Biology subjects

Ranft, J.

Publications and source records attributed to Ranft, J..

6 recordsLinked to original sources

bioRxiv2026

Neural networks as decision trees: an analytical framework for learning and neural selectivity

Nonlinear neural networks develop structured internal representations, yet how their geometry is determined by the tasks being learned remains poorly understood. Here, we develop an analytical framework for piecewise-linear feedforward and recurrent networks that links learning, activation-region structure, and neural selectivity. We show that, at any stationary point of gradient-aligned learning, a nonlinear network decomposes into local linear regressions over its activation regions. Deviations from the corresponding least-squares solutions are jointly constrained by network weights shared across regions and vanish in the low-error regime, yielding an approximate piecewise least-squares decomposition of the task. This structure admits a decision-tree interpretation, which we recover numerically by fitting trees to predict network activation patterns from the input. We further derive how the regions in which neurons are active determine the task statistics they capture, thereby organizing neural selectivity into distinct subpopulations. The resulting predictions closely match the selectivity geometry observed in simulated networks and two empirical neural datasets. Finally, we show that neural baseline regulates activation pattern diversity, placing networks along a continuum between coarse, generalizing representations and fine-grained, expressive representations. Together, these results establish activation regions as a unifying framework for describing how nonlinear networks decompose task structure into local computations and how those computations can be revealed through neural activity.

neuroscience↗

bioRxiv2022

Beta oscillations and waves in motor cortex can be accounted for by the interplay of spatially-structured connectivity and fluctuating inputs

The beta rhythm (13-30 Hz) is a prominent brain rhythm. Recordings in primates during instructed-delay reaching tasks have shown that different types of traveling waves of oscillatory activity are associated with episodes of beta oscillations in motor cortex during movement preparation. We propose here a simple model of motor cortex based on local excitatory-inhibitory neuronal populations coupled by longer range excitation, where additionally inputs to the motor cortex from other neural structures are represented by stochastic inputs on the different model populations. We show that the model accurately reproduces the statistics of recording data when these external inputs are correlated on a short time scale (25 ms) and have two different components, one that targets the motor cortex locally and another one that targets it in a global and synchronized way. The model reproduces the distribution of beta burst durations, the proportion of the different observed wave types, and wave speeds, which we show not to be linked to axonal propagation speed. When the long-range connectivity is anisotropic, traveling waves are found to preferentially propagate along the axis where connectivity decays the fastest. Different from previously proposed mechanistic explanations, the model suggests that traveling waves in motor cortex are the reflection of the dephasing by external inputs, putatively of thalamic origin, of an oscillatory activity that would otherwise be spatially synchronized by recurrent connectivity.

neuroscience↗

bioRxiv2022

Alterations of the axon initial segment in multiple sclerosis

Grey matter damage has been established as a key contributor to disability progression in multiple sclerosis. Aside from neuronal loss and axonal transections, which predominate in cortical demyelinated lesions, synaptic alterations have been detected in both demyelinated plaques and normal-appearing grey matter, resulting in functional neuronal damage. The axon initial segment is a key element of neuronal function, responsible for action potential initiation and maintenance of neuronal polarity. Despite several reports of profound axon initial segment alterations in different pathological models, among which experimental auto-immune encephalomyelitis, whether the axon initial segment is affected in multiple sclerosis is still unknown. Using immunohistochemistry, we analyzed axon initial segments from control and multiple sclerosis tissue, focusing on layer 5/6 pyramidal neurons in the neocortex and Purkinje cells in the cerebellum and performed analysis on the parameters known to control neuronal excitability, i.e., axon initial segment length and position. We found that the axon initial segment length was unchanged among the different multiple sclerosis samples, and not different from controls. In contrast, in both cell types, the axon initial segment position was altered, with an increased soma-axon initial segment gap, in both active and inactive demyelinated lesions. In addition, using a computational model, we show that this increased gap between soma and axon initial segment might increase neuronal excitability. Taken together, these results show for the first time changes of axon initial segments in multiple sclerosis, in active as well as inactive grey matter lesions in both neocortex and cerebellum, which might alter neuronal function.

neuroscience↗

bioRxiv2020

Reciprocal stabilisation of glycine receptors and gephyrin scaffold proteins at inhibitory synapses

Postsynaptic scaffold proteins immobilise neurotransmitter receptors in the synaptic membrane opposite to presynaptic vesicle release sites, thus ensuring efficient synaptic transmission. At inhibitory synapses in the spinal cord, the main scaffold protein gephyrin assembles in dense molecule clusters that provide binding sites for glycine receptors (GlyRs). Gephyrin and GlyRs can also interact outside of synapses where they form receptor-scaffold complexes. While several models for the formation of postsynaptic scaffold domains in the presence of receptor-scaffold interactions have been advanced, a clear picture of the coupled dynamics of receptors and scaffold proteins at synapses is lacking. To characterise the GlyR and gephyrin dynamics at inhibitory synapses we performed fluorescence time-lapse imaging after photoconversion in order to directly visualise the exchange kinetics of recombinant Dendra2-gephyrin in cultured spinal cord neurons. Immuno-immobilisation of endogenous GlyRs with specific antibodies abolished their lateral diffusion in the plasma membrane, as judged by the lack of fluorescence recovery after photobleaching. Moreover, the crosslinking of GlyRs significantly reduced the exchange of Dendra2-gephyrin compared to control conditions, suggesting that the kinetics of the synaptic gephyrin pool is strongly dependent on GlyR-gephyrin interactions. We did not observe any change in the total synaptic gephyrin levels after GlyR crosslinking, however, indicating that the number of gephyrin molecules at synapses is not primarily dependent on the exchange of GlyR-gephyrin complexes. We further show that our experimental data can be quantitatively accounted for by a model of receptor-scaffold dynamics that includes a tightly interacting receptor-scaffold domain, as well as more loosely bound receptor and scaffold populations that exchange with extrasynaptic pools. The model can make predictions for single molecule data such as typical dwell times of synaptic proteins. Taken together, our data demonstrate the reciprocal stabilisation of GlyRs and gephyrin at inhibitory synapses and provide a quantitative understanding of their dynamic organisation. Statement of significanceThe efficiency of signal transmission between neurons depends strongly on the number of available neurotransmitter receptors in the postsynaptic membrane. Postsynaptic scaffold proteins provide binding sites for receptors, thus setting the gain of synaptic transmission. However, the importance of receptor-scaffold interactions for the stability of the postsynaptic scaffold itself has received relatively little attention. Using time-lapse imaging of glycine receptors and gephyrin scaffolds at inhibitory synapses in spinal cord neurons together with biophysical modelling, we show that receptor mobility controls the exchange but not the total number of gephyrin molecules at the synapse, and predict that glycine receptors and gephyrin scaffolds dynamically organise into different subpopulations with varying degrees of reciprocal stabilisation.

neuroscience↗

bioRxiv2020

Synchronization, stochasticity and phase waves in neuronal networks with spatially-structured connectivity

Oscillations in the beta/low gamma range (10-45 Hz) are recorded in diverse neural structures. They have successfully been modeled as sparsely synchronized oscillations arising from reciprocal interactions between randomly connected excitatory (E) pyramidal cells and local interneurons (I). The synchronization of spatially distant oscillatory spiking E-I modules has been well studied in the rate model framework but less so for modules of spiking neurons. Here, we first show that previously proposed modifications of rate models provide a quantitative description of spiking E-I modules of Exponential Integrate-and-Fire (EIF) neurons. This allows us to analyze the dynamical regimes of sparsely synchronized oscillatory E-I modules connected by long-range excitatory interactions, for two modules, as well as for a chain of such modules. For modules with a large number of neurons (> 105), we obtain results similar to previously obtained ones based on the classic deterministic Wilson-Cowan rate model, with the added bonus that the results quantitatively describe simulations of spiking EIF neurons. However, for modules with a moderate (~ 104) number of neurons, stochastic variations in the spike emission of neurons are important and need to be taken into account. On the one hand, they modify the oscillations in a way that tends to promote synchronization between different modules. On the other hand, independent fluctuations on different modules tend to disrupt synchronization. The correlations between distant oscillatory modules can be described by stochastic equations for the oscillator phases that have been intensely studied in other contexts. On shorter distances, we develop a description that also takes into account amplitude modes and that quantitatively accounts for our simulation data. Stochastic dephasing of neighboring modules produces transient phase gradients and the transient appearance of phase waves. We propose that these stochastically-induced phase waves provide an explanative framework for the observations of traveling waves in the cortex during beta oscillations.

neuroscience↗

bioRxiv2019

Lifetime of a structure evolving by cluster aggregation and particle loss, and application to postsynaptic scaffold domains

The dynamics of several mesoscopic biological structures depend on the interplay of growth through the incorporation of components of different sizes laterally diffusing along the cell membrane, and loss by component turnover. In particular, a model of such an out-of-equilibrium dynamics has recently been proposed for postsynaptic scaffold domains which are key structures of neuronal synapses. It is of interest to estimate the lifetime of these mesoscopic structures, especially in the context of synapses where this time is related to memory retention. The lifetime of a structure can be very long as compared to the turnover time of its components and it can be difficult to estimate it by direct numerical simulations. Here, in the context of the model proposed for postsynaptic scaffold domains, we approximate the aggregation-turnover dynamics by a shot-noise process. This enables us to analytically compute the quasi-stationary distribution describing the sizes of the surviving structures as well as their characteristic lifetime. We show that our analytical estimate agrees with numerical simulations of a full spatial model, in a regime of parameters where a direct assessment is computationally feasible. We then use our approach to estimate the lifetime of mesoscopic structures in parameter regimes where computer simulations would be prohibitively long. For gephyrin, the scaffolding protein specific to inhibitory synapses, we estimate a lifetime longer than several months for a scaffold domain when the single gephyrin protein turnover time is about half an hour, as experimentally measured. While our focus is on postsynaptic domains, our formalism and techniques should be applicable to other biological structures that are also formed by a balance of condensation and turnover.

neuroscience↗