of awake behaving monkeys. Multiple screwdrives can be mounted on a grid over a single cranial opening. This method allows many electrodes to be implanted chronically in the brain and adjusted as needed to maintain isolation. rights reserved.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Descending Control of Limb Movements in Drosophila melanogaster

Because the interactions between feedforward influences are inextricably linked during many motor outputs (including but not limited to walking), the contribution of descending inputs to the generation of movements is difficult to study. Here we take advantage of the relatively small number of descending neurons (DNs) in the Drosophila melanogaster model system. We first characterize the number and distribution of the DN populations, then present a novel load free preparation, which enables the study of descending control on limb movements in a context where sensory feedback can be is reduced while leaving the nervous system, musculature, and cuticle of the animal relatively intact. Lastly we use in-vivo whole cell patch clamp electrophysiology to characterize the role of individual DNs in response to specific sensory stimuli and in relationship to movement. We find that there are approximately 1100 DNs in Drosophila that are distributed across six clusters. Input from these DNs is not necessary for coordinated motor activity, which can be generated by the thoracic ganglion, but is necessary for the specific combinations of joint movements typically observed in walking. Lastly, we identify a particular cluster of DNs that are tuned to sensory stimuli and innervate the leg neuromeres. We propose that a multi-layered interaction between these DNs, other DNs, and motor circuits in the thoracic ganglia enable the diverse but well-coordinated range of motor outputs an animal might exhibit.