- Frankfurt Institute for Advanced Studies (16)
Learning more by sampling less: subsampling effects are model specific
- Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013.
When studying real world complex networks, one rarely has full access to all their components. As an example, the central nervous system of the human consists of 1011 neurons which are each connected to thousands of other neurons . Of these 100 billion neurons, at most a few hundred can be recorded in parallel. Thus observations are hampered by immense subsampling. While subsampling does not affect the observables of single neuron activity, it can heavily distort observables which characterize interactions between pairs or groups of neurons . Without a precise understanding how subsampling affects these observables, inference on neural network dynamics from subsampled neural data remains limited.
We systematically studied subsampling effects in three self-organized critical (SOC) models, since this class of models can reproduce the spatio-temporal activity of spontaneous activity observed in vivo [2,3]. The models differed in their topology and in their precise interaction rules. The first model consisted of locally connected integrate- and fire units, thereby resembling cortical activity propagation mechanisms . The second model had the same interaction rules but random connectivity . The third model had local connectivity but different activity propagation rules . As a measure of network dynamics, we characterized the spatio-temporal waves of activity, called avalanches. Avalanches are characteristic for SOC models and neural tissue . Avalanche measures A (e.g. size, duration, shape) were calculated for the fully sampled and the subsampled models. To mimic subsampling in the models, we considered the activity of a subset of units only, discarding the activity of all the other units.
Under subsampling the avalanche measures A depended on three main factors: First, A depended on the interaction rules of the model and its topology, thus each model showed its own characteristic subsampling effects on A. Second, A depended on the number of sampled sites n. With small and intermediate n, the true A¬ could not be recovered in any of the models. Third, A depended on the distance d between sampled sites. With small d, A was overestimated, while with large d, A was underestimated.
Since under subsampling, the observables depended on the model's topology and interaction mechanisms, we propose that systematic subsampling can be exploited to compare models with neural data: When changing the number and the distance between electrodes in neural tissue and sampled units in a model analogously, the observables in a correct model should behave the same as in the neural tissue. Thereby, incorrect models can easily be discarded. Thus, systematic subsampling offers a promising and unique approach to model selection, even if brain activity was far from being fully sampled.
NMR Solution Structure of a Chymotrypsin Inhibitor from the Taiwan Cobra Naja naja atra
- The Taiwan cobra (Naja naja atra) chymotrypsin inhibitor (NACI) consists of 57 amino acids and is related to other Kunitz-type inhibitors such as bovine pancreatic trypsin inhibitor (BPTI) and Bungarus fasciatus fraction IX (BF9), another chymotrypsin inhibitor. Here we present the solution structure of NACI. We determined the NMR structure of NACI with a root-mean-square deviation of 0.37 Å for the backbone atoms and 0.73 Å for the heavy atoms on the basis of 1,075 upper distance limits derived from NOE peaks measured in its NOESY spectra. To investigate the structural characteristics of NACI, we compared the three-dimensional structure of NACI with BPTI and BF9. The structure of the NACI protein comprises one 310-helix, one α-helix and one double-stranded antiparallel β-sheet, which is comparable with the secondary structures in BPTI and BF9. The RMSD value between the mean structures is 1.09 Å between NACI and BPTI and 1.27 Å between NACI and BF9. In addition to similar secondary and tertiary structure, NACI might possess similar types of protein conformational fluctuations as reported in BPTI, such as Cys14–Cys38 disulfide bond isomerization, based on line broadening of resonances from residues which are mainly confined to a region around the Cys14–Cys38 disulfide bond.
Neuronal avalanches change from wakefulness to deep sleep - a study of intracranial depth recordings in humans
Michel Le Van Quyen
- Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013.
Neuronal dynamics differs between wakefulness and sleep stages, so does the cognitive state . In contrast, a single attractor state, called self-organized critical (SOC), has been proposed to govern human brain dynamics for its optimal information coding and processing capabilities . Here we address two open questions: First, does the human brain always operate in this computationally optimal state, even during deep sleep? Second, previous evidence for SOC was based on activity within single brain areas [3-5], however, the interaction between brain areas may be organized differently. Here we asked whether the interaction between brain areas is SOC.
We addressed these questions by characterizing neuronal avalanches  - spatiotemporal waves of enhanced activity - from up to 61 local field potential (LFP) channels of intracranial depth recordings (5 human patients, two recording nights each, summing up to ~100h of recordings). The recording contacts were distributed inside the entire brain. Note that ~60 contacts are sufficient to avoid major subsampling effects: Subsampling may heavily distort results in SOC systems due to an insufficient number of sampling sites . In addition, we compared the experimental results to results from a subsampled SOC model of integrate- and fire neurons, which can be tuned to the sub- and supercritical regime.
We show that avalanche distributions closely follow a power law - the hall mark feature of SOC systems. This result held for each vigilance state, and independent of the threshold and the temporal scale. This indicates first that the interaction between brain areas are close to SOC, and second that the dynamics of all cognitive states, from wakefulness to deep sleep are close to SOC. Minor differences between cognitive states are, however, reflected in the avalanche distributions: Slow wave sleep (s3/s4) showed larger and longer neuronal avalanches than REM sleep, while wakefulness showed intermediate ones (p < 0.05). The SOC neuronal model, together with the data, suggested first that these differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate in the SOC state proper - contrary to previous believes. Independent of criticality, the analysis confirmed that slow wave sleep shows increased correlations between cortical areas, and revealed that REM sleep shows more fragmented cortical dynamics.
Distributed fading memory for stimulus properties in the primary visual cortex
- It is currently not known how distributed neuronal responses in early visual areas carry stimulus-related information. We made multielectrode recordings from cat primary visual cortex and applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons. We used sequences of up to three different visual stimuli (letters of the alphabet) presented for 100 ms and with intervals of 100 ms or larger. Most of the information about visual stimuli extractable by sophisticated methods of machine learning, i.e., support vector machines with nonlinear kernel functions, was also extractable by simple linear classification such as can be achieved by individual neurons. New stimuli did not erase information about previous stimuli. The responses to the most recent stimulus contained about equal amounts of information about both this and the preceding stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and, when using short time constants for integration (e.g., 20 ms), in the precise timing of individual spikes (<= ~20 ms), and persisted for several 100 ms beyond the offset of stimuli. The results indicate that the network from which we recorded is endowed with fading memory and is capable of performing online computations utilizing information about temporally sequential stimuli. This result challenges models assuming frame-by-frame analyses of sequential inputs.
Genome-wide multi-parametric analysis of H2AX or γH2AX distributions during ionizing radiation-induced DNA damage response
Maria Cristina Cardoso
- Background: After induction of DNA double strand breaks (DSBs), the DNA damage response (DDR) is activated. One of the earliest events in DDR is the phosphorylation of serine 139 on the histone variant H2AX (gH2AX) catalyzed by phosphatidylinositol 3-kinases-related kinases. Despite being extensively studied, H2AX distribution across the genome and gH2AX spreading around DSBs sites in the context of different chromatin compaction states or transcription are yet to be fully elucidated.
Materials and methods: gH2AX was induced in human hepatocellular carcinoma cells (HepG2) by exposure to 10 Gy X-rays (250 kV, 16 mA). Samples were incubated 0.5, 3 or 24 hours post irradiation to investigate early, intermediate and late stages of DDR, respectively. Chromatin immunoprecipitation was performed to select H2AX, H3 and gH2AX-enriched chromatin fractions. Chromatin-associated DNA was then sequenced by Illumina ChIP-Seq platform. HepG2 gene expression and histone modification (H3K36me3, H3K9me3) ChIP-Seq profiles were retrieved from Gene Expression Omnibus (accession numbers GSE30240 and GSE26386, respectively).
Results: First, we combined G/C usage, gene content, gene expression or histone modification profiles (H3K36me3, H3K9me3) to define genomic compartments characterized by different chromatin compaction states or transcriptional activity. Next, we investigated H3, H2AX and gH2AX distributions in such defined compartments before and after exposure to ionizing radiation (IR) to study DNA repair kinetics during DDR. Our sequencing results indicate that H2AX distribution followed H3 occupancy and, thus, the nucleosome pattern. The highest H2AX and H3 enrichment was observed in transcriptionally active compartments (euchromatin) while the lowest was found in low G/C and gene-poor compartments (heterochromatin). Under physiological conditions, the body of highly and moderately transcribed genes was devoid of gH2AX, despite presenting high H2AX levels. gH2AX accumulation was observed in 5’ or 3’ flanking regions, instead. The same genes showed a prompt gH2AX accumulation during the early stage of DDR which then decreased over time as DDR proceeded.
Finally, during the late stage of DDR the residual gH2AX signal was entirely retained in heterochromatic compartments. At this stage, euchromatic compartments were completely devoid of gH2AX despite presenting high levels of non-phosphorylated H2AX.
Conclusions: We show that gH2AX distribution ultimately depends on H2AX occupancy, the latter following H3 occupancy and, thus, nucleosome pattern. Both H2AX and H3 levels were higher in actively transcribed compartments. However, gH2AX levels were remarkably low over the body of actively transcribed genes suggesting that transcription levels antagonize gH2AX spreading. Moreover, repair processes did not take place uniformly across the genome; rather, DNA repair was affected by genomic location and transcriptional activity. We propose that higher H2AX density in euchromaticcompartments results in high relative gH2AXconcentration soon after the activation of DDR, thus favoring the recruitment of the DNA repair machinery to those compartments. When the damage is repaired and gH2AX is removed, its residual fraction is retained in the heterochromatic compartments which are then targeted and repaired at later times.
Emergence of the mitochondrial reticulum from fission and fusion dynamics
Valerii M. Sukhorukov
Andreas S. Reichert
- Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging.
Coordinated optimization of visual cortical maps (II) numerical studies
Justin C. Crowley
- In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations.
Network self-organization explains the statistics and dynamics of synaptic connection strengths in cortex
- The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.
Feedforward inhibition and synaptic scaling - two sides of the same coin?
- Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing.
Deceleration of fusion–fission cycles improves mitochondrial quality control during aging
Marc Thilo Figge
Andreas S. Reichert
Heinz D. Osiewacz
- Mitochondrial dynamics and mitophagy play a key role in ensuring mitochondrial quality control. Impairment thereof was proposed to be causative to neurodegenerative diseases, diabetes, and cancer. Accumulation of mitochondrial dysfunction was further linked to aging. Here we applied a probabilistic modeling approach integrating our current knowledge on mitochondrial biology allowing us to simulate mitochondrial function and quality control during aging in silico. We demonstrate that cycles of fusion and fission and mitophagy indeed are essential for ensuring a high average quality of mitochondria, even under conditions in which random molecular damage is present. Prompted by earlier observations that mitochondrial fission itself can cause a partial drop in mitochondrial membrane potential, we tested the consequences of mitochondrial dynamics being harmful on its own. Next to directly impairing mitochondrial function, pre-existing molecular damage may be propagated and enhanced across the mitochondrial population by content mixing. In this situation, such an infection-like phenomenon impairs mitochondrial quality control progressively. However, when imposing an age-dependent deceleration of cycles of fusion and fission, we observe a delay in the loss of average quality of mitochondria. This provides a rational why fusion and fission rates are reduced during aging and why loss of a mitochondrial fission factor can extend life span in fungi. We propose the ‘mitochondrial infectious damage adaptation’ (MIDA) model according to which a deceleration of fusion–fission cycles reflects a systemic adaptation increasing life span.