PINP: a new method of tagging neuronal populations for identification during in vivo electrophysiological recording

Neural circuits are exquisitely organized, consisting of many different neuronal subpopulations. However, it is difficult to assess the functional roles of these subpopulations using conventional extracellular recording techniques because these techniques do not easily distinguish spikes from different neuronal populations. To overcome this limitation, we have developed PINP (Photostimulation-assisted Identification of Neuronal Populations), a method of tagging neuronal populations for identification during in vivo electrophysiological recording. The method is based on expressing the light-activated channel channelrhodopsin-2 (ChR2) to restricted neuronal subpopulations. ChR2-tagged neurons can be detected electrophysiologically in vivo since illumination of these neurons with a brief flash of blue light triggers a short latency reliable action potential. We demonstrate the feasibility of this technique by expressing ChR2 in distinct populations of cortical neurons using two different strategies. First, we labeled a subpopulation of cortical neurons-mainly fast-spiking interneurons-by using adeno-associated virus (AAV) to deliver ChR2 in a transgenic mouse line in which the expression of Cre recombinase was driven by the parvalbumin promoter. Second, we labeled subpopulations of excitatory neurons in the rat auditory cortex with ChR2 based on projection target by using herpes simplex virus 1 (HSV1), which is efficiently taken up by axons and transported retrogradely; we find that this latter population responds to acoustic stimulation differently from unlabeled neurons. Tagging neurons is a novel application of ChR2, used in this case to monitor activity instead of manipulating it. PINP can be readily extended to other populations of genetically identifiable neurons, and will provide a useful method for probing the functional role of different neuronal populations in vivo

Computational Vector Mechanics in Atmospheric and Climate Modeling

The mathematical underpinnings of vector analysis are reviewed as they are applied in the development of the ensemble of numeric statements for subsequent matrix solution. With the continued advances in computational power, there is increased interest in the field of atmospheric modelling to decrease the computational scale to a micro‐scale. This interest is partially motivated by the ability to solve large scale matrix systems in the number of occasions to enable a small‐scale time advancement to be approximated in a finite‐difference scheme. Solving entire large scale matrix systems several times a modelling second is now computationally feasible. Hence the motivation to increase computational detail by reducing modelling scale

Manning’s equation and two-dimensional flow analogs

Two-dimensional (2D) flow models based on the well-known governing 2D flow equations are applied to floodplain analysis purposes. These 2D models numerically solve the governing flow equations simultaneously or explicitly on a discretization of the floodplain using grid tiles or similar tile cell geometry, called " elements" By use of automated information systems such as digital terrain modeling, digital elevation models, and GIS, large-scale topographic floodplain maps can be readily discretized into thousands of elements that densely cover the floodplain in an edge-to-edge form. However, the assumed principal flow directions of the flow model analog, as applied across an array of elements, typically do not align with the floodplain flow streamlines. This paper examines the mathematical underpinnings of a four-direction flow analog using an array of square elements with respect to floodplain flow streamlines that are not in alignment with the analog's principal flow directions. It is determined that application of Manning's equation to estimate the friction slope terms of the governing flow equations, in directions that are not coincident with the flow streamlines, may introduce a bias in modeling results, in the form of slight underestimation of flow depths. It is also determined that the maximum theoretical bias, occurs when a single square element is rotated by about 13°, and not 45° as would be intuitively thought. The bias as a function of rotation angle for an array of square elements follows approximately the bias for a single square element. For both the theoretical single square element and an array of square elements, the bias as a function of alignment angle follows a relatively constant value from about 5° to about 85°, centered at about 45°. This bias was first noted about a decade prior to the present paper, and the magnitude of this bias was estimated then to be about 20% at about 10° misalignment. An adjustment of Manning's n is investigated based on a considered steady state uniform flow problem, but the magnitude of the adjustment (about 20%) is on the order of the magnitude of the accepted ranges of friction factors. For usual cases where random streamline trajectory variability within the floodplain flow is greater than a few degrees from perfect alignment, the apparent bias appears to be implicitly included in the Manning's n values. It can be concluded that the array of square elements may be applied over the digital terrain model without respect to topographic flow directions. © 2010 Elsevier B.V

Mathematical Model of Cryospheric Response to Climate Changes

Abstract: This paper focuses on the development of simplified mathematical models of the cryosphere which may be useful in further understanding possible global climate change impacts and in further assessing future impacts captured by global circulation models (GCMs). The mathematical models developed by leveraging the dominating effects of freezing and thawing within the cryosphere to simplify the relevant heat transport equations are tractable to direct solution or numerical modeling. In this paper, the heat forcing function is assumed to be a linear transformation of temperature (assumed to be represented by proxy realizations). The output from the governing mathematical model is total ice volume of the cryosphere. The basic mathematical model provides information as a systems modeling approach that includes sufficient detail to explain ice volume given the estimation of the heat forcing function. A comparison between modeling results in the estimation of ice volume versus ice volume estimates developed from use of proxy data are shown in the demonstration problems presented

Cumulative Departure Model of the Cryosphere During the Pleistocene

Abstract: A mathematical model is developed to describe changes in ice volume in the cryosphere. Modeling the cryosphere may be useful in assessing future climate impacts currently captured by global circulation models (GCMs) by providing an opportunity to validate GCMs. Leveraging the dominating effects of freezing and thawing in the cryosphere to simplify relevant heat transport equations allows for the derivation of a mathematical model that can be solved exactly. Such exact solutions are useful in investigating other climatic components that may be similarly analyzed for possible GCM validation. The current trend in GCM advancement is to increase the complexity and sophistication of the various heat transport effects that are represented in the governing mathematical model in cumulative form as the heat forcing function. In this paper, simplified models are developed whose solution can be directly compared with available data forms representing temperature and ice volume during the Pleistocene. With careful integration of the Pleistocene temperature term in the mathematical solution, the well-known cumulative departure method can be resolved from the mathematical solution using a two-term expansion of the corresponding Taylor series. This simplification is shown to be a good approximation of the Pleistocene ice volume for given Pleistocene temperatures

Propagation of Tau Pathology: Integrating Insights From Postmortem and In Vivo Studies

Cellular accumulation of aggregated forms of the protein tau is a defining feature of so-called tauopathies such as Alzheimer's disease, progressive supranuclear palsy, and chronic traumatic encephalopathy. A growing body of literature suggests that conformational characteristics of tau filaments, along with regional vulnerability to tau pathology, account for the distinct histopathological morphologies, biochemical composition, and affected cell types seen across these disorders. In this review, we describe and discuss recent evidence from human postmortem and clinical biomarker studies addressing the differential vulnerability of brain areas to tau pathology, its cell-to-cell transmission, and characteristics of the different strains that tau aggregates can adopt. Cellular biosensor assays are increasingly used in human tissue to detect the earliest forms of tau pathology, before overt histopathological lesions (i.e., neurofibrillary tangles) are apparent. Animal models with localized tau expression are used to uncover the mechanisms that influence spreading of tau aggregates. Further, studies of human postmortem-derived tau filaments from different tauopathies injected in rodents have led to striking findings that recapitulate neuropathology-based staging of tau. Furthermore, the recent advent of tau positron emission tomography and novel fluid-based biomarkers render it possible to study the temporal progression of tau pathology in vivo. Ultimately, evidence from these approaches must be integrated to better understand the onset and progression of tau pathology across tauopathies. This will lead to improved methods for the detection and monitoring of disease progression and, hopefully, to the development and refinement of tau-based therapeutics

Summary statistics in auditory perception

Sensory signals are transduced at high resolution, but their structure must be stored in a more compact format. Here we provide evidence that the auditory system summarizes the temporal details of sounds using time-averaged statistics. We measured discrimination of 'sound textures' that were characterized by particular statistical properties, as normally result from the superposition of many acoustic features in auditory scenes. When listeners discriminated examples of different textures, performance improved with excerpt duration. In contrast, when listeners discriminated different examples of the same texture, performance declined with duration, a paradoxical result given that the information available for discrimination grows with duration. These results indicate that once these sounds are of moderate length, the brain's representation is limited to time-averaged statistics, which, for different examples of the same texture, converge to the same values with increasing duration. Such statistical representations produce good categorical discrimination, but limit the ability to discern temporal detail.Howard Hughes Medical Institut

A Corticothalamic Circuit Model for Sound Identification in Complex Scenes

The identification of the sound sources present in the environment is essential for the survival of many animals. However, these sounds are not presented in isolation, as natural scenes consist of a superposition of sounds originating from multiple sources. The identification of a source under these circumstances is a complex computational problem that is readily solved by most animals. We present a model of the thalamocortical circuit that performs level-invariant recognition of auditory objects in complex auditory scenes. The circuit identifies the objects present from a large dictionary of possible elements and operates reliably for real sound signals with multiple concurrently active sources. The key model assumption is that the activities of some cortical neurons encode the difference between the observed signal and an internal estimate. Reanalysis of awake auditory cortex recordings revealed neurons with patterns of activity corresponding to such an error signal

Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep