arXiv subjects

Claus Metzner

Publications and source records attributed to Claus Metzner.

35 records · Page 2Linked to original sources

arXiv2021

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. 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.

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arXiv2019

Inferring long-range interactions between immune and tumor cells -- pitfalls and (partial) solutions

Upcoming immunotherapies for cancer treatment rely on the ability of the immune system to detect and eliminate tumors in the body. A highly simplified version of this process can be studied in a Petri dish: starting with a random distribution of immune and tumor cells, it can be observed in detail how individual immune cells migrate towards nearby tumor cells, establish contact, and attack. Nevertheless, it remains unclear whether the immune cells find their targets by chance, or if they approach them 'on purpose', using remote sensing mechanisms such as chemotaxis. In this work, we present methods to infer the strength and range of long-range cell-cell interactions from time-lapse recorded cell trajectories, using a maximum likelihood method to fit the model parameters. First, we model the interactions as a distance-dependent 'force' that attracts immune cells towards their nearest tumor cell. While this approach correctly recovers the interaction parameters of simulated cells with constant migration properties, it detects spurious interactions in the case of independent cells that spontaneously change their migration behavior over time. We therefore use an alternative approach that models the interactions by distance-dependent probabilities for positive and negative turning angles of the migrating immune cell. We demonstrate that the latter approach finds the correct interaction parameters even with temporally switching cell migration.

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arXiv2019

How deep is deep enough? -- Quantifying class separability in the hidden layers of deep neural networks

Deep neural networks typically outperform more traditional machine learning models in their ability to classify complex data, and yet is not clear how the individual hidden layers of a deep network contribute to the overall classification performance. We thus introduce a Generalized Discrimination Value (GDV) that measures, in a non-invasive manner, how well different data classes separate in each given network layer. The GDV can be used for the automatic tuning of hyper-parameters, such as the width profile and the total depth of a network. Moreover, the layer-dependent GDV(L) provides new insights into the data transformations that self-organize during training: In the case of multi-layer perceptrons trained with error backpropagation, we find that classification of highly complex data sets requires a temporal {\em 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. Furthermore, applying the GDV to Deep Belief Networks reveals that also unsupervised training with the Contrastive Divergence method can systematically increase class separability over tens of layers, even though the system does not 'know' the desired class labels. These results indicate that the GDV may become a useful tool to open the black box of deep learning.

cs.LG↗

arXiv2019

Detecting long-range attraction between migrating cells based on p-value distributions

Immune cells have evolved to recognize and eliminate pathogens, and the efficiency of this process can be measured in a Petri dish. Yet, even if the cells are time-lapse recorded and tracked with high resolution, it is difficult to judge whether the immune cells find their targets by mere chance, or if they approach them in a goal-directed way, perhaps using remote sensing mechanisms such as chemotaxis. To answer this question, we assign to each step of an immune cell a 'p-value', the probability that a move, at least as target-directed as observed, can be explained with target-independent migration behavior. The resulting distribution of p-values is compared to the distribution of a reference system with randomized target positions. By using simulated data, based on various chemotactic search mechanisms, we demonstrate that our method can reliably distinguish between blind migration and target-directed 'hunting' behavior.

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arXiv2019

Principles of efficient chemotactic pursuit

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 an 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 takle 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 the principles of efficient chemotactic pursuit under different biologically realistic boundary conditions. Remarkably, the numerical optimization rediscovers chemotactic strategies that are well-known in biological systems, such as the gradient-dependent swimming and tumbling modes of E.coli. Some of our results may also be useful 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.

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arXiv2018

Stochastic resonance in three-neuron motifs

Stochastic resonance is a non-linear phenomenon, in which the sensitivity of signal detectors can be enhanced by adding random noise to the detector input. Here, we demonstrate that noise can also improve the information flux in recurrent neural networks. In particular, we show for the case of three-neuron motifs 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.

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arXiv2018

Analysis of structure and dynamics in three-neuron motifs

In neural networks with identical neurons, the matrix of connection weights completely describes the network structure and thereby determines how it is processing information. However, due to the non-linearity of these systems, it is not clear if similar microscopic connection structures also imply similar functional properties, or if a network is impacted more by macroscopic structural quantities, such as the ratio of excitatory and inhibitory connections (balance), or the ratio of non-zero connections (density). To clarify these questions, we focus on motifs of three binary neurons with discrete ternary connection strengths, an important class of network building blocks that can be analyzed exhaustively. We develop new, permutation-invariant metrics to quantify the structural and functional distance between two given network motifs. We then use multidimensional scaling to identify and visualize clusters of motifs with similar structural and functional properties. Our comprehensive analysis reveals that the function of a neural network is only weakly correlated with its microscopic structure, but depends strongly on the balance of the connections.

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arXiv2018

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 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 neonatales, thresholds have to be derived from neural recordings. In such cases when the threshold is estimated based on neuronal measures, the standard approach is still the subjective setting of the threshold to the value where at least a "clear" neuronal 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. It is universally applicable to all types of sensory systems, ranging from somatosensory stimulus processing in the cortex to auditory processing in the brain stem.

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arXiv2018

Open(G)PIAS: An open source solution for the construction of a high-precision Acoustic-Startle-Response (ASR) setup for tinnitus screening and threshold estimation in rodents

The acoustic startle reflex (ASR) that can be induced by a loud sound stimulus can be used as a versatile tool to, e.g., estimate hearing thresholds or identify subjective tinnitus percepts in rodents. These techniques are based on the fact that the ASR amplitude can be suppressed by a pre-stimulus of lower, non-startling intensity, an effect named pre-pulse inhibition (PPI). For hearing threshold estimation, pure tone pre-stimuli of varying amplitudes are presented before an intense noise burst serving as startle stimulus. The amount of suppression of the ASR amplitude as a function of the pre-stimulus intensity can be used as a behavioral correlate to determine the hearing ability. For tinnitus assessment, the pure-tone pre-stimulus is replaced by a gap of silence in a narrowband noise background, a paradigm termed GPIAS (gap-pre-pulse inhibition of the acoustic startle response). A proper application of these paradigms depend on a reliable measurement of the ASR amplitudes, 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 for the above mentioned purpose. 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 sensory system based on low-cost hardware components. Exemplary data show that the ratios (1-PPI) of the pre and post trauma ASR amplitudes can be well described by a lognormal distribution being in good accordance to previous studies with already established setups. Hence, the open access solution described here will help to further establish the ASR method in many laboratories and thus facilitate and standardize research in animal models of tinnitus or hearing loss.

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arXiv2016

A statistical method for analyzing and comparing spatiotemporal cortical activation patterns

We present a new statistical method to analyze multichannel steady-state local field potentials (LFP) recorded within different sensory cortices of different rodent species. Our spatiotemporal multi-dimensional cluster statistics (MCS) method enables statistical analyzing and comparing clusters of data points in n-dimensional space. We demonstrate that using this approach stimulus-specific attractor-like spatiotemporal activity patterns can be detected and be significantly different from each other during stimulation with long-lasting stimuli. Our method may be applied to other types of multichannel neuronal data, like EEG, MEG or spiking responses and used for the development of new read-out algorithms of brain activity and by that opens new perspectives for the development of brain-computer interfaces.

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arXiv2016

Stochastic resonance controlled upregulation of internal noise after hearing loss as a putative correlate of tinnitus-related neuronal hyperactivity

Subjective tinnitus (ST) is generally assumed to be a consequence of hearing loss (HL). In animal studies acoustic trauma can lead to behavioral signs of ST, in human studies ST patients without increased hearing thresholds were found to suffer from so called hidden HL. Additionally, ST is correlated with pathologically increased spontaneous firing rates and neuronal hyperactivity (NH) along the auditory pathway. Homeostatic plasticity (HP) has been proposed as a compensation mechanism leading to the development of NH, arguing that after HL initially decreased mean firing rates of neurons are subsequently restored by increased spontaneous rates. However all HP models fundamentally lack explanatory power since the function of keeping mean firing rate constant remains elusive as does the benefit this might have in terms of information processing. Furthermore the neural circuitry being able to perform the comparison of preferred with actual mean firing rate remains unclear. Here we propose an entirely new interpretation of ST related development of NH in terms of information theory. We suggest that stochastic resonance (SR) plays a key role in short- and long-term plasticity within the auditory system and is the ultimate cause of NH and ST. SR has been found ubiquitous in neuroscience and refers to the phenomenon that sub-threshold, unperceivable signals can be transmitted by adding noise to sensor input. We argue that after HL, SR serves to lift signals above the increased hearing threshold, hence subsequently decreasing thresholds again. The increased amount of internal noise is the correlate of the NH, which finally leads to the development of ST, due to neuronal plasticity along the auditory pathway. We demonstrate the plausibility of our hypothesis by using a computational model and provide exemplarily findings of human and animal studies that are consistent with our model.

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arXiv2015

Adaptive stochastic resonance based on output autocorrelations

Successful detection of weak signals is a universal challenge for numerous technical and biological systems and crucially limits signal transduction and transmission. Stochastic resonance (SR) has been identified to have the potential to tackle this problem, namely to enable non-linear systems to detect small, otherwise sub-threshold signals by means of added non-zero noise. This has been demonstrated within a wide range of systems in physical, technological and biological contexts. Based on its ubiquitous importance, numerous theoretical and technical approaches aim at an optimization of signal transduction based on SR. Several quantities like mutual information, signal-to-noise-ratio, or the cross-correlation between input stimulus and resulting detector response have been used to determine optimal noise intensities for SR. The fundamental shortcoming with all these measures is that knowledge of the signal to be detected is required to compute them. This dilemma prevents the use of adaptive SR procedures in any application where the signal to be detected is unknown. We here show that the autocorrelation function (AC) of the detector response fundamentally overcomes this drawback. For a simplified model system, the equivalence of the output AC with the measures mentioned above is proven analytically. In addition, we test our approach numerically for a variety of systems comprising different input signals and different types of detectors. The results indicate a strong similarity between mutual information and output AC in terms of the optimal noise intensity for SR. Hence, using the output AC to adaptively vary the amount of added noise in order to maximize information transmission via SR might be a fundamental processing principle in nature, in particular within neural systems which could be implemented in future technical applications.

cs.IT↗

arXiv2014

Bayesian inference of time varying parameters in autoregressive processes

In the autoregressive process of first order AR(1), a homogeneous correlated time series $u_t$ is recursively constructed as $u_t = q\; u_{t-1} + σ\;ε_t$, using random Gaussian deviates $ε_t$ and fixed values for the correlation coefficient $q$ and for the noise amplitude $σ$. To model temporally heterogeneous time series, the coefficients $q_t$ and $σ_t$ can be regarded as time-dependend variables by themselves, leading to the time-varying autoregressive processes TVAR(1). We assume here that the time series $u_t$ is known and attempt to infer the temporal evolution of the 'superstatistical' parameters $q_t$ and $σ_t$. We present a sequential Bayesian method of inference, which is conceptually related to the Hidden Markov model, but takes into account the direct statistical dependence of successively measured variables $u_t$. The method requires almost no prior knowledge about the temporal dynamics of $q_t$ and $σ_t$ and can handle gradual and abrupt changes of these superparameters simultaneously. We compare our method with a Maximum Likelihood estimate based on a sliding window and show that it is superior for a wide range of window sizes.

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arXiv2012

1D analysis of 2D isotropic random walks

Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of the underlying stochastic process. Often, it can be assumed a priori that the underlying discrete-time random walk model is independent from absolute position (homogeneity), direction (isotropy) and time (stationarity), as well as ergodic. In this article we first review some common statistical methods for analyzing 2D trajectories, based on quantities with built-in rotational invariance. We then discuss an alternative approach in which the two-dimensional trajectories are reduced to one dimension by projection onto an arbitrary axis and rotational averaging. Each step of the resulting 1D trajectory is further factorized into sign and magnitude. The statistical properties of the signs and magnitudes are mathematically related to those of the step lengths and turning angles of the original 2D trajectories, demonstrating that no essential information is lost by this data reduction. The resulting binary sequence of signs lends itself for a pattern counting analysis, revealing temporal properties of the random process that are not easily deduced from conventional measures such as the velocity autocorrelation function. In order to highlight this simplified 1D description, we apply it to a 2D random walk with restricted turning angles (RTA model), defined by a finite-variance distribution $p(L)$ of step length and a narrow turning angle distribution $p(ϕ)$, assuming that the lengths and directions of the steps are independent.

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arXiv2012

Scaling properties of correlated random walks

Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length $δx$ is performed after each time interval $δt$. In correlated discrete time random walks (CDTRWs), the probability $q$ for two successive steps having the same sign is unequal 1/2. The resulting probability distribution $P(Δx,Δt)$ that a displacement $Δx$ is observed after a lagtime $Δt$ is known analytically for arbitrary persistence parameters $q$. In this short note we show how a CDTRW with parameters $[δt, δx, q]$ can be mapped onto another CDTRW with rescaled parameters $[δt/s, δx\cdot g(q,s), q^{\prime}(q,s)]$, for arbitrary scaling parameters $s$, so that both walks have the same displacement distributions $P(Δx,Δt)$ on long time scales. The nonlinear scaling functions $g(q,s)$ and $q^{\prime}(q,s)$ and derived explicitely. This scaling method can be used to model time series measured at discrete sample intervals $δt$ but actually corresponding to continuum processes with variations occuring on a much shorter time scale $δt/s$.

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arXiv2011

Reconstructing fiber networks from confocal image stacks

We present a numerically efficient method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. Our 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 $3\times3$ neighborhood. This optimization criterion makes our method free of user-defined parameters and the output exceptionally robust against imaging noise.

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arXiv2011

Poresizes in random line networks

Many natural fibrous networks with fiber diameters much smaller than the average poresize can be described as three-dimensional (3D) random line networks. We consider here a `Mikado' model for such systems, consisting of straight line segments of equal length, distributed homogeneously and isotropically in space. First, we derive analytically the probability density distribution $p(r_{no})$ for the `nearest obstacle distance' $r_{no}$ between a randomly chosen test point within the network pores and its closest neighboring point on a line segment. Second, we show that in the limit where the line segments are much longer than the typical pore size, $p(r_{no})$ becomes a Rayleigh distribution. The single parameter $σ$ of this Rayleigh distribution represents the most probable nearest obstacle distance and can be expressed in terms of the total line length per unit volume. Finally, we show by numerical simulations that $σ$ differs only by a constant factor from the intuitive notion of average `pore size', defined by finding the maximum sphere that fits into each pore and then averaging over the radii of these spheres.

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