Quantifying and Maximizing the Information Flux in Recurrent Neural Networks

Free-running recurrent neural networks (RNNs), especially probabilistic models, generate an ongoing information flux that can be quantified with the mutual information I[x→(t),x→(t+1)] between subsequent system states x→. Although previous studies have shown that I depends on the statistics of the network's connection weights, it is unclear how to maximize I systematically and how to quantify the flux in large systems where computing the mutual information becomes intractable. Here, we address these questions using Boltzmann machines as model systems. We find that in networks with moderately strong connections, the mutual information I is approximately a monotonic transformation of the root-mean-square averaged Pearson correlations between neuron pairs, a quantity that can be efficiently computed even in large systems. Furthermore, evolutionary maximization of I[x→(t),x→(t+1)] reveals a general design principle for the weight matrices enabling the systematic construction of systems with a high spontaneous information flux. Finally, we simultaneously maximize information flux and the mean period length of cyclic attractors in the state-space of these dynamical networks. Our results are potentially useful for the construction of RNNs that serve as short-time memories or pattern generators.

Predictive coding and stochastic resonance as fundamental principles of auditory phantom perception

Mechanistic insight is achieved only when experiments are employed to test formal or computational models. Furthermore, in analogy to lesion studies, phantom perception may serve as a vehicle to understand the fundamental processing principles underlying healthy auditory perception. With a special focus on tinnitus-as the prime example of auditory phantom perception-we review recent work at the intersection of artificial intelligence, psychology and neuroscience. In particular, we discuss why everyone with tinnitus suffers from (at least hidden) hearing loss, but not everyone with hearing loss suffers from tinnitus. We argue that intrinsic neural noise is generated and amplified along the auditory pathway as a compensatory mechanism to restore normal hearing based on adaptive stochastic resonance. The neural noise increase can then be misinterpreted as auditory input and perceived as tinnitus. This mechanism can be formalized in the Bayesian brain framework, where the percept (posterior) assimilates a prior prediction (brain's expectations) and likelihood (bottom-up neural signal). A higher mean and lower variance (i.e. enhanced precision) of the likelihood shifts the posterior, evincing a misinterpretation of sensory evidence, which may be further confounded by plastic changes in the brain that underwrite prior predictions. Hence, two fundamental processing principles provide the most explanatory power for the emergence of auditory phantom perceptions: predictive coding as a top-down and adaptive stochastic resonance as a complementary bottom-up mechanism. We conclude that both principles also play a crucial role in healthy auditory perception. Finally, in the context of neuroscience-inspired artificial intelligence, both processing principles may serve to improve contemporary machine learning techniques.

Extracting continuous sleep depth from EEG data without machine learning

The human sleep-cycle has been divided into discrete sleep stages that can be recognized in electroencephalographic (EEG) and other bio-signals by trained specialists or machine learning systems. It is however unclear whether these human-defined stages can be re-discovered with unsupervised methods of data analysis, using only a minimal amount of generic pre-processing. Based on EEG data, recorded overnight from sleeping human subjects, we investigate the degree of clustering of the sleep stages using the General Discrimination Value as a quantitative measure of class separability. Virtually no clustering is found in the raw data, even after transforming the EEG signals of each 30-s epoch from the time domain into the more informative frequency domain. However, a Principal Component Analysis (PCA) of these epoch-wise frequency spectra reveals that the sleep stages separate significantly better in the low-dimensional sub-space of certain PCA components. In particular the component C₁(t) can serve as a robust, continuous 'master variable' that encodes the depth of sleep and therefore correlates strongly with the 'hypnogram', a common plot of the discrete sleep stages over time. Moreover, C₁(t) shows persistent trends during extended time periods where the sleep stage is constant, suggesting that sleep may be better understood as a continuum. These intriguing properties of C₁(t) are not only relevant for understanding brain dynamics during sleep, but might also be exploited in low-cost single-channel sleep tracking devices for private and clinical use.

Body mass index and Mini Nutritional Assessment-Short Form as predictors of in-geriatric hospital mortality in older adults with COVID-19

BACKGROUND & AIMS

Overweight and obesity have been consistently reported to carry an increased risk for poorer outcomes in coronavirus disease 2019 (COVID-19) in adults. Existing reports mainly focus on in-hospital and intensive care unit mortality in patient cohorts usually not representative of the population with the highest mortality, i.e. the very old and frail patients. Accordingly, little is known about the risk patterns related to body mass and nutrition in very old patients. Our aim was to assess the relationship between body mass index (BMI), nutritional status and in-geriatric hospital mortality among geriatric patients treated for COVID-19. As a reference, the analyses were performed also in patients treated for other diagnoses than COVID-19.

METHODS

We analyzed up to 10,031 geriatric patients with a median age of 83 years of which 1409 (14%) were hospitalized for COVID-19 and 8622 (86%) for other diagnoses in seven geriatric hospitals in the Stockholm region, Sweden during March 2020-January 2021. Data were available in electronic hospital records. The associations between 1) BMI and 2) nutritional status, assessed using the Mini-Nutritional Assessment - Short Form (MNA-SF) scale, and short-term in-geriatric hospital mortality were analyzed using logistic regression.

RESULTS

After adjusting for age, sex, comorbidity, polypharmacy, frailty and the wave of the pandemic (first vs. second), underweight defined as BMI<18.5 increased the risk of in-hospital mortality in COVID-19 patients (odds ratio [OR] = 2.30; confidence interval [CI] = 1.17-4.31). Overweight and obesity were not associated with in-hospital mortality. Malnutrition; i.e. MNA-SF 0-7 points, increased the risk of in-hospital mortality in patients treated for COVID-19 (OR = 2.03; CI = 1.16-3.68) and other causes (OR = 6.01; CI = 2.73-15.91).

CONCLUSIONS

Our results indicate that obesity is not a risk factor for very old patients with COVID-19, but emphasize the role of underweight and malnutrition for in-hospital mortality in geriatric patients with COVID-19.

Intrinsic Noise Improves Speech Recognition in a Computational Model of the Auditory Pathway

Noise is generally considered to harm information processing performance. However, in the context of stochastic resonance, noise has been shown to improve signal detection of weak sub- threshold signals, and it has been proposed that the brain might actively exploit this phenomenon. Especially within the auditory system, recent studies suggest that intrinsic noise plays a key role in signal processing and might even correspond to increased spontaneous neuronal firing rates observed in early processing stages of the auditory brain stem and cortex after hearing loss. Here we present a computational model of the auditory pathway based on a deep neural network, trained on speech recognition. We simulate different levels of hearing loss and investigate the effect of intrinsic noise. Remarkably, speech recognition after hearing loss actually improves with additional intrinsic noise. This surprising result indicates that intrinsic noise might not only play a crucial role in human auditory processing, but might even be beneficial for contemporary machine learning approaches.

Dynamics and Information Import in Recurrent Neural Networks

Recurrent neural networks (RNNs) are complex dynamical systems, capable of ongoing activity without any driving input. The long-term behavior of free-running RNNs, described by periodic, chaotic and fixed point attractors, is controlled by the statistics of the neural connection weights, such as the density d of non-zero connections, or the balance b between excitatory and inhibitory connections. However, for information processing purposes, RNNs need to receive external input signals, and it is not clear which of the dynamical regimes is optimal for this information import. We use both the average correlations C and the mutual information I between the momentary input vector and the next system state vector as quantitative measures of information import and analyze their dependence on the balance and density of the network. Remarkably, both resulting phase diagrams C(b, d) and I(b, d) are highly consistent, pointing to a link between the dynamical systems and the information-processing approach to complex systems. Information import is maximal not at the "edge of chaos," which is optimally suited for computation, but surprisingly in the low-density chaotic regime and at the border between the chaotic and fixed point regime. Moreover, we find a completely new type of resonance phenomenon, which we call "Import Resonance" (IR), where the information import shows a maximum, i.e., a peak-like dependence on the coupling strength between the RNN and its external input. IR complements previously found Recurrence Resonance (RR), where correlation and mutual information of successive system states peak for a certain amplitude of noise added to the system. Both IR and RR can be exploited to optimize information processing in artificial neural networks and might also play a crucial role in biological neural systems.

Control of noise-induced coherent oscillations in three-neuron motifs

The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris–Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (1) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (2) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.

Sleep as a random walk: a super-statistical analysis of EEG data across sleep stages

In clinical practice, human sleep is classified into stages, each associated with different levels of muscular activity and marked by characteristic patterns in the EEG signals. It is however unclear whether this subdivision into discrete stages with sharply defined boundaries is truly reflecting the dynamics of human sleep. To address this question, we consider one-channel EEG signals as heterogeneous random walks: stochastic processes controlled by hyper-parameters that are themselves time-dependent. We first demonstrate the heterogeneity of the random process by showing that each sleep stage has a characteristic distribution and temporal correlation function of the raw EEG signals. Next, we perform a super-statistical analysis by computing hyper-parameters, such as the standard deviation, kurtosis, and skewness of the raw signal distributions, within subsequent 30-second epochs. It turns out that also the hyper-parameters have characteristic, sleep-stage-dependent distributions, which can be exploited for a simple Bayesian sleep stage detection. Moreover, we find that the hyper-parameters are not piece-wise constant, as the traditional hypnograms would suggest, but show rising or falling trends within and across sleep stages, pointing to an underlying continuous rather than sub-divided process that controls human sleep. Based on the hyper-parameters, we finally perform a pairwise similarity analysis between the different sleep stages, using a quantitative measure for the separability of data clusters in multi-dimensional spaces.

To improve our understand of how EEG activity reflects the dynamics of human sleep, Metzner et al. use human EEG data and superstatistical analysis to demonstrate that each sleep stage has a characteristic distribution and temporal correlation function of raw EEG signals. They also show that the hyper-parameters controlling the EEG signals have characteristic, sleep-stage-dependent distributions, which can be exploited for a simple Bayesian sleep stage detection.

Detecting long-range interactions between migrating cells

Chemotaxis enables cells to systematically approach distant targets that emit a diffusible guiding substance. However, the visual observation of an encounter between a cell and a target does not necessarily indicate the presence of a chemotactic approach mechanism, as even a blindly migrating cell can come across a target by chance. To distinguish between the chemotactic approach and blind migration, we present an objective method that is based on the analysis of time-lapse recorded cell migration trajectories: For each movement step of a cell relative to the position of a potential target, we compute a p value that quantifies the likelihood of the movement direction under the null-hypothesis of blind migration. The resulting distribution of p values, pooled over all recorded cell trajectories, is then compared to an ensemble of reference distributions in which the positions of targets are randomized. First, we validate our method with simulated data, demonstrating that it reliably detects the presence or absence of remote cell-cell interactions. In a second step, we apply the method to data from three-dimensional collagen gels, interspersed with highly migratory natural killer (NK) cells that were derived from two different human donors. We find for one of the donors an attractive interaction between the NK cells, pointing to a cooperative behavior of these immune cells. When adding nearly stationary K562 tumor cells to the system, we find a repulsive interaction between K562 and NK cells for one of the donors. By contrast, we find attractive interactions between NK cells and an IL-15-secreting variant of K562 tumor cells. We therefore speculate that NK cells find wild-type tumor cells only by chance, but are programmed to leave a target quickly after a close encounter. We provide a freely available Python implementation of our p value method that can serve as a general tool for detecting long-range interactions in collective systems of self-driven agents.

Analysis and visualization of sleep stages based on deep neural networks

Automatic sleep stage scoring based on deep neural networks has come into focus of sleep researchers and physicians, as a reliable method able to objectively classify sleep stages would save human resources and simplify clinical routines. Due to novel open-source software libraries for machine learning, in combination with enormous recent progress in hardware development, a paradigm shift in the field of sleep research towards automatic diagnostics might be imminent. We argue that modern machine learning techniques are not just a tool to perform automatic sleep stage classification, but are also a creative approach to find hidden properties of sleep physiology. We have already developed and established algorithms to visualize and cluster EEG data, facilitating first assessments on sleep health in terms of sleep-apnea and consequently reduced daytime vigilance. In the following study, we further analyze cortical activity during sleep by determining the probabilities of momentary sleep stages, represented as hypnodensity graphs and then computing vectorial cross-correlations of different EEG channels. We can show that this measure serves to estimate the period length of sleep cycles and thus can help to find disturbances due to pathological conditions.

Quantifying the separability of data classes in neural networks

We introduce the Generalized Discrimination Value (GDV) that measures, in a non-invasive manner, how well different data classes separate in each given layer of an artificial neural network. It turns out that, at the end of the training period, the GDV in each given layer L attains a highly reproducible value, irrespective of the initialization of the network's connection weights. In the case of multi-layer perceptrons trained with error backpropagation, we find that classification of highly complex data sets requires a temporal reduction of class separability, marked by a characteristic 'energy barrier' in the initial part of the GDV(L) curve. Even more surprisingly, for a given data set, the GDV(L) is running through a fixed 'master curve', independently from the total number of network layers. Finally, due to its invariance with respect to dimensionality, the GDV may serve as a useful tool to compare the internal representational dynamics of artificial neural networks with different architectures for neural architecture search or network compression; or even with brain activity in order to decide between different candidate models of brain function.

On the efficiency of chemotactic pursuit - Comparing blind search with temporal and spatial gradient sensing

In chemotaxis, cells are modulating their migration patterns in response to concentration gradients of a guiding substance. Immune cells are believed to use such chemotactic sensing for remotely detecting and homing in on pathogens. Considering that immune cells may encounter a multitude of targets with vastly different migration properties, ranging from immobile to highly mobile, it is not clear which strategies of chemotactic pursuit are simultaneously efficient and versatile. We tackle this problem theoretically and define a tunable response function that maps temporal or spatial concentration gradients to migration behavior. The seven free parameters of this response function are optimized numerically with the objective of maximizing search efficiency against a wide spectrum of target cell properties. Finally, we reverse-engineer the best-performing parameter sets to uncover strategies of chemotactic pursuit that are efficient under different biologically realistic boundary conditions. Although strategies based on the temporal or spatial sensing of chemotactic gradients are significantly more efficient than unguided migration, such ‘blind search’ turns out to work surprisingly well, in particular if the immune cells are fast and directionally persistent. The resulting simulated data can be used for the design of chemotaxis experiments and for the development of algorithms that automatically detect and quantify goal oriented behavior in measured immune cell trajectories.

Recurrence Resonance" in Three-Neuron Motifs

Stochastic Resonance (SR) and Coherence Resonance (CR) are non-linear phenomena, in which an optimal amount of noise maximizes an objective function, such as the sensitivity for weak signals in SR, or the coherence of stochastic oscillations in CR. Here, we demonstrate a related phenomenon, which we call "Recurrence Resonance" (RR): noise can also improve the information flux in recurrent neural networks. In particular, we show for the case of three-neuron motifs with ternary connection strengths that the mutual information between successive network states can be maximized by adding a suitable amount of noise to the neuron inputs. This striking result suggests that noise in the brain may not be a problem that needs to be suppressed, but indeed a resource that is dynamically regulated in order to optimize information processing.

Open(G)PIAS: An Open-Source Solution for the Construction of a High-Precision Acoustic Startle Response Setup for Tinnitus Screening and Threshold Estimation in Rodents

The modulation of the acoustic startle reflex (ASR) by a pre-stimulus called pre-pulse inhibition (PPI, for gap of silence pre-stimulus: GPIAS) is a versatile tool to, e.g., estimate hearing thresholds or identify subjective tinnitus percepts in rodents. A proper application of these paradigms depends on a reliable measurement of the ASR amplitudes and an exact stimulus presentation in terms of frequency and intensity. Here, we introduce a novel open-source solution for the construction of a low-cost ASR setup. The complete software for data acquisition and stimulus presentation is written in Python 3.6 and is provided as an Anaconda package. Furthermore, we provide a construction plan for the sensor system based on low-cost hardware components. Exemplary GPIAS data from two animal models (Mus musculus, Meriones unguiculatus) show that the ratio histograms (1-GPIAS) of the gap-pre-stimulus and no pre-stimulus ASR amplitudes can be well described by a log-normal distribution being in good accordance to previous studies with already established setups. Furthermore, it can be shown that the PPI as a function of pre-stimulus intensity (threshold paradigm) can be approximated with a hard-sigmoid function enabling a reproducible sensory threshold estimation. Thus, we show that the open-source solution could help to further establish the ASR method in many laboratories and, thus, facilitate and standardize research in animal models of tinnitus and/or hearing loss.

Objective Estimation of Sensory Thresholds Based on Neurophysiological Parameters

Reliable determination of sensory thresholds is the holy grail of signal detection theory. However, there exists no assumption-independent gold standard for the estimation of thresholds based on neurophysiological parameters, although a reliable estimation method is crucial for both scientific investigations and clinical diagnosis. Whenever it is impossible to communicate with the subjects, as in studies with animals or neonates, thresholds have to be derived from neural recordings or by indirect behavioral tests. Whenever the threshold is estimated based on such measures, the standard approach until now is the subjective setting-either by eye or by statistical means-of the threshold to the value where at least a "clear" signal is detectable. These measures are highly subjective, strongly depend on the noise, and fluctuate due to the low signal-to-noise ratio near the threshold. Here we show a novel method to reliably estimate physiological thresholds based on neurophysiological parameters. Using surrogate data we demonstrate that fitting the responses to different stimulus intensities with a hard sigmoid function, in combination with subsampling, provides a robust threshold value as well as an accurate uncertainty estimate. This method has no systematic dependence on the noise and does not even require samples in the full dynamic range of the sensory system. We prove that this method is universally applicable to all types of sensory systems, ranging from somatosensory stimulus processing in the cortex to auditory processing in the brain stem.

Weight statistics controls dynamics in recurrent neural networks

Recurrent neural networks are complex non-linear systems, capable of ongoing activity in the absence of driving inputs. The dynamical properties of these systems, in particular their long-time attractor states, are determined on the microscopic level by the connection strengths wij between the individual neurons. However, little is known to which extent network dynamics is tunable on a more coarse-grained level by the statistical features of the weight matrix. In this work, we investigate the dynamics of recurrent networks of Boltzmann neurons. In particular we study the impact of three statistical parameters: density (the fraction of non-zero connections), balance (the ratio of excitatory to inhibitory connections), and symmetry (the fraction of neuron pairs with wij = wji). By computing a 'phase diagram' of network dynamics, we find that balance is the essential control parameter: Its gradual increase from negative to positive values drives the system from oscillatory behavior into a chaotic regime, and eventually into stationary fixed points. Only directly at the border of the chaotic regime do the neural networks display rich but regular dynamics, thus enabling actual information processing. These results suggest that the brain, too, is fine-tuned to the 'edge of chaos' by assuring a proper balance between excitatory and inhibitory neural connections.

Analysis of Structure and Dynamics in Three-Neuron Motifs

Recurrent neural networks can produce ongoing state-to-state transitions without any driving inputs, and the dynamical properties of these transitions are determined by the neuronal connection strengths. Due to non-linearity, it is not clear how strongly the system dynamics is affected by discrete local changes in the connection structure, such as the removal, addition, or sign-switching of individual connections. Moreover, there are no suitable metrics to quantify structural and dynamical differences between two given networks with arbitrarily indexed neurons. In this work, we present such permutation-invariant metrics and apply them to motifs of three binary neurons with discrete ternary connection strengths, an important class of building blocks in biological networks. Using multidimensional scaling, we then study the similarity relations between all 3,411 topologically distinct motifs with regard to structure and dynamics, revealing a strong clustering and various symmetries. As expected, the structural and dynamical distance between pairs of motifs show a significant positive correlation. Strikingly, however, the key parameter controlling motif dynamics turns out to be the ratio of excitatory to inhibitory connections.

Pressure-driven collective growth mechanism of planar cell colonies

The growth of cell colonies is determined by the migration and proliferation of the individual cells. This is often modeled with the Fisher-Kolmogorov (FK) equation, which assumes that cells diffuse independently from each other, but stop to proliferate when their density reaches a critial limit. However, when using measured, cell-line specific parameters, we find that the FK equation drastically underestimates the experimentally observed increase of colony radius with time. Moreover, cells in real colonies migrate radially outward with superdiffusive trajectories, in contrast to the assumption of random diffusion. We demonstrate that both dicrepancies can be resolved by assuming that cells in dense colonies are driven apart by repulsive, pressure-like forces. Using this model of proliferating repelling particles (PRP), we find that colony growth exhibits different dynamical regimes, depending on the ratio between a pressure-related equilibrium cell density and the critial density of proliferation arrest.

A statistical method for analyzing and comparing spatiotemporal cortical activation patterns

Information in the cortex is encoded in spatiotemporal patterns of neuronal activity, but the exact nature of that code still remains elusive. While onset responses to simple stimuli are associated with specific loci in cortical sensory maps, it is completely unclear how the information about a sustained stimulus is encoded that is perceived for minutes or even longer, when discharge rates have decayed back to spontaneous levels. Using a newly developed statistical approach (multidimensional cluster statistics (MCS)) that allows for a comparison of clusters of data points in n-dimensional space, we here demonstrate that the information about long-lasting stimuli is encoded in the ongoing spatiotemporal activity patterns in sensory cortex. We successfully apply MCS to multichannel local field potential recordings in different rodent models and sensory modalities, as well as to human MEG and EEG data, demonstrating its universal applicability. MCS thus indicates novel ways for the development of powerful read-out algorithms of spatiotemporal brain activity that may be implemented in innovative brain-computer interfaces (BCI).

Analysis of Multichannel EEG Patterns During Human Sleep: A Novel Approach

Classic visual sleep stage scoring is based on electroencephalogram (EEG) frequency band analysis of 30 s epochs and is commonly performed by highly trained medical sleep specialists using additional information from submental EMG and eye movements electrooculogram (EOG). In this study, we provide the proof-of-principle in 40 subjects that sleep stages can be consistently differentiated solely on the basis of spatial 3-channel EEG patterns based on root-mean-square (RMS) amplitudes. The polysomnographic 3-channel EEG data are pre-processed by RMS averaging over intervals of 30 s leading to spatial cortical activity patterns represented by 3-dimensional vectors. These patterns are visualized using multidimensional scaling (MDS), allowing a comparison of the spatial cortical activity patterns with the conventional visual sleep scoring system according to the American Academy of Sleep Medicine (AASM). Spatial cortical activity patterns based on RMS amplitudes naturally divide into different clusters that correspond to visually scored sleep stages. Furthermore, these clusters are reproducible between different subjects. Especially the cluster associated with the REM sleep stage seems to be very different from the one associated with the wake state. This study provides a proof-of-principle that it is possible to separate sleep stages solely by analyzing spatially distributed EEG RMS amplitudes reflecting cortical activity and without classical EEG feature extractions like power spectrum analysis.

A New Statistical Approach for the Evaluation of Gap-prepulse Inhibition of the Acoustic Startle Reflex (GPIAS) for Tinnitus Assessment

Background: An increasingly used behavioral paradigm for the objective assessment of a possible tinnitus percept in animal models has been proposed by Turner and coworkers in 2006. It is based on gap-prepulse inhibition (PPI) of the acoustic startle reflex (ASR) and usually referred to as GPIAS. As it does not require conditioning it became the method of choice to study neuroplastic phenomena associated with the development of tinnitus. Objective: It is still controversial if GPIAS is really appropriate for tinnitus screening, as the hypothesis that a tinnitus percept impairs the gap detection ability ("filling-in interpretation" is still questioned. Furthermore, a wide range of criteria for positive tinnitus detection in GPIAS have been used across different laboratories and there still is no consensus on a best practice for statistical evaluation of GPIAS results. Current approaches are often based on simple averaging of measured PPI values and comparisons on a population level without the possibility to perform valid statistics on the level of the single animal. Methods: A total number of 32 animals were measured using the standard GPIAS paradigm with varying number of measurement repetitions. Based on this data further statistical considerations were performed. Results: We here present a new statistical approach to overcome the methodological limitations of GPIAS. In a first step we show that ASR amplitudes are not normally distributed. Next we estimate the distribution of the measured PPI values by exploiting the full combinatorial power of all measured ASR amplitudes. We demonstrate that the amplitude ratios (1-PPI) are approximately lognormally distributed, allowing for parametrical testing of the logarithmized values and present a new statistical approach allowing for a valid and reliable statistical assessment of PPI changes in GPIAS. Conclusion: Based on our statistical approach we recommend using a constant criterion, which does not systematically depend on the number of measurement repetitions, in order to divide animals into a tinnitus and a non-tinnitus group. In particular, we recommend using a constant threshold based on the effect size as criterion, as the effect size, in contrast to the p-value, does not systematically depend on the number of measurement repetitions.

A Chemical Reaction Network to Generate Random, Power-Law-Distributed Time Intervals

In Lévy walks (LWs), particles move with a fixed speed along straight line segments and turn in new directions after random time intervals that are distributed according to a power law. Such LWs are thought to be an advantageous foraging and search strategy for organisms. While complex nervous systems are certainly capable of producing such behavior, it is not clear at present how single-cell organisms can generate the long-term correlated control signals required for a LW. Here, we construct a biochemical reaction system that generates long-time correlated concentration fluctuations of a signaling substance, with a tunable fractional exponent of the autocorrelation function. The network is based on well-known modules, and its basic function is highly robust with respect to the parameter settings.

Adaptive stochastic resonance for unknown and variable input signals

All sensors have a threshold, defined by the smallest signal amplitude that can be detected. The detection of sub-threshold signals, however, is possible by using the principle of stochastic resonance, where noise is added to the input signal so that it randomly exceeds the sensor threshold. The choice of an optimal noise level that maximizes the mutual information between sensor input and output, however, requires knowledge of the input signal, which is not available in most practical applications. Here we demonstrate that the autocorrelation of the sensor output alone is sufficient to find this optimal noise level. Furthermore, we demonstrate numerically and analytically the equivalence of the traditional mutual information approach and our autocorrelation approach for a range of model systems. We furthermore show how the level of added noise can be continuously adapted even to highly variable, unknown input signals via a feedback loop. Finally, we present evidence that adaptive stochastic resonance based on the autocorrelation of the sensor output may be a fundamental principle in neuronal systems.

Unbiased High-Precision Cell Mechanical Measurements with Microconstrictions

We describe a quantitative, high-precision, high-throughput method for measuring the mechanical properties of cells in suspension with a microfluidic device, and for relating cell mechanical responses to protein expression levels. Using a high-speed (750 fps) charge-coupled device camera, we measure the driving pressure Δp, maximum cell deformation εmax, and entry time tentry of cells in an array of microconstrictions. From these measurements, we estimate population averages of elastic modulus E and fluidity β (the power-law exponent of the cell deformation in response to a step change in pressure). We find that cell elasticity increases with increasing strain εmax according to E ∼ εmax, and with increasing pressure according to E ∼ Δp. Variable cell stress due to driving pressure fluctuations and variable cell strain due to cell size fluctuations therefore cause significant variability between measurements. To reduce measurement variability, we use a histogram matching method that selects and analyzes only those cells from different measurements that have experienced the same pressure and strain. With this method, we investigate the influence of measurement parameters on the resulting cell elastic modulus and fluidity. We find a small but significant softening of cells with increasing time after cell harvesting. Cells harvested from confluent cultures are softer compared to cells harvested from subconfluent cultures. Moreover, cell elastic modulus increases with decreasing concentration of the adhesion-reducing surfactant pluronic. Lastly, we simultaneously measure cell mechanics and fluorescence signals of cells that overexpress the GFP-tagged nuclear envelope protein lamin A. We find a dose-dependent increase in cell elastic modulus and decrease in cell fluidity with increasing lamin A levels. Together, our findings demonstrate that histogram matching of pressure, strain, and protein expression levels greatly reduces the variability between measurements and enables us to reproducibly detect small differences in cell mechanics.

Prediction of individual prosthesis size for valve-sparing aortic root reconstruction based on geometric features

Valve-sparing aortic root reconstruction is an up- and-coming approach for patients suffering from aortic valve insufficiencies which promises to significantly reduce complications. However, the success of the treatment strongly depends on the challenging task of choosing the correct size of the prosthesis, for which, up to now, surgeons solely have to rely on their experience. Here, we present a novel machine learning based approach, which might make it possible to predict the size of the prosthesis from pre-operatively acquired ultrasound images. We utilize support vector regression to train a prediction model on three geometric features extracted from the ultrasound data. In order to evaluate the accuracy and robustness of our approach we created a large data base of porcine aortic root geometries in a healthy state and an artificially dilated state. Our results indicate that prediction of correct prosthesis sizes is feasible. Furthermore, they suggest that it is crucial that the training data set faithfully represents the diversity of aortic root geometries.

Stochastic Resonance Controlled Upregulation of Internal Noise after Hearing Loss as a Putative Cause of Tinnitus-Related Neuronal Hyperactivity

Subjective tinnitus is generally assumed to be a consequence of hearing loss. In animal studies it has been demonstrated that acoustic trauma induced cochlear damage can lead to behavioral signs of tinnitus. In addition it was shown that noise trauma may lead to deafferentation of cochlear inner hair cells (IHC) even in the absence of elevated hearing thresholds, and it seems conceivable that such hidden hearing loss may be sufficient to cause tinnitus. Numerous studies have indicated that tinnitus is correlated with pathologically increased spontaneous firing rates and hyperactivity of neurons along the auditory pathway. It has been proposed that this hyperactivity is the consequence of a mechanism aiming to compensate for reduced input to the auditory system by increasing central neuronal gain, a mechanism referred to as homeostatic plasticity (HP), thereby maintaining mean firing rates over longer timescales for stabilization of neuronal processing. Here we propose an alternative, new interpretation of tinnitus-related development of neuronal hyperactivity in terms of information theory. In particular, we suggest that stochastic resonance (SR) plays a key role in both short- and long-term plasticity within the auditory system and that SR is the primary cause of neuronal hyperactivity and tinnitus. We argue that following hearing loss, SR serves to lift signals above the increased neuronal thresholds, thereby partly compensating for the hearing loss. In our model, the increased amount of internal noise-which is crucial for SR to work-corresponds to neuronal hyperactivity which subsequently causes neuronal plasticity along the auditory pathway and finally may lead to the development of a phantom percept, i.e., subjective tinnitus. We demonstrate the plausibility of our hypothesis using a computational model and provide exemplary findings in human patients that are consistent with that model. Finally we discuss the observed asymmetry in human tinnitus pitch distribution as a consequence of asymmetry of the distribution of auditory nerve type I fibers along the cochlea in the context of our model.

Migration in Confined 3D Environments Is Determined by a Combination of Adhesiveness, Nuclear Volume, Contractility, and Cell Stiffness

In cancer metastasis and other physiological processes, cells migrate through the three-dimensional (3D) extracellular matrix of connective tissue and must overcome the steric hindrance posed by pores that are smaller than the cells. It is currently assumed that low cell stiffness promotes cell migration through confined spaces, but other factors such as adhesion and traction forces may be equally important. To study 3D migration under confinement in a stiff (1.77 MPa) environment, we use soft lithography to fabricate polydimethylsiloxane (PDMS) devices consisting of linear channel segments with 20 μm length, 3.7 μm height, and a decreasing width from 11.2 to 1.7 μm. To study 3D migration in a soft (550 Pa) environment, we use self-assembled collagen networks with an average pore size of 3 μm. We then measure the ability of four different cancer cell lines to migrate through these 3D matrices, and correlate the results with cell physical properties including contractility, adhesiveness, cell stiffness, and nuclear volume. Furthermore, we alter cell adhesion by coating the channel walls with different amounts of adhesion proteins, and we increase cell stiffness by overexpression of the nuclear envelope protein lamin A. Although all cell lines are able to migrate through the smallest 1.7 μm channels, we find significant differences in the migration velocity. Cell migration is impeded in cell lines with larger nuclei, lower adhesiveness, and to a lesser degree also in cells with lower contractility and higher stiffness. Our data show that the ability to overcome the steric hindrance of the matrix cannot be attributed to a single cell property but instead arises from a combination of adhesiveness, nuclear volume, contractility, and cell stiffness.

Emergence of Asynchronous Local Clocks in Excitable Media

Excitable media such as the myocardium or the brain consist of arrays of coupled excitable elements, in which the local excitation of a single element can propagate to its neighbors in the form of a non-linear autowave. Since each element has to pass through a refractory period immediately after excitation, the frequency of autowaves is self-limiting. In this work, we consider the case where each element is spontaneously excited at a fixed average rate and thereby initiates a new autowave. Although these spontaneous self-excitation events are modelled as independent Poisson point processes with exponentially distributed waiting times, the travelling autowaves lead collectively to a non-exponential, unimodal waiting time distribution for the individual elements. With increasing system size, a global 'clock' period T emerges as the most probable waiting time for each element, which fluctuates around T with an increasingly small but non-zero variance. This apparent synchronization between asynchronous, temporally uncorrelated point processes differs from synchronization effects between perfect oscillators interacting in a phase-aligning manner. Finally, we demonstrate that asynchronous local clocks also emerge in non-homogeneous systems in which the rates of self-excitation are different for all individuals, suggesting that this novel mechanism can occur in a wide range of excitable media.

A machine learning approach for planning valve-sparing aortic root reconstruction

Choosing the optimal prosthesis size and shape is a difficult task during surgical valve-sparing aortic root reconstruction. Hence, there is a need for surgery planning tools. Common surgery planning approaches try to model the mechanical behaviour of the aortic valve and its leaflets. However, these approaches suffer from inaccuracies due to unknown biomechanical properties and from a high computational complexity. In this paper, we present a new approach based on machine learning that avoids these problems. The valve geometry is described by geometrical features obtained from ultrasound images. We interpret the surgery planning as a learning problem, in which the features of the healthy valve are predicted from these of the dilated valve using support vector regression (SVR). Our first results indicate that a machine learning based surgery planning can be possible.

Superstatistical analysis and modelling of heterogeneous random walks

Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

Conventional methods to quantify the migratory behaviour of cells assume that underlying parameters are constant. Mark et al. apply a superstatistical approach to extract time-dependent parameters of motile cells, and demonstrate an enhanced ability to distinguish between different migration strategies.

Estimating the 3D pore size distribution of biopolymer networks from directionally biased data

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter--the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.

Parameter-free binarization and skeletonization of fiber networks from confocal image stacks

We present a method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. The method is based on a template matching algorithm that simultaneously performs a binarization and skeletonization of the network. The size and intensity pattern of the template is automatically adapted to the input data so that the method is scale invariant and generic. Furthermore, the template matching threshold is iteratively optimized to ensure that the final skeletonized network obeys a universal property of voxelized random line networks, namely, solid-phase voxels have most likely three solid-phase neighbors in a 3 x 3 x 3 neighborhood. This optimization criterion makes our method free of user-defined parameters and the output exceptionally robust against imaging noise.

Fluctuations of cytoskeleton-bound microbeads--the effect of bead-receptor binding dynamics

The cytoskeleton (CSK) of living cells is a crosslinked fiber network, subject to ongoing biochemical remodeling processes that can be visualized by tracking the spontaneous motion of CSK-bound microbeads. The bead motion is characterized by anomalous diffusion with a power-law time evolution of the mean square displacement (MSD), and can be described as a stochastic transport process with apparent diffusivity D and power-law exponent β: MSD ∼ D (t/t(0))(β). Here we studied whether D and β change with the time that has passed after the initial bead-cell contact, and whether they are sensitive to bead coating (fibronectin, integrin antibodies, poly-L-lysine, albumin) and bead size (0.5-4.5 µm). The measurements are interpreted in the framework of a simple model that describes the bead as an overdamped particle coupled to the fluctuating CSK network by an elastic spring. The viscous damping coefficient characterizes the degree of bead internalization into the cell, and the spring constant characterizes the strength of the binding of the bead to the CSK. The model predicts distinctive signatures of the MSD that change with time as the bead couples more tightly to the CSK and becomes internalized. Experimental data show that the transition from the unbound to the tightly bound state occurs in an all-or-nothing manner. The time point of this transition shows considerable variability between individual cells (2-30 min) and depends on the bead size and bead coating. On average, this transition occurs later for smaller beads and beads coated with ligands that trigger the formation of adhesion complexes (fibronectin, integrin antibodies). Once the bead is linked to the CSK, however, the ligand type and bead size have little effect on the MSD. On longer timescales of several hours after bead addition, smaller beads are internalized into the cell more readily, leading to characteristic changes in the MSD that are consistent with increased viscous damping by the cytoplasm and reduced binding strength.

Noise and critical phenomena in biochemical signaling cycles at small molecule numbers

Biochemical reaction networks in living cells usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells, mass-action theory fails to describe the dynamics of such systems. Instead, the biochemical reactions must be treated as stochastic processes that intrinsically generate concentration fluctuations of the chemicals. We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modeling and numerically exact Monte Carlo simulation of the temporally fluctuating concentration. Depending on the parameter regime, we find for the probability density of the concentration qualitatively distinct classes of distribution functions including power-law distributions with a fractional and tunable exponent. These findings challenge the traditional view of biochemical control networks as deterministic computational systems and suggest that CMCs in cells can function as versatile and tunable noise generators.

Simple model of cytoskeletal fluctuations

The spontaneous motion of microbeads bound to the cytoskeleton of living cells is not an ordinary random walk. Unlike Brownian motion, the mean-square displacement undergoes a transition from subdiffusive to superdiffusive behavior with time. This transition is associated with characteristic changes of the turning angle distribution. Recent experimental data demonstrated that force fluctuations measured in an elastic hydrogel matrix beneath the cell correlate with the bead motion [C. Raupach, Phys. Rev. E 76, 011918 (2007)]. These data indicate that the bead trajectory is driven by motor forces originating from the actomyosin network and that cytoskeletal remodeling processes with short- and long-time dynamics are mainly responsible for the non-Brownian behavior. We show that the essential statistical properties of the spontaneous bead motion can be reproduced by a particle diffusing in a potential well with a slowly drifting minimum position. Based on this simple model, which can be solved analytically, we develop a biologically plausible numerical model of a tensed and continuously remodeling actomyosin network that accounts quantitatively for the measured data.

Stress fluctuations and motion of cytoskeletal-bound markers

Cytoskeletal (CSK) dynamics such as remodeling and reorganization can be studied by tracking the spontaneous motion of CSK-bound particles. Particle motion is thought to be driven by local, ATP-dependent intracellular force fluctuations due to polymerization processes and motor proteins, and to be impeded by a viscoelastic, metastable cytoskeletal network. The mechanisms that link particle motion to force fluctuations and the CSK dynamics remain unclear. We report simultaneous measurements of the spontaneous motion of CSK-bound particles and of cellular force fluctuations. Cellular force fluctuations were measured by tracking fluorescent markers embedded in an elastic polyacrylamide hydrogel substrate that served as an extracellular matrix (ECM). The motion of CSK-bound particles and markers embedded in the ECM showed both persistence and superdiffusive behavior. Moreover, the movements of CSK-bound beads were temporally and spatially correlated with force fluctuations in the ECM. The findings suggest that the spontaneous motion of CSK-bound beads is driven not by random, local stress fluctuations within a viscoelastic continuum or cage, but rather by stress fluctuations within a tensed and constantly remodeling CSK network that transmits stresses over considerable distances to the ECM.

[Bone metastasis of prostatic cancer imitating Paget's sarcoma]

HISTORY AND CLINICAL FINDINGS

A 74-year-old man presented with bone pain of the right hip, night sweat and weight loss for 18 months. The diagnosis of Paget's disease was confirmed four months before admission, but pain and elevated serum alkaline phosphatase levels remained despite treatment with i.v. bisphosphonates. The physical examination showed no specific abnormalities.

INVESTIGATIONS

Laboratory findings were elevated levels of serum alkaline phosphatase (AP), CA 19-9 and CEA. Radiological and tomographic images showed an aggressive periostal reaction consistent with Paget's sarcoma. The bone biopsy revealed the presence of prostatic cancer which was confirmed in a subsequent prostate biopsy.

TREATMENT AND COURSE

Because of the multiple bone and lung metastases the disease proved to be incurable and the patient received palliative therapy with flutamide. He died 12 months later.

CONCLUSION

In patients with Paget's disease lacking of response to bisphosphonate administration (permanently increased AP and sustained pain) radiological and clinical re-assessment of the diagnosis is indicated and may sometimes also include bone biopsy.

Resonant impurity bands in semiconductor superlattices

It is shown that the confined impurity state of a semiconductor quantum well develops into an excited impurity band in the case of a superlattice. This is studied by following theoretically the transition from a single to a multiple quantum well or superlattice by exactly diagonalizing the three-dimensional Hamiltonian for a quantum well system with random impurities. Intersubband absorption experiments, which can be nearly perfectly reproduced by the theory, corroborate this interpretation, which also requires reinterpretation of previous data.