Illuminating dendritic function with computational models.

Dendrites have always fascinated researchers: from the artistic drawings by Ramon y Cajal to the beautiful recordings of today, neuroscientists have been striving to unravel the mysteries of these structures. Theoretical work in the 1960s predicted important dendritic effects on neuronal processing, establishing computational modelling as a powerful technique for their investigation. Since then, modelling of dendrites has been instrumental in driving neuroscience research in a targeted manner, providing experimentally testable predictions that range from the subcellular level to the systems level, and their relevance extends to fields beyond neuroscience, such as machine learning and artificial intelligence. Validation of modelling predictions often requires - and drives - new technological advances, thus closing the loop with theory-driven experimentation that moves the field forward. This Review features the most important, to our understanding, contributions of modelling of dendritic computations, including those pending experimental verification, and highlights studies of successful interactions between the modelling and experimental neuroscience communities.

Basal tree complexity shapes functional pathways in the prefrontal cortex.

While the morphology of basal dendritic trees in cortical pyramidal neurons varies, the functional implications of this diversity are just starting to emerge. In layer 5 pyramidal neurons of the prefrontal cortex, for example, increased basal tree complexity determines the recruitment of these neurons into functional circuits. Here, we use a modeling approach to investigate whether and how the morphology of the basal tree mediates the functional output of neurons. We implemented 57 basal tree morphologies of layer 5 prefrontal pyramidal neurons of the rat and identified morphological types that were characterized by different response features, forming distinct functional types. These types were robust to a wide range of manipulations (distribution of active ionic mechanisms, NMDA conductance, somatic and apical tree morphology, or the number of activated synapses) and supported different temporal coding schemes at both the single neuron and the microcircuit level. We predict that the basal tree morphological diversity among neurons of the same class mediates their segregation into distinct functional pathways. Extension of our approach/findings to other cortical areas and/or layers or under pathological conditions may provide a generalized role of the basal trees for neuronal function.NEW & NOTEWORTHY Our results suggest that the segregation of neurons to different functional types based on their basal tree morphology is in large part independent of the distribution of active ionic mechanisms, NMDA conductance, somatic and apical tree morphology, and the number of activated synapses; different functional types support distinct temporal coding schemes. This can be exploited to create networks with diverse coding characteristics, thus contributing to the functional heterogeneity within the same layer and area.

Dendritic nonlinearities reduce network size requirements and mediate ON and OFF states of persistent activity in a PFC microcircuit model.

Technological advances have unraveled the existence of small clusters of co-active neurons in the neocortex. The functional implications of these microcircuits are in large part unexplored. Using a heavily constrained biophysical model of a L5 PFC microcircuit, we recently showed that these structures act as tunable modules of persistent activity, the cellular correlate of working memory. Here, we investigate the mechanisms that underlie persistent activity emergence (ON) and termination (OFF) and search for the minimum network size required for expressing these states within physiological regimes. We show that (a) NMDA-mediated dendritic spikes gate the induction of persistent firing in the microcircuit. (b) The minimum network size required for persistent activity induction is inversely proportional to the synaptic drive of each excitatory neuron. (c) Relaxation of connectivity and synaptic delay constraints eliminates the gating effect of NMDA spikes, albeit at a cost of much larger networks. (d) Persistent activity termination by increased inhibition depends on the strength of the synaptic input and is negatively modulated by dADP. (e) Slow synaptic mechanisms and network activity contain predictive information regarding the ability of a given stimulus to turn ON and/or OFF persistent firing in the microcircuit model. Overall, this study zooms out from dendrites to cell assemblies and suggests a tight interaction between dendritic non-linearities and network properties (size/connectivity) that may facilitate the short-memory function of the PFC.

Modeling apical and basal tree contribution to orientation selectivity in a mouse primary visual cortex layer 2/3 pyramidal cell.

Pyramidal neurons, a mainstay of cortical regions, receive a plethora of inputs from various areas onto their morphologically distinct apical and basal trees. Both trees differentially contribute to the somatic response, defining distinct anatomical and possibly functional sub-units. To elucidate the contribution of each tree to the encoding of visual stimuli at the somatic level, we modeled the response pattern of a mouse L2/3 V1 pyramidal neuron to orientation tuned synaptic input. Towards this goal, we used a morphologically detailed computational model of a single cell that replicates electrophysiological and two-photon imaging data. Our simulations predict a synergistic effect of apical and basal trees on somatic action potential generation: basal tree activity, in the form of either depolarization or dendritic spiking, is necessary for producing somatic activity, despite the fact that most somatic spikes are heavily driven by apical dendritic spikes. This model provides evidence for synergistic computations taking place in the basal and apical trees of the L2/3 V1 neuron along with mechanistic explanations for tree-specific contributions and emphasizes the potential role of predictive and attentional feedback input in these cells.

Dendritic action potentials and computation in human layer 2/3 cortical neurons.

The active electrical properties of dendrites shape neuronal input and output and are fundamental to brain function. However, our knowledge of active dendrites has been almost entirely acquired from studies of rodents. In this work, we investigated the dendrites of layer 2 and 3 (L2/3) pyramidal neurons of the human cerebral cortex ex vivo. In these neurons, we discovered a class of calcium-mediated dendritic action potentials (dCaAPs) whose waveform and effects on neuronal output have not been previously described. In contrast to typical all-or-none action potentials, dCaAPs were graded; their amplitudes were maximal for threshold-level stimuli but dampened for stronger stimuli. These dCaAPs enabled the dendrites of individual human neocortical pyramidal neurons to classify linearly nonseparable inputs-a computation conventionally thought to require multilayered networks.

Contribution of apical and basal dendrites to orientation encoding in mouse V1 L2/3 pyramidal neurons.

Pyramidal neurons integrate synaptic inputs from basal and apical dendrites to generate stimulus-specific responses. It has been proposed that feed-forward inputs to basal dendrites drive a neuron's stimulus preference, while feedback inputs to apical dendrites sharpen selectivity. However, how a neuron's dendritic domains relate to its functional selectivity has not been demonstrated experimentally. We performed 2-photon dendritic micro-dissection on layer-2/3 pyramidal neurons in mouse primary visual cortex. We found that removing the apical dendritic tuft did not alter orientation-tuning. Furthermore, orientation-tuning curves were remarkably robust to the removal of basal dendrites: ablation of 2 basal dendrites was needed to cause a small shift in orientation preference, without significantly altering tuning width. Computational modeling corroborated our results and put limits on how orientation preferences among basal dendrites differ in order to reproduce the post-ablation data. In conclusion, neuronal orientation-tuning appears remarkably robust to loss of dendritic input.

Optically Induced Calcium-Dependent Gene Activation and Labeling of Active Neurons Using CaMPARI and Cal-Light.

The advent of optogenetic methods has made it possible to use endogeneously produced molecules to image and manipulate cellular, subcellular, and synaptic activity. It has also led to the development of photoactivatable calcium-dependent indicators that mark active synapses, neurons, and circuits. Furthermore, calcium-dependent photoactivation can be used to trigger gene expression in active neurons. Here we describe two sets of protocols, one using CaMPARI and a second one using Cal-Light. CaMPARI, a calcium-modulated photoactivatable ratiometric integrator, enables rapid network-wide, tunable, all-optical functional circuit mapping. Cal-Light, a photoactivatable calcium sensor, while slower to respond than CaMPARI, has the capacity to trigger the expression of genes, including effectors, activators, indicators, or other constructs. Here we describe the rationale and provide procedures for using these two calcium-dependent constructs (1) in vitro in dissociated primary neuronal cell cultures (CaMPARI & Cal-Light); (2) in vitro in acute brain slices for circuit mapping (CaMPARI); (3) in vivo for triggering photoconversion or gene expression (CaMPARI & Cal-Light); and finally, (4) for recovering photoconverted neurons post-fixation with immunocytochemistry (CaMPARI). The approaches and protocols we describe are examples of the potential uses of both CaMPARI & Cal-Light. The ability to mark and manipulate neurons that are active during specific epochs of behavior has a vast unexplored experimental potential.

Modulatory effects of inhibition on persistent activity in a cortical microcircuit model.

Neocortical network activity is generated through a dynamic balance between excitation, provided by pyramidal neurons, and inhibition, provided by interneurons. Imbalance of the excitation/inhibition ratio has been identified in several neuropsychiatric diseases, such as schizophrenia, autism and epilepsy, which also present with other cognitive deficits and symptoms associated with prefrontal cortical (PFC) dysfunction. We undertook a computational approach to study how changes in the excitation/inhibition balance in a PFC microcircuit model affect the properties of persistent activity, considered the cellular correlate of working memory function in PFC. To this end, we constructed a PFC microcircuit, consisting of pyramidal neuron models and all three different interneuron types: fast-spiking (FS), regular-spiking (RS), and irregular-spiking (IS) interneurons. Persistent activity was induced in the microcircuit model with a stimulus to the proximal apical dendrites of the pyramidal neuron models, and its properties were analyzed, such as the induction profile, the interspike intervals (ISIs) and neuronal synchronicity. Our simulations showed that (a) the induction but not the firing frequency or neuronal synchronicity is modulated by changes in the NMDA-to-AMPA ratio on FS interneuron model, (b) removing or decreasing the FS model input to the pyramidal neuron models greatly limited the biophysical modulation of persistent activity induction, decreased the ISIs and neuronal synchronicity during persistent activity, (c) the induction and firing properties could not be altered by the addition of other inhibitory inputs to the soma (from RS or IS models), and (d) the synchronicity change could be reversed by the addition of other inhibitory inputs to the soma, but beyond the levels of the control network. Thus, generic somatic inhibition acts as a pacemaker of persistent activity and FS specific inhibition modulates the output of the pacemaker.

Coding and decoding with dendrites.

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.

A simulation study on the effects of dendritic morphology on layer V prefrontal pyramidal cell firing behavior.

Pyramidal cells, the most abundant neurons in neocortex, exhibit significant structural variability across different brain areas and layers in different species. Moreover, in response to a somatic step current, these cells display a range of firing behaviors, the most common being (1) repetitive action potentials (Regular Spiking-RS), and (2) an initial cluster of 2-5 action potentials with short interspike interval (ISIs) followed by single spikes (Intrinsic Bursting-IB). A correlation between firing behavior and dendritic morphology has recently been reported. In this work we use computational modeling to investigate quantitatively the effects of the basal dendritic tree morphology on the firing behavior of 112 three-dimensional reconstructions of layer V PFC rat pyramidal cells. Particularly, we focus on how different morphological (diameter, total length, volume, and branch number) and passive [Mean Electrotonic Path length (MEP)] features of basal dendritic trees shape somatic firing when the spatial distribution of ionic mechanisms in the basal dendritic trees is uniform or non-uniform. Our results suggest that total length, volume and branch number are the best morphological parameters to discriminate the cells as RS or IB, regardless of the distribution of ionic mechanisms in basal trees. The discriminatory power of total length, volume, and branch number remains high in the presence of different apical dendrites. These results suggest that morphological variations in the basal dendritic trees of layer V pyramidal neurons in the PFC influence their firing patterns in a predictive manner and may in turn influence the information processing capabilities of these neurons.

Induction and modulation of persistent activity in a layer V PFC microcircuit model.

Working memory refers to the temporary storage of information and is strongly associated with the prefrontal cortex (PFC). Persistent activity of cortical neurons, namely the activity that persists beyond the stimulus presentation, is considered the cellular correlate of working memory. Although past studies suggested that this type of activity is characteristic of large scale networks, recent experimental evidence imply that small, tightly interconnected clusters of neurons in the cortex may support similar functionalities. However, very little is known about the biophysical mechanisms giving rise to persistent activity in small-sized microcircuits in the PFC. Here, we present a detailed biophysically-yet morphologically simplified-microcircuit model of layer V PFC neurons that incorporates connectivity constraints and is validated against a multitude of experimental data. We show that (a) a small-sized network can exhibit persistent activity under realistic stimulus conditions. (b) Its emergence depends strongly on the interplay of dADP, NMDA, and GABAB currents. (c) Although increases in stimulus duration increase the probability of persistent activity induction, variability in the stimulus firing frequency does not consistently influence it. (d) Modulation of ionic conductances (I h , I D , I sAHP, I caL, I caN, I caR) differentially controls persistent activity properties in a location dependent manner. These findings suggest that modulation of the microcircuit's firing characteristics is achieved primarily through changes in its intrinsic mechanism makeup, supporting the hypothesis of multiple bi-stable units in the PFC. Overall, the model generates a number of experimentally testable predictions that may lead to a better understanding of the biophysical mechanisms of persistent activity induction and modulation in the PFC.