Daniele Linaro

Pyramidal Neurons Derived from Human Pluripotent Stem Cells Integrate Efficiently into Mouse Brain Circuits In Vivo

The study of human cortical development has major implications for brain evolution and diseases but has remained elusive due to paucity of experimental models. Here we found that human embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs), cultured without added morphogens, recapitulate corticogenesis leading to the sequential generation of functional pyramidal neurons of all six layer identities. After transplantation into mouse neonatal brain, human ESC-derived cortical neurons integrated robustly and established specific axonal projections and dendritic patterns corresponding to native cortical neurons. The differentiation and connectivity of the transplanted human cortical neurons complexified progressively over several months in vivo, culminating in the establishment of functional synapses with the host circuitry. Our data demonstrate that human cortical neurons generated in vitro from ESC/iPSC can develop complex hodological properties characteristic of the cerebral cortex in vivo, thereby offering unprecedented opportunities for the modeling of human cortex diseases and brain repair.

The Hindmarsh-Rose neuron model: Bifurcation analysis and piecewise-linear approximations

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters.

Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.

High bandwidth synaptic communication and frequency tracking in human neocortex

Because of fast recovery from synaptic depression and fast-initiated action potentials, neuronal information transfer can have a substantially higher bandwidth in human neocortical circuits than in those of rodents.

Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster

The Hindmarsh--Rose model of neural action potential is revisited from the point of view of global bifurcation analysis, with the singular perturbation parameter held fixed. Of particular concern is a parameter regime where lobe-shaped regions of irregular bursting undergo a transition to stripe-shaped regions of periodic bursting. The boundary of each stripe represents a fold bifurcation that causes a smooth spike adding transition where the number of spikes in each burst is increased by one. It is shown via numerical path-following that the lobe-to-stripe transition is organized by a sequence of codimension-one and -two homoclinic bifurcations. Specifically, each of a sequence of homoclinic bifurcation curves in the parameter plane is found to undergo a sharp turn, due to interaction between a two-dimensional unstable manifold and the one-dimensional slow manifold that persists from the singular limit. Local analysis using approximate Poincare maps shows that each turning point induces an inclination-fl...

Command-line cellular electrophysiology for conventional and real-time closed-loop experiments

BACKGROUND Current software tools for electrophysiological experiments are limited in flexibility and rarely offer adequate support for advanced techniques such as dynamic clamp and hybrid experiments, which are therefore limited to laboratories with a significant expertise in neuroinformatics. NEW METHOD We have developed lcg, a software suite based on a command-line interface (CLI) that allows performing both standard and advanced electrophysiological experiments. Stimulation protocols for classical voltage and current clamp experiments are defined by a concise and flexible meta description that allows representing complex waveforms as a piece-wise parametric decomposition of elementary sub-waveforms, abstracting the stimulation hardware. To perform complex experiments lcg provides a set of elementary building blocks that can be interconnected to yield a large variety of experimental paradigms. RESULTS We present various cellular electrophysiological experiments in which lcg has been employed, ranging from the automated application of current clamp protocols for characterizing basic electrophysiological properties of neurons, to dynamic clamp, response clamp, and hybrid experiments. We finally show how the scripting capabilities behind a CLI are suited for integrating experimental trials into complex workflows, where actual experiment, online data analysis and computational modeling seamlessly integrate. COMPARISON WITH EXISTING METHODS We compare lcg with two open source toolboxes, RTXI and RELACS. CONCLUSIONS We believe that lcg will greatly contribute to the standardization and reproducibility of both simple and complex experiments. Additionally, on the long run the increased efficiency due to a CLI will prove a great benefit for the experimental community.

Nonlinear behavioural model of charge pump PLLs

SUMMARY Despite the nonlinear nature of even the simplest versions of phase locked loops (PLLs), linear models are still used during the first phases of the design of modern PLLs. Even though the linear model may represent a crude approach, its use is justified by the fact that accurate numerical simulations often require a too large amount of CPU time, being PLLs by construction stiff circuits, characterised by very different time scales. This aspect has triggered the need for compact models that allow fast and accurate numerical simulations. The scientific literature numbers several models that have been developed with different approaches and tailored to different simulation environments. In this context, we propose a nonlinear model of a type-II PLL, which (1) considers both the switching behaviour of the phase/frequency detector and charge pump and the complex dynamics (including the presence of amplitude and phase noise) of the voltage controlled oscillator, (2) is compact and can be easily implemented in modern mixed analog/digital simulators as a behavioural block, and (3) allows the simulation of spurs owing to the nonlinearities of both the charge pump and the fractional frequency divider. Copyright

On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.

Inferring network dynamics and neuron properties from population recordings.

Understanding the computational capabilities of the nervous system means to “identify” its emergent multiscale dynamics. For this purpose, we propose a novel model-driven identification procedure and apply it to sparsely connected populations of excitatory integrate-and-fire neurons with spike frequency adaptation (SFA). Our method does not characterize the system from its microscopic elements in a bottom-up fashion, and does not resort to any linearization. We investigate networks as a whole, inferring their properties from the response dynamics of the instantaneous discharge rate to brief and aspecific supra-threshold stimulations. While several available methods assume generic expressions for the system as a black box, we adopt a mean-field theory for the evolution of the network transparently parameterized by identified elements (such as dynamic timescales), which are in turn non-trivially related to single-neuron properties. In particular, from the elicited transient responses, the input–output gain function of the neurons in the network is extracted and direct links to the microscopic level are made available: indeed, we show how to extract the decay time constant of the SFA, the absolute refractory period and the average synaptic efficacy. In addition and contrary to previous attempts, our method captures the system dynamics across bifurcations separating qualitatively different dynamical regimes. The robustness and the generality of the methodology is tested on controlled simulations, reporting a good agreement between theoretically expected and identified values. The assumptions behind the underlying theoretical framework make the method readily applicable to biological preparations like cultured neuron networks and in vitro brain slices.

Piecewise-linear approximation of the Hindmarsh-Rose neuron model

This paper is concerned with the approximation of the Hindmarsh and Rose neuron model, which is able to reproduce the main neuronal behaviours, in view of its circuit implementation. The method is based on two main tools: a piecewise-linear approximation technique and bifurcation analysis. The piecewise-linear approximation of the Hindmarsh and Rose model is obtained by solving a mixed-integer optimization problem by a genetic algorithm. The result obtained exhibits a good degree of similarity to the original model, both from a qualitative and a quantitative standpoint.