Nonlinear signalling networks and cell-to-cell variability transform external signals into broadly distributed or bimodal responses

We show theoretically and experimentally a mechanismbehind the emergence of wide or bimodal protein distributions in biochemical networks with nonlinear input-output characteristics (the dose-response curve) and variability in protein abundance. Large cell-to-cell variation in the nonlinear dose-response characteristics can be beneficial to facilitate two distinct groups of response levels as opposed to a graded response. Under the circumstances that we quantify mathematically, the two distinct responses can coexist within a cellular population, leading to the emergence of a bimodal protein distribution. Using flow cytometry, we demonstrate the appearance of wide distributions in the hypoxia-inducible factor-mediated response network in HCT116 cells. With help of our theoretical framework, we perform a novel calculation of the magnitude of cell-to-cell heterogeneity in the dose-response obtained experimentally. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Pathological changes in the primary visual cortex (Area V1) in Creutzfeldt-Jakob syndrome

About 10% of patients with Creutzfeldt-Jakob syndrome (disease) (CJD) exhibit visual symptoms at presentation and approximately 50% during the course of the disease. The objectives of the present study were to determine, in two subtypes of CJD, viz., sporadic CJD (sCJD) and variant CJD (vCJD), the degree of pathological change in the primary visual cortex (area V1) and the extent to which pathology in V1 may influence visual function. The vacuolation (‘spongiform change’), surviving neurons, glial cell nuclei, and deposits of prion protein (PrP) were quantified in V1 obtained post-mortem in nine cases of sCJD and eleven cases of vCJD. In sCJD, the vacuoles and PrP deposits were regularly distributed along the cortex parallel to the pia mater in clusters with a mean dimension from 450 to 1000 µm. Across the cortex, the vacuolation was most severe in laminae II/III and the glial cell reaction in laminae V/VI. Surviving neurons were most abundant in laminae II/III while PrP deposition either affected all laminae equally or was maximal in lamina II/III. In vCJD, the vacuoles and diffuse PrP deposits were distributed relatively uniformly parallel to the pia mater while the florid deposits were consistently distributed in regular clusters. Across V1, the vacuoles either exhibited a bimodal distribution or were uniformly distributed. The diffuse PrP deposits occurred most frequently in laminae II/III while the florid deposits were more generally distributed. The data suggest that in both sCJD and vCJD, pathological changes in area V1 may affect the processing of visual information in laminae II/III and its transmission from V1 to V2 and to subcortical visual areas. In addition, the data suggest an association in sCJD between the developing pathology and the functional domains of V1 while in vCJD the pathology is more uniformly distributed. These changes could be a factor in the development of poor visual acuity, visual field defects, cortical blindness, diplopia, and vertical gaze palsy that have been observed in Creutzfeldt-Jakob syndrome.

Laminar distribution of neurofilament inclusions and swollen achromatic neurons in neurofilament inclusion disease (NID)

The laminar distribution of the neurofilament inclusions (NI) and swollen achromatic neurons (SN) was studied in gyri of the temporal cortex in four patients with neurofilament inclusion disease (NID). In 84% of gyri analysed, the density of the NI was maximal in the lower cortical laminae. The distribution of the SN was more variable than the NI. Density was maximal in the lower cortex in 46% of gyri, in the upper cortical laminae in 8% of gyri, and a bimodal distribution in 15% of gyri. In the remaining gyri, there was a more even distribution of SN with cortical depth. In 31% of gyri, the vertical density of the NI was positively correlated with that of the SN. The data suggest that cortical degeneration in the temporal lobe of NID initially affects neurons in the lower laminae. Subsequently, the pathology may spread to affect much of the cortical profile, the SN preceding the appearance of the NI.

Structured neural network modelling of multi-valued functions for wind retrieval from scatterometer measurements

A conventional neural network approach to regression problems approximates the conditional mean of the output vector. For mappings which are multi-valued this approach breaks down, since the average of two solutions is not necessarily a valid solution. In this article mixture density networks, a principled method to model conditional probability density functions, are applied to retrieving Cartesian wind vector components from satellite scatterometer data. A hybrid mixture density network is implemented to incorporate prior knowledge of the predominantly bimodal function branches. An advantage of a fully probabilistic model is that more sophisticated and principled methods can be used to resolve ambiguities.

First year qualifying report: neural networks for extracting wind vectors from satellite scatterometer data

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about km800, carrying a C-band scatterometer. A scatterometer measures the amount of radar back scatter generated by small ripples on the ocean surface induced by instantaneous local winds. Operational methods that extract wind vectors from satellite scatterometer data are based on the local inversion of a forward model, mapping scatterometer observations to wind vectors, by the minimisation of a cost function in the scatterometer measurement space.par This report uses mixture density networks, a principled method for modelling conditional probability density functions, to model the joint probability distribution of the wind vectors given the satellite scatterometer measurements in a single cell (the `inverse' problem). The complexity of the mapping and the structure of the conditional probability density function are investigated by varying the number of units in the hidden layer of the multi-layer perceptron and the number of kernels in the Gaussian mixture model of the mixture density network respectively. The optimal model for networks trained per trace has twenty hidden units and four kernels. Further investigation shows that models trained with incidence angle as an input have results comparable to those models trained by trace. A hybrid mixture density network that incorporates geophysical knowledge of the problem confirms other results that the conditional probability distribution is dominantly bimodal.par The wind retrieval results improve on previous work at Aston, but do not match other neural network techniques that use spatial information in the inputs, which is to be expected given the ambiguity of the inverse problem. Current work uses the local inverse model for autonomous ambiguity removal in a principled Bayesian framework. Future directions in which these models may be improved are given.

Structured neural network modelling of multi-valued functions for wind retrieval from scatterometer measurements

A conventional neural network approach to regression problems approximates the conditional mean of the output vector. For mappings which are multi-valued this approach breaks down, since the average of two solutions is not necessarily a valid solution. In this article mixture density networks, a principled method to model conditional probability density functions, are applied to retrieving Cartesian wind vector components from satellite scatterometer data. A hybrid mixture density network is implemented to incorporate prior knowledge of the predominantly bimodal function branches. An advantage of a fully probabilistic model is that more sophisticated and principled methods can be used to resolve ambiguities.

Laminar distribution of the pathological changes in frontal and temporal cortex in 8 patients with progressive supranuclear palsy

OBJECTIVE: To determine the laminar distribution of the pathological changes in the cerebral cortex in progressive supranuclear palsy (PSP). METHOD: The distribution of the abnormally enlarged neurons (EN), surviving neurons, neurofibrillary tangles (NFT), glial inclusions (GI), tufted astrocytes (TA), and neuritic plaques (NP) were studied across the cortex in tau immunolabeled sections of frontal and temporal cortex in 8 cases of PSP. RESULTS: The distribution of the NFT was highly variable with no consistent pattern of laminar distribution. The GI were distributed either in the lower laminae or uniformly across the cortex. Surviving neurons exhibited either a density peak in the upper laminae or a bimodal distribution was present with density peaks in the upper and lower laminae. The EN and glial cell nuclei were distributed primarily in the lower cortical laminae. There were positive correlations between the densities of the EN and glial cell nuclei and negative correlations between the surviving neurons and glial cells. No correlations were present between the densities of the NFT and GI. CONCLUSION: Cortical pathology in PSP predominantly affects the lower laminae but may spread to affect the upper laminae in some cases. The NFT and GI may have different laminar distributions and gliosis occurs concurrently with neuronal enlargement.

Laminar distribution of β-amyloid deposits in dementia with Lewy bodies and in Alzheimer's disease

This study tested whether the laminar distribution of the β-amyloid (Aβ) deposits in dementia with Lewy bodies (DLB) cases with significant Alzheimer's disease (AD) pathology (DLB/AD) was similar to "pure" AD. In DLB/AD, the maximum density of the diffuse and primitive deposits occurred either in the upper laminae or a bimodal distribution was present with density peaks in the upper and lower laminae. A bimodal distribution of the classic Aβ deposits was also observed. Compared with AD, DLB/AD cases had fewer primitive deposits relative to the diffuse and classic deposits; the primitive deposits exhibited a bimodal distribution more frequently, and the diffuse deposits occurred more often in the upper laminae. These results suggest that Aβ pathology in DLB/AD may not simply represent the presence of associated AD. © 2006 Sage Publications.

Multiple system atrophy: laminar distribution of the pathological changes in frontal and temporal neocortex--a study in ten patients

OBJECTIVE: To determine the distribution of the pathological changes in the neocortex in multiple-system atrophy (MSA). METHOD: The vertical distribution of the abnormal neurons (neurons with enlarged or atrophic perikarya), surviving neurons, glial cytoplasmic inclusions (GCI) and neuronal cytoplasmic inclusions (NI) were studied in alpha-synuclein-stained material of frontal and temporal cortex in ten cases of MSA. RESULTS: Abnormal neurons exhibited two common patterns of distribution, viz., density was either maximal in the upper cortex or a bimodal distribution was present with a density peak in the upper and lower cortex. The NI were either located in the lower cortex or were more uniformly distributed down the cortical profile. The distribution of the GCI varied considerably between gyri and cases. The density of the glial cell nuclei was maximal in the lower cortex in the majority of gyri. In a number of gyri, there was a positive correlation between the vertical densities of the abnormal neurons, the total number of surviving neurons, and the glial cell nuclei. The vertical densities of the GCI were not correlated with those of the surviving neurons or glial cells but the GCI and NI were positively correlated in a small number of gyri. CONCLUSION: The data suggest that there is significant degeneration of the frontal and temporal lobes in MSA, the lower laminae being affected more significantly than the upper laminae. Cortical degeneration in MSA is likely to be secondary to pathological changes occurring within subcortical areas.

Quantification of the pathological changes with laminar depth in the cortex in sporadic Creutzfeldt-Jakob disease

The laminar distribution of the vacuolation ('spongiform change'), surviving neurons, glial cell nuclei, and prion protein (PrP) deposits was studied in the frontal, parietal and temporal cortex in 11 cases of sporadic Creutzfeldt-Jakob disease (CJD). The distribution of the vacuolation was mainly bimodal with peaks of density in the upper and lower cortical laminae. The density of surviving neurons was greatest in the upper cortex while glial cell nuclei were distributed largely in the lower cortex. PrP deposits exhibited either a bimodal distribution or reached a maximum density in the lower cortex. The vertical density of the vacuoles was positively correlated with the surviving neurons in 12/44 of cortical areas studied, with glial cell nuclei in 16/44 areas and with PrP deposition in 15/28 areas. PrP deposits were positively correlated with glial cell nuclei in 12/31 areas. These results suggest that in sporadic CJD: (1) the lower cortical laminae are the most affected by the pathological changes; (2) the development of the vacuolation may precede that of the extracellular PrP deposits and the glial cell reaction; and (3) the pathological changes may develop initially in the lower cortical laminae and spread to affect the upper cortical laminae. © 2001 Elsevier Science Ireland Ltd. All rights reserved.

Laminar degeneration of the frontal and temporal cortex in neuronal intermediate filament inclusion disease (NIFID): a study using a-internexin immunohistochemistry

Objective: To determine the laminar distribution of the pathological changes in the frontal and temporal lobe in neuronal intermediate filament inclusion disease (NIFID). Method: The distribution of the alpha-intenexin-positive neuronal cytoplasmic inclusions (NCI), surviving neurons, swollen achromatic neurons (SN) and glial cell nuclei was studied across the cortex in gyri of the frontal and temporal lobe in 10 cases of NIFID. Results: The distribution of the NCI was highly variable within different gyri, a peak in the upper cortex, a bimodal distribution with peaks of density in the upper and lower laminae, or no significant variation in density across the cortex. The surviving neurons were either bimodally distributed or exhibited no significant change in density across the cortex. The SN and glial cell nuclei were most abundant in the lower cortical laminae. In half of the gyri, variations in density of the NCI across the cortex were positively correlated with the SN. In some gyri, the surviving neurons were positively correlated with the SN and negatively correlated with the glial cell nuclei. In addition, the SN and glial cell nuclei were positively correlated in over half the gyri studied. Conclusion: The data suggest that frontal and temporal lobe degeneration in NIFID characterized by NCI, SN, neuronal loss and gliosis extends across the cortical laminae with considerable variation between cases and gyri. alpha-internexin-positive neurons in the upper laminae appear to be particularly vulnerable. The gliosis appears to be largely correlated with the appearance of SN and with neuronal loss and not related to the NCI.

Laminar distribution of the pathological changes in the cerebral cortex in variant Creutzfeldt-Jakob disease (vCJD)

To determine the pattern of cortical degeneration in cases of variant Creutzfeldt-Jakob disease (vCJD), the laminar distribution of the vacuolation ("spongiform change"), surviving neurones, glial cell nuclei, and prion protein (PrP) deposits was studied in the frontal, parietal and temporal lobes. The vacuolation exhibited two common patterns of distribution: either the vacuoles were present throughout the cortex or a bimodal distribution was present with peaks of density in the upper and lower cortical laminae. The distribution of the surviving neurones was highly variable in different regions; the commonest pattern being a uniform distribution with cortical depth. Glial cell nuclei were distributed largely in the lower cortical laminae. The non-florid PrP deposits exhibited either a bimodal distribution or exhibited a peak of density in the upper cortex while the florid deposits were either uniformly distributed down the cortex or were present in the upper cortical laminae. In a significant proportion of areas, the density of the vacuoles was positively correlated with either the surviving neurones or with the glial cell nuclei. These results suggest similarities and differences in the laminar distributions of the pathogenic changes in vCJD compared with cases of sporadic CJD (sCJD). The laminar distribution of vacuoles was more extensive in vCJD than in sCJD whereas the distribution of the glial cell nuclei was similar in the two disorders. In addition, PrP deposits in sCJD were localised mainly in the lower cortical laminae while in vCJD, PrP deposits were either present in all laminae or restricted to the upper cortical laminae. These patterns of laminar distribution suggest that the process of cortical degeneration may be distinctly different in vCJD compared with sCJD.

Laminar distribution of Pick bodies, Pick cells and Alzheimer disease pathology in the frontal and temporal cortex in Pick's disease

Lesions in Alzheimer's disease (AD) and dementia with Lewy bodies (DLB) have distinct laminar distributions in the cortex. The objective of the present study was to test the hypothesis that the lesions characteristic of Pick's disease (PD) and AD have distinctly different laminar distributions in cases of PD. Hence, the laminar distribution of Pick bodies (PB), Pick cells (PC), senile plaques (SP) and neurofibrillary tangles (NFT) was studied in the frontal and temporal cortex in nine patients with PD. In 57% of analyses of individual cortical areas, the density of PB was maximal in the upper cortex while in 25% of analyses, the distribution of PB was bimodal with density peaks in the upper and lower cortex. The density of PC was maximal in the lower cortex in 77% of analyses while a bimodal distribution was present in 5% of analyses. The density of NFT was maximal in the upper cortex in 50% of analyses, in the lower cortex in 15% of analyses, with a bimodal distribution in 4% of analyses. The density of SP did not vary significantly with cortical depth in 86% of analyses. The vertical densities of PB and PC were negatively correlated in 12/21 (57%) of brain areas. The maximum density of PB in the upper cortex was positively correlated with the maximum density of PC in the lower cortex. In 17/25 (68%) of brain areas, there was no significant correlation between the vertical densities of PB and NFT. The data suggest that the pathogenesis of PB may be related to that of the PC. In addition, although in many areas PB and NFT occur predominantly in the upper cortex, the two lesions appeared to affect different neuronal populations.

Laminar distribution of amyloid-beta (Abeta) deposits in dementia with Lewy bodies: comparison with Alzheimer's disease

Significant amyloid-beta (Abeta) deposition in cases of dementia with Lewy bodies (DLB) may represent concurrent Alzheimer's disease (AD). To test this hypothesis, the laminar distribution of the diffuse, primitive, and classic Abeta deposits was studied in the frontal and temporal cortex in cases of DLB and were compared with AD. In DLB, the diffuse and primitive deposits exhibited two common patterns of distribution; either maximum density occurred in the upper cortical laminae or a bimodal distribution was present with density peaks in the upper and lower laminae. In addition, a bimodal distribution of the classic deposits was observed in approximately half of the cortical areas analysed. A number of differences in the laminar distributions of Abeta deposits were observed in DLB and AD. First, the proportion of the primitive relative to the diffuse and classic deposits present was lower in DLB compared with AD. Second, the primitive deposits were more frequently bimodally distributed in DLB. Third, the density of the diffuse deposits reached a maximum lower in the cortical profile in AD. These data suggest differences in the pattern of cortical degeneration in the two disorders and therefore, DLB cases with significant Abeta pathology may not represent the coexistence of DLB and AD.

Laminar distribution of cortical Lewy bodies and neurofibrillary tangles in dementia with Lewy bodies

The laminar distribution of Lewy bodies (LB) and neurofibrillary tangles (NFT) was studied in twelve cases of dementia with Lewy bodies (DLB). LB density was maximal in the lower cortex in 59% of cortical areas, in the upper cortex in 31% of areas while densities were similar in the upper and lower cortex in 9% of areas. The distribution of LB was either unimodal with a lower cortical peak, or bimodal with density peaks in the upper and lower cortex. The density of NFT was maximal in the upper cortex in all tissues. The distributions of LB and NFT were similar in temporal and frontal cortex and in cases with and without Alzheimer’s disease (AD). The vertical densities of LB and NFT were not significantly correlated. LB formation may affect the feedback cortico-cortical pathway and the efferent cortical projections whereas NFT formation may affect the feedforward cortico-cortical pathway.