Hermann Cuntz

The dentate gyrus’ principal neuron, the granule cell (GC), plays a key role in pattern separation, transforming similar inputs into dissimilar outputs. We used a new measure based on information theory to evaluate this transformation in an experimentally derived in silico GC model with realistic ion channel distributions across its dendrites. We found that model performance aligned well with current-clamp recordings from mouse brain slices. However, it was also possible to find artificial parameter combinations in the model that functionally outperformed the recorded cells while matching their action potential shapes. Rather than maximising computational power, the biologically realistic GC model balanced energy efficiency against increased functionality in a Pareto optimal way: No possible parameter combination was found to improve one of the objectives without impairing the other. Interestingly, immature GCs adopted a different weighted trade-off with a stronger emphasis on energy efficiency than pattern separation, but they remained Pareto optimal over their putative developmental trajectory. Our results support the idea that evolution favours neurons that can satisfy functional and energetic demands simultaneously. Abstract Figure: In brief: We find that dentate gyrus granule cells are Pareto optimal for the simultaneous performance of pattern separation and energy economy, adopting a differently weighted trade-off depending on their developmental stage. Highlights: An experimentally constrained single granule cell (GC) model can perform temporal pattern separation in line with real data. Artificial channel configurations can improve pattern separation, but strictly at the cost of increased ATP consumption. GCs with realistic channel configurations appear Pareto optimal for the simultaneous performance of pattern separation and energy economy. Immature GCs remain on the Pareto front but prioritise low energy expenditure over pattern separation.

Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila, where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES toolbox (www.treestoolbox.org).

Dendritic spines are crucial for excitatory synaptic transmission as the size of a spine head correlates with the strength of its synapse. The distribution of spine head sizes follows a lognormal-like distribution with more small spines than large ones. We analysed the impact of synaptic activity and plasticity on the spine size distribution in adult-born hippocampal granule cells from rats with induced homo- and heterosynaptic long-term plasticity in vivo and CA1 pyramidal cells from Munc13–1/Munc13–2 knockout mice with completely blocked synaptic transmission. Neither the induction of extrinsic synaptic plasticity nor the blockage of presynaptic activity degrades the lognormal-like distribution but changes its mean, variance and skewness. The skewed distribution develops early in the life of the neuron. Our findings and their computational modelling support the idea that intrinsic synaptic plasticity is sufficient for the generation, while a combination of intrinsic and extrinsic synaptic plasticity maintains lognormal-like distribution of spines.

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown, given that simpler models with fewer ion channels are also able to functionally reproduce the behaviour of some neurons. Here, we stochastically varied the ion channel densities of a biophysically detailed dentate gyrus granule cell model to produce a large population of putative granule cells, comparing those with all 15 original ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were dramatically more frequent at ~6% vs. ~1% in the simpler model. The full models were also more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve a target excitability.

Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila , where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES Toolbox ( www.treestoolbox.org ). In brief: We use morphological modelling inspired by the regeneration of various artificially cut neuron types and repair incomplete human and nonhuman neuronal dendritic reconstructions. Author summary: Reconstructing neuronal dendrites by drawing their 3D branching structures in the computer has proven to be crucial for interpreting the flow of electrical signals and therefore the computations that dendrites implement on their inputs. These reconstructions are tedious and prone to disruptive limitations imposed by experimental procedures. In recent years, complementary computational procedures have emerged that reproduce the fine details of morphology in theoretical models. These models allow, for example, to populate large-scale neural networks and to study structure-function relationships. In this work we use a morphological model based on optimised wiring for signal conduction and material cost to repair faulty reconstructions, in particular those of human hippocampal dendrites, which are rare and precious but often cut due to technical limitations. Interestingly, we find that our synthetic repair mechanism reproduces the two distinct modes of repair observed in real dendrites: regeneration from the severed branch and invasion from neighbouring branches. Our model therefore provides both a useful tool for single-cell electrophysiological simulations and a useful theoretical concept for studying the biology of dendrite repair. Highlights: Optimal wiring-based growth algorithm replicates regrowth of artificially cut dendrites The growth algorithm repairs cut dendrites in incomplete reconstructions The algorithm works for diverse neuron types in multiple species The repair of morphology restores original electrophysiology The repair of morphology supports simulations of high synaptic thresholds for NMDA spikes in human dendrites The repair tool with user interface is available in the TREES Toolbox

Summary: Dendritic spines are crucial for excitatory synaptic transmission as the size of a spine head correlates with the strength of its synapse. The distribution of spine head sizes follows a lognormal-like distribution with more small spines than large ones. We analysed the impact of synaptic activity and plasticity on the spine size distribution in adult-born hippocampal granule cells from rats with induced homo- and heterosynaptic long-term plasticity in vivo and CA1 pyramidal cells from Munc-13-1-Munc13-2 knockout mice with completely blocked synaptic transmission. Neither induction of extrinsic synaptic plasticity nor the blockage of presynaptic activity degrades the lognormal-like distribution but changes its mean, variance and skewness. The skewed distribution develops early in the life of the neuron. Our findings and their computational modelling support the idea that intrinsic synaptic plasticity is sufficient for the generation, while a combination of intrinsic and extrinsic synaptic plasticity maintains lognormal like distribution of spines.

Branching of dendrites and axons allows neurons to make synaptic contacts with large numbers of other neurons, facilitating the high connectivity of the nervous system. Neurons have geometric properties, such as the lengths and diameters of their branches, that change systematically throughout the arbor in ways that are thought to minimize construction costs and to optimize the transmission of electrical signals and the intracellular transport of materials. In this work, we investigated whether neuronal arbors also have topological properties that reflect the growth and/or functional properties of their dendritic arbors. In our efforts to uncover possible topological rules, we discovered a function that depends only on the topology of bifurcating trees such as dendritic arbors: the tip-support distribution , which is the average number of branches that support n dendrite tips. We found that for many, but not all, neurons from a wide range of invertebrate and vertebrate species, the tip-support distribution follows a power law with slopes ranging from -1.4 and -1.8 on a log-log plot. The slope is invariant under iterative trimming of terminal branches and under random ablation of internal branches. We found that power laws with similar slopes emerge from a variety of iterative growth processes including the Galton-Watson (GW) process, where the power-law behavior occurs after the percolation threshold. Through simulation, we show the slope of the power-law increases with the branching probability of a GW process, which corresponds to a more regular tree. Furthermore, the inclusion of postsynaptic spines and other terminal processes on branches causes a characteristic deviation of the tip-support distribution from a power law. Therefore, the tip-support function is a topological property that reflects the underlying branching morphogenesis of dendritic trees.

Neuronal hyperexcitability is a pathological characteristic of Alzheimer's disease (AD). Three main mechanisms have been proposed to explain it: (i) dendritic degeneration leading to increased input resistance, (ii) ion channel changes leading to enhanced intrinsic excitability, and (iii) synaptic changes leading to excitation–inhibition (E/I) imbalance. However, the relative contribution of these mechanisms is not fully understood. Therefore, we performed biophysically realistic multi‐compartmental modelling of neuronal excitability in reconstructed CA1 pyramidal neurons from wild‐type and APP/PS1 mice, a well‐established animal model of AD. We show that, for synaptic activation, the excitability‐promoting effects of dendritic degeneration are cancelled out by decreased excitation due to synaptic loss. We find an interesting balance between excitability regulation and an enhanced degeneration in the basal dendrites of APP/PS1 cells, potentially leading to increased excitation by the apical but decreased excitation by the basal Schaffer collateral pathway. Furthermore, our simulations reveal three pathomechanistic scenarios that can account for the experimentally observed increase in firing and bursting of CA1 pyramidal neurons in APP/PS1 mice: scenario 1: enhanced E/I ratio; scenario 2: alteration of intrinsic ion channels (I_AHP down‐regulated; I_Nap, I_Na and I_CaT up‐regulated) in addition to enhanced E/I ratio; and scenario 3: increased excitatory burst input. Our work supports the hypothesis that pathological network and ion channel changes are major contributors to neuronal hyperexcitability in AD. Overall, our results are in line with the concept of multi‐causality according to which multiple different disruptions are separately sufficient but no single particular disruption is necessary for neuronal hyperexcitability. image Key points: This work presents simulations of synaptically driven responses in pyramidal cells (PCs) with Alzheimer's disease (AD)‐related dendritic degeneration. Dendritic degeneration alone alters PC responses to layer‐specific input but additional pathomechanistic scenarios are required to explain neuronal hyperexcitability in AD as follows. Possible scenario 1: AD‐related increased excitatory input together with decreased inhibitory input (E/I imbalance) can lead to hyperexcitability in PCs. Possible scenario 2: changes in E/I balance combined with altered ion channel properties can account for hyperexcitability in AD. Possible scenario 3: burst hyperactivity of the surrounding network can explain hyperexcitability of PCs during AD.

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.

Neuronal hyperexcitability is a feature of Alzheimer’s disease (AD). Three main mechanisms have been proposed to explain it: i), dendritic degeneration leading to increased input resistance, ii), ion channel changes leading to enhanced intrinsic excitability, and iii), synaptic changes leading to excitation-inhibition ( E/I ) imbalance. However, the relative contribution of these mechanisms is not fully understood. Therefore, we performed biophysically realistic multi-compartmental modelling of excitability in reconstructed CA1 pyramidal neurons of wild-type and APP/PS1 mice, a well-established animal model of AD. We show that, for synaptic activation, the excitability promoting effects of dendritic degeneration are cancelled out by excitability decreasing effects of synaptic loss. We find an interesting balance of excitability regulation with enhanced degeneration in the basal dendrites of APP/PS1 cells potentially leading to increased excitation by the apical but decreased excitation by the basal Schaffer collateral pathway. Furthermore, our simulations reveal that three additional pathomechanistic scenarios can account for the experimentally observed increase in firing and bursting of CA1 pyramidal neurons in APP/PS1 mice. Scenario 1: increased excitatory burst input; scenario 2: enhanced E/I ratio and scenario 3: alteration of intrinsic ion channels ( I _AHP down-regulated; I _Nap , I _Na and I _CaT up-regulated) in addition to enhanced E/I ratio. Our work supports the hypothesis that pathological network and ion channel changes are major contributors to neuronal hyperexcitability in AD. Overall, our results are in line with the concept of multi-causality and degeneracy according to which multiple different disruptions are separately sufficient but no single disruption is necessary for neuronal hyperexcitability. In brief: Using a computational model, we find that changes in the extrinsic network and intrinsic biophysical neuronal properties rather than dendritic degeneration alone explain the altered firing behaviour observed in Alzheimer’s disease (AD). Highlights: Simulations of synaptically driven responses in PCs with AD-related dendritic degeneration. Dendritic degeneration alone alters PC responses to layer-specific input but additional pathomechanistic scenarios are required to explain neuronal hyperexcitability in AD. Possible scenario 1: Burst hyperactivity of the surrounding network can explain hyper-excitability of PCs during AD. Possible scenario 2: AD-related increased excitatory input together with decreased inhibitory input ( E/I imbalance) can lead to hyperexcitability in PCs. Possible scenario 3: Changes in E/I balance combined with altered ion channel properties can account for hyperexcitability in AD.