For my parents For Anna For Davide 1

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For my parents

For Anna

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Abstract

A vast amount of experimental evidence hints that astrocytes could be active players in information processing of the brain. It remains unclear nevertheless how these cells could encode synaptic stimuli through variations of their intracellular Ca2+_{levels as well}

as how they could influence the timing of neuronal activity. In this study, we adopt a dynamical system approach and use tools of bifurcation theory and statistics in order to address both these issues. We consider a Li-Rinzel description of astrocyte Ca2+

sig-nalling and we show that thanks to specific choices of biophysical parameters, synaptic activity could be encoded by modulations of Ca2+ _{oscillations in amplitude (AM), in}

frequency (FM), or in both (AFM). Interestingly, AM- and FM-encoding pertain to dif-ferent classes of Ca2+_{excitability that are reminiscent of the analogous neuronal ones. In}

addition, any transition from AM to FM and viceversa is accomplished through a char-acteristic “Bautin-cusp” bifurcation sequence which could hint the conditions for the coexistence of both these encoding modes. Such a possibility is throughout investigated and eventually formalized in the “CPB rule”, a heuristic criterion valid for any system of the Li-Rinzel type that allow us to determine several biophysical conditions under which AFM Ca2+ _{dynamics could occur in astrocytes. Successively, we demonstrate}

that different encoding modes could be accomplished not only on the basis of inher-ent heterogeneities of cellular properties but also thanks to the existence of differinher-ent (opposite) Ca2+ _{feedbacks on IP}

3 production. In this regard we modify the Li-Rinzel

system in order to include a third equation for IP3 metabolism which also considers

Ca2+ _{activation of PLC (positive feedback) and Ca}2+ _{activation of IP}

3 3-kinase

(neg-ative feedback). In agreement with experimental data and recent theoretical studies, our analysis hints that Ca2+_{-dependent activation of PLC could account for a much}

richer variety of oscillatory regimes and encoding modes with respect to the case of negative feedback. An inspection of the parameter space reveals that this is possible because positive Ca2+ _{feedback on IP}

3 production modifies the structure of the system

towards the appearance of multistationarity which could also account for Ca2+ _dynamics

of bursting type. Moreover, we show that the lifetime of IP3 could be a critical limiting

factor for the effects of both feedbacks. Meaningfully, IP3 turnover could influence the

integrative properties of astrocytic Ca2+ _{signalling by affecting both the frequency band}

of Ca2+ _{oscillations and the threshold stimulus for their onset. In addition, IP}

3 turnover

could regulate the expression of mGlu receptors on the astrocyte plasma membrane. 2

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In this regard, we show that the density of mGlu receptors could be proportional to the rate of IP3 turnover and accordingly we provide an estimation of this parameter

which otherwise would remain experimentally unknown. In particular, on the basis of our bifurcation data, we estimate that AM-encoding astrocytes could express an average mGluR density between 1–50 receptors/µm2 _{that is of the same order of AMPA}

recep-tor density measured on Bergmann glia somas. We show however that FM-encoding astrocytes could be consistent with an overexpression of mGluRs by a factor of 8 or 10 with respect to AM-encoding cells. In the last part of our study, we finally consider the characterization of the possible integrative properties of astrocyte Ca2+ _signalling

and the effects of astrocytic Ca2+_{-dependent glutamate exocytosis on neuronal activity.}

For this purpose we develop a mathematical description of neuron-glial interactions at the level of a single astrocytic microdomain in which our modified Li-Rinzel model of astrocyte Ca2+_/IP

3 dynamics is coupled with an ensemble of Tsodyks-Uziel-Markram

synapses on the soma a regular spiking Izhikevich neuron. We show that astrocytes of different classes of excitability could respond differently to stimuli of equal intensities and identical interspike-interval (ISI) statistics. On the other hand, stimuli at the same frequency but with different ISI statistics could trigger distinct Ca2+_{responses in cells of}

the same type. All these possibilities are also dependent on the nature of the stimulatory pathway. Astrocyte Ca2+ _{signalling could therefore result from a complex integration of}

spatiotemporal features of synaptic stimuli which could represent a form of processing of neuronal activity. Perhaps even more intriguingly, Ca2+ _{signals could encode}

infor-mation on the past history of synaptic activity which in turn would be transferred back to neuron through Ca2+_{-dependent glutamate exocytosis with deep consequences on the}

informational content of postsynaptic neuronal activity. Computation of Fano Factors on simulated time series of postsynaptic action potentials reveal in fact that neuron-astrocyte interactions could substantially affect the rate of neuronal firing by adding long-range correlations to the timing of neuronal spikes. These results are consistent with the possibility that neuron-astrocyte bidirectional signalling could influence infor-mation processing of the brain by increasing the inforinfor-mation-coding dimension of the neural code.

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Declaration

This dissertation is the result of my own work, except where explicit reference is made to work of others, and has not been submitted for another qualification to this or any other university.

Maurizio De Pitt`a

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Acknowledgements

I am deeply indebted to my supervisors, Professor Danilo De Rossi, Professor Eshel Ben-Jacob (Tel Aviv University, Israel), Dr. Giovanni Pioggia and Dr. Vladislav Volman (Uni-versity of California at San Diego, CA, USA) for their guidance and support throughout this work. All of them equally contributed to my passion for Neuroscience and made unique the experience behind this thesis. I am very grateful to them for many inspiring discussions as well as for their constructive criticism, their meaningful advices and their enthusing suggestions.

I wish also to thank sincerely Prof. Vladimir Parpura (University of California at River-side, CA), Prof. Giorgio Carmignoto and Dr. Micaela Zonta (University of Padua, Italy) for enlightening conversations on many aspects of the physiology of neuron-glial inter-actions.

I am grateful to Prof. Bard Ermentrout (University of Pittsburg, PA), Prof. Jonathan Lytton (University of Calgary, Canada), Prof. Thomas C. S¨udhof and Dr. Ilya Bezproz-vanny (University of Texas Southwestern Medical Center at Dallas, TX), Dr. Michail Sta-matakis (Rice University, TX), Dr. Tommaso Fellin (University of Pennsylvania School of Medicine, PA), Dr. Maria Cecilia Angulo (Laboratoire de Neurophysiologie et Nou-velles Microscopies, CNRS FRE 2500, Paris) and Dr. Alfonso Araque (Instituto Cajal, CISC, Madrid) for providing original ideas, experimental data, figures and software in-cluded in this thesis.

I benefited much of technical assistance from Dr. Bart Soutois (University of Gent, Belgium), Dr. Einat Bielopolsky (Tel Aviv University, Israel), and Dr. Marcello Ferro (University of Pisa, Italy).

During my stay at Tel Aviv University I enjoyed daily conversations with Dr. Na-dav Raichmann, Noga Yaniv, Dr. Raya Sorkin, Dr. Einat Fuchs, Dr. Liel Rubinsky and Dr. Mark Shein. In this regard, I would like to thank Tel Aviv University for hos-pitality and especially Ms. Kineret Ben-Knaan and Mrs. Dikla Lubaton for their help with Israeli bureaucracy.

I am also grateful to Dr. Aleandro Mariotti (Servizio Bibliotecario, Faculty of Engineer-ing, University of Pisa, Italy) for his assistance in seeking part of the reference at the basis of this work.

During these academic years life has been challenging. Many people have contributed to my growth, my education, my ethics and my karma but among all I am mostly

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indebted to Dr. Eugenio Poggetti, Dr. Giorgio Tazzioli and Dr. Maria Fiorenza Lollo, Prof. Claudio Casarosa, Prof. Bruno Pellegrini and Prof. Maurizio Ciampa.

My life would be meaningless without my friends who fill it with their advices, jokes and conversations. I deeply thank Anna, Giovanna, Daniele, Alessandro, Antonio, Silvia and Claudia, Marco and Claudia, Cristina, Giulia, Brunello and Stefania, Niccol`o and Alvise, Paolo, Claudio, Pietro, Dario, Alex, Marco, Luca and Matteo and the Serraglini family.

Finally, my last words are for my parents. This thesis and all the history behind it have been made possible by their (almost) constant support. Thanks.

This research has been partially supported by the Tauber Fund at Tel Aviv University, and the University of Pisa Scholarship for students who carry out their MSc research abroad.

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Preface

This thesis approaches the study of neuron-glial interactions from a computational per-spective. Two aspects are considered in particular, these are how calcium signalling in astrocytes could integrate and encode synaptic stimuli and how astrocytes could affect information processing of neuronal activity.

The essential physiology of neuron-astrocyte interactions is summarized in Chapter 1 with particular attention to glutamatergic signalling. This chapter ends with the intro-duction of the concept of “tripartite synapse” which emblematically describes the tight interactions between synaptic terminals and their surrounding astrocytic processes.

Chapter 2 focuses on modelling of neuron-glial interactions and probably constitutes the main theoretical effort of this study. Through four sections, named respectively as “The synapse”, “The interaction pathway neuron-to-astrocyte”, “The astrocyte” and “The interaction pathway astrocyte-to-neuron”, a mathematical description of tripartite synapse is introduced together with an extensive estimation of the physiological ranges of all the parameters of the model. The last part of this chapter also reviews and dis-cusses preexisting models of the tripartite synapse by comparing these latter with ours. Chapter 3 introduces the results of our study on dynamical properties of astrocyte calcium signalling. Tools of bifurcation theory are extensively adopted to characterize calcium encoding of synaptic stimuli. In this regards, this chapter consists of two main parts. In the first section the Li-Rinzel model of calcium dynamics is considered with the aim to characterize astrocyte calcium signalling on the basis of inherent cellular prop-erties. The hypothesis of different classes of astrocyte excitability is discussed together with the theoretical bases for the existence of AM-, FM- or AFM-encoding calcium os-cillations. In the following section instead, the Li-Rinzel model is modified in order to investigate the dynamical consequences following the inclusion of calcium feedbacks on the metabolism of inositol 1,4,5-trisphosphate.

In Chapter 4 the tripartite synapse model introduced in Chapter 2 is extended to ensembles of synapses ensheathed by the same astrocytic microdomain. Tables of pa-rameter values that were used in all the simulations considered in this thesis are also reported here at the very end of the last section.

Chapter 5 introduces the results of our study on the possible role of astrocytes in information processing of the brain. General consistency of our model with experimental data is first demonstrated as a premise for the following analysis. Successively, theo-retical investigations are carried out in order to characterize the possible integrative

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properties of astrocyte calcium signalling and the effects of this latter on the timing of neuronal firing.

Finally, discussion of the results and conclusions are in Chapter 6. Maurizio De Pitt`a

Venice, Italy

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Abbreviations:

AMPA Amino-3-hydroxy-5-methyl-4-isoxazole propionic acid AMPAR (NMDAR) AMPA (NMDA) receptor

AP Action potential

AP5 d-2-amino-5-phosphonopentanoic acid

BAPTA 1,2-bis(o-aminophenoxy)ethane-N,N,N’,N’-tetraacetic acid

BG Bergmann glia

CICR Calcium-induced calcium release CNQX 6-cyano-7-nitroquinoxaline-2,3-dione

EC50 Apparent half affinity/half maximal effective concentration

ER Endoplasmic reticulum

GPCR G-protein coupled receptor

(m)(E)PSC (miniature) (Excitatory) Postsynaptic current IP3R Inositol (1,4,5)-trisphosphate receptor

IP3K IP3 3-kinase

IP5P IP 5-phosphatase

LAP-4 l-(S)-2-amino-2-methyl-4-phosphonobutanoic acid mGluR Metabotropic glutamate receptor

MK-801 Dizocilpine

NMDA n-methyl-d-aspartatic acid

(NP)EGTA o-nitrophenyl ethylene glycol tetraacetic acid Pxx Post-natal days (for rats/mice used in experiments)

pSD Presynaptic depression

PSD Postsynaptic density

SERCA Sarco(endo)plasmic-reticulum Ca2+_-ATPase

Syt Synaptotagmin

TTX Tetrodoxin

VGLUT Vesicular glutamate transporter

Concentrations of chemical substances are indicated by case letters whereas calligraphic style is adopted to denote the number of molecules of a chemical substance.

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For my parents For Anna For Davide 1

Abstract

Declaration

Acknowledgements

Preface

Contents