Research Topics


Morphology reconstruction Neura

Neural network generator NeuGEN

Detailed modeling of neuronal signal processing

Basis for all three-dimensional and detailed modeling approaches is an accurate description of the underlying morphology of a neuron, a cell nucleus or any other organelle of interest. Raw morphological image data recorded from microscopy-techniques such as two-photon, confocal or electron microscopy can form the basis for the automatic reconstruction of surface and volume-representation of the recorded organelle.

Since raw image data contains “contamination”, gaps in the structures, background noise etc. the first step is to eliminate these critical factors by applying sophisticated image filters. To this end an intertia-based non-linear anisotropic diffusion filter has been developed and incorporated in the Reconstruction Toolbox Neuron Reconstruction Algorithm (NeuRA).

Grid Generators that compute surface triangulations and tetrahedral volume representations of the object are applied to the pre-processed image data and yield a discrete geometry representation for the numerical computation of neuronal signal processes in three space dimensions and in time.

Grid refinement methods in numerical solvers

3D grid generation

Figure 1 – From raw microscopy data (top) to three-dimensional morphologies (bottom).

Simulations of neuronal network dynamics require information about cell morphology, physiology and connectivity. Such simulations can be carried out in compartmental modeling software such as the NEURON simulator. The neuron network generator NeuGen allows the user to generate large networks of neurons, making use of accessible neuronal anatomical data to generate highly realistic neuron morphologies for any given class of cell. Network files can be exported to standard formats, such as .hoc, .xml, etc.

In addition to compartmental representations, NeuGen offers the possibility to create three-dimensional geometries of cells, which allows systematic investigation of morphology influences when modeling three-dimensional signal processing in neurons. 

Figure 2 – NeuGen: Neuron Network Generator (top), creates realistic networks from defined neuron types (middle). Anatomical information is recruited from data bases and published data. Networks can be imported to the NEURON-Simulator or export three-dimensional morphologies (bottom)

The defining feature of a neuron is its plasma membrane that regulates intra/extracellular communication. The result of this is the controlled variation of the cell’s membrane potential. This electrical signal is a space- and time dependent code produced by a wide range of ion channels and receptors embedded in the plasma membrane. Standard approaches to model the electrical response of a neuron range from unifying Integrate and Fire models to space and time dependent compartmental models. The latter still lack the representation of the intra- and extracellular space. Therefore, neither extracellular effects can be included, nor can such models be directly coupled to intracellular signals.

To this end, a full three-dimensional model of electrical Hodgkin-Huxley-like equations has been developed allowing the investigation of the fully resolved neuron, including intra- and extracellular space.

Electrical Signaling in Three Dimensions

Figure 3 – Three-dimensional modeling of the electrical signaling of neurons. Action potential propagation can be modeled in the full three-dimensional space (top) and evaluated under intra- and extracellular properties or channel distributions and densities (bottom).

Although the electrical communication in large neuron ensembles carries unimaginable levels of complexity, already each single neuron in this network performs complex intracellular signal responsible for neuronal plasticity, development, learning, survival and death. One of the major players on the intracellular level is calcium.

To investigate the role of calcium, how calcium signals can be controlled by the cell, we are developing detailed three-dimensional models of cellular calcium signaling. One application of these models has been to analyse the influence of nuclear morphology on nuclear calcium signaling. Further advances in this area include the interplay between cytosolic and stored calcium in the endoplasmic reticulum or mitochondria.

We are further linking the 3D-model for the plasma membrane to the sub-cellular signaling scale to establish a full cellular model operating on various signaling scales.

Cellular Calcium Signaling

Figure 4 – The nuclear morphology of hippocampal neurons (top) plays a critical role in controlling nuclear calcium signals (bottom). Depicted here is the regulation of calcium amplitudes by the shape of nuclear membrane infoldings.

Synaptic transmission at chemical synapses is very complex and influenced by many factors. Roughly one can separate the synapse’s functionality into pre- and postsynaptic areas. While postsynaptic function is regulated by the cell’s postsynaptic receptors, the presynaptic area controls vesicle filling and vesicle recycling. Changes in synaptic transmission are a result of variations in pre- and postsynaptic processes.

In various projects, we are investigating the presynaptic processes on a level of detail where single vesicles are fully resolved. We model vesicle filling, vesicle motion, exocytosis and recycling in GAGAergic neurons to identify the interplay between the most relevant presynaptic components.

A slightly more macroscopic depiction is accounted for in the investigation of presynaptic boutons of motor neurons at the drosophila neuromuscular junction (NMJ). Here we have been investigating the influence of bouton size on the function of signal transduction at the NMJ.

Modeling Synaptic Transmission

Figure 5 – Detailed modeling of synaptic transmission, resolving single vesicles at GABAergic neurons (top), investigating the bouton morphology at the drosophila NMJ (middle) as a function of synaptic transmission (bottom).

Modeling neuronal processes in three space dimensions on realistic cellular morphologies requires efficient numerical tools. In our modeling approaches we make use of the simulation plattform uG (unstructured grids). Sophisticated multigrid solvers make use of grid hierarchies which are generated by refinement methods building upon the coarsest grid.

To overcome problems that occur in grid refinement due to traditional projection schemes, especially when dealing with highly complex morphologies such as neuron structures and their organelles, we have been developing new and stable grid refinement methods.

These are employable in the general context of neuroscientific problems and beyond.

Figure 6 – Reconstruction of cell nucleus (top left) and its corresponding coarse grid (top right). Grid refinement using the novel non-projection refinement scheme for multigrid solvers (center left and right) and a simulation of calcium diffusion in the depicted nucleus (bottom).

Find below some selected examples of our work

Our research comprises three main areas

Numerics and Scientific Computing

  1. Partial Differential Equations

  2. Ordinary Differential Equations

  3. Discretization Methods

  4. Fast Solvers, Multigrid Methods

  5. Grid Generation from various sources

  6. Software development

High-Performance Computing

  1. Parallelization

  2. Scalable Algorithms for High-Performance Computing

  3. GPU Programing

  4. Software development

Application to Life Science

  1. Development of new models in life science

  2. Modeling and Simulation of highly detailed models of signaling in brain cells

  3. Solving Structure-Function problems