Structural and fu functional properties of f a nervous system: : Modelling tadpole lo locomotor behaviour in in response to sensory ry sig ignals Roman Borisyuk, Andrea Ferrario University of Exeter, UK Robert Merrison-Hort City Research, Exeter UK In collaboration with neurobiological laboratories of Alan Roberts, Steve Soffe ( University of Bristol ) Wenchang Li ( University of St. Andrews )
Outline • Introduction: structure and function of Neural Network (NN) • Hatchling Xenopus tadpole is a unique animal to study structure and function of NN • Developmental approach: axon grows and pair-wise connectivity • Probabilistic model: generalisation from anatomical modelling • Biologically realistic modelling of the tadpole nervous system • Conclusions
Introduction • Information processing in the brain is based on communication between spiking neurons that are embedded in a network of connections (current dogma). • A resulting NN (Neuronal Circuit) is a traditional object for mathematical/computational modelling. https://deskarati.com/2011/12/19/new-wonder-drug-could-give-us-all-super-memory/
Introduction • Information processing in the brain is based on communication between spiking neurons that are embedded in a network of connections (current dogma). • A resulting NN (Neuronal Circuit) is a traditional object for mathematical/computational modelling. https://deskarati.com/2011/12/19/new-wonder-drug-could-give-us-all-super-memory/
Introduction To design a Neural Network (NN) model the following three key characteristics have to be specified: • Description of unit ’s dynamics • Connectivity (interactions) between units • Learning rule (adjustment of connection strength) – we do not consider learning in our model After that, the dynamics of neural activity can be simulated and activity patterns can be investigated. From mathematical point of view, the NN activity is a solution of a large system of ODEs (or DDEs or stochastic DDEs).
Unit (Neuron) Activity: Action Potential (Spike) Hodgkin-Huxley model (1952, Nobel Prize) 50 0 V -50 -100 0 5 10 15 20 25 30 35 40 dV t 1 3 4 C g m h ( V E ) g n ( V E ) g ( V E ) I n 0.5 Na Na K K L L app dt 0 0 5 10 15 20 25 30 35 40 t 1 dn m 0.5 ( V ) n n ( V ) n 0 0 5 10 15 20 25 30 35 40 dt t 1 h 0.5 dm V m m V ( ) ( ) 0 0 5 10 15 20 25 30 35 40 m t dt dh ( V ) h h ( V ) h dt Action Potential
There are two major connection types: Chemical synaptic connection Electrical coupling (gap junction) http://www.ncbi.nlm.nih.gov/books/NBK11164/
Connections and spiking From modelling point of view, there are two major types of synaptic connections: excitatory and inhibitory connections. It means that a probability of action potential increases or decreases respectively. However, the neurobiology is much more complicated than this simple modelling scheme. For example, the Post- Inhibitory Rebound (PIR) mechanism provides a possibility to generate an action potential after inhibition:
Action potential Response to a short excitatory current injection and threshold property Post-Inhibitory Rebound: Spike is generated after inhibitory current injection
A large number of connections Connections between units (connectome) is the most difficult part of NN specification. • Usually, the number of units (N) is large and the number of connections grows as N 2 . Therefore, finding the connection architecture is a complex experimental problem. • Theoretically, standard approaches of dimensionality reduction (e.g. from statistical physics) are not applicable because the neurons and their interactions are heterogeneous. There are many different types of neurons with specific properties for each cell type. • Also, synaptic transmission is a very complex machinery with multiple interactive stochastic processes and components.
Variability of connectomes • It is known that brain development involves multiple stochastic processes and the individual connectomes are all different . • Although, in most animals, the brain connectivity varies between individuals, behaviour is often similar across species. Other words, despite differences in connectivity , most individuals under normal conditions are able to demonstrate similar functionalities.
Model of the nervous system • Difference in connectivity - similarity on functionality means that different connectomes include sufficient key structural features to produce a common repertoire of functionalities and behaviours. • What are the key connectivity properties that define the network functionality? • Motivated by this question, we developed a model of pair- wise connectivity in the nervous system of the hatchling Xenopus tadpole which, when combined with a spiking model of the Hodgkin-Huxley type, reliably reproduces appropriate motor behaviours mimicking the interaction with external environment. • This biologically realistic model ( VIRTUAL TADPOLE) can be used as a computational platform to crack a structure- function puzzle and find the key functional properties defining similarity of individual behaviours.
Xenopus tadpole spinal cord CPG 5mm long There are 3 types of CPG neurons (ascending and descending interneurons (aIN and dIN) as well as commissural interneurons (cIN). Motor neurons (mn). There are 3 types of sensory pathway interneurons: touch skin sensors (RB), dorso-lateral ascending and commissural neurons (dla and dlc).
Spinal cord CPG We start from studying the connectivity and spiking activity of spinal cord neuronal circuit in 2-day old Xenopus tadpoles . ~ 1500 neurons, 90K synapses and two behaviours: swimming and struggling
2D plan of tadpole spinal cord
Can sim imple le rule les control development of a pio ioneer vertebrate neuronal network generating behavior? A. Roberts, D. Conte, Mike Hull, R. Journal of Neuroscience Merrison-Hort, A. Azad, E.Buhl, R.Borisyuk, S.R. Soffe (2014) Journal of Neuroscience J of Neuroscience, 34: 608-621
From Connectome to Swimming Function • Conductance based model of the Hodgkin- Huxley type. • Connections between neurons are defined by the generated connectome. • There are several characteristic electro- physiological features typical for tadpole swimming pattern (e.g. post-inhibitory rebound of dIN neurons, NMDA synapses). • Model includes both electrical and synaptic connections, delays and noise in the parameters. Experiment: swimming on touch Roberts et al, J of Neurosci, 2014
Swimming Pattern Stimulus is here Left Right
Sensory pathways Photo receptors Touch skin Touch head Head pressure Li, Wagner, Porter, 2014 J Undergraduate Neuroscience Education
Initiation of swimming Bi-stability: Short-term 0.45 Anti-phase 0.4 stimulation moves system cIN 0.35 from a stable equilibrium 0.3 0.25 to stable oscillations Anti-phase 0.2 Touch skin population activity dIN 0.15 0.1 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 STIMULUS 0.04 0.035 0.03 0.025 0.02 0.015 0.01 Left side motor neuron population activity 0.005 and right side motor neuron population activity 0 200 300 400 500 600 700 800 900 1000 time
Stopping Swimming tadpoles stop when their head bumps into the water’s surface or objects like vegetation and the side of a dish Can stop spontaneously and sink down to the ground Roberts, Li, Soffe, 2010 Front Behavioral Neuroscince http://frogsaregreen.org/tag/froglet/
Struggling (escaping) behaviour Struggling is a slower, stronger series of rhythmic alternating trunk flexions seen while tadpoles are grasped by predators. https://www.youtube.com/watch?v=SJiwcRt-gQw https://www.youtube.com/watch?v=knlXTU1R_rE Roberts, Li, Soffe, 2010 Front Behavioral Neurosc
Locomotor actions in the model of the nervous system The repertoire of possible locomotor actions of the model includes: • (a) start swimming (on sensory signal or spontaneously); • (b) stop swimming (on sensory signal or spontaneously); • (c) accelerating swimming; • (d) struggling is not included yet Roberts, Li, Soffe, 2010 Front Behavioral Neuroscience
Model of the nervous system • We consider three sensory pathways : Skin Touch (ST), Head Touch (HT), and Head Pressure (HP). The hind brain decision making population processes the sensory information and sends a signal to CPG – to swim or not to swim. • The total number of neuronal populations (neuronal types) K=12. The number of neurons in the model is about 2000. The total number of connections is about 100K. • We design the biologically realistic model of connectivity and functionality. Building the model, we use a numerous data to reproduce activity patterns of initiation, continuation, acceleration and termination of swimming.
Tadpole Nervous System Nervous system model includes sensory pathways, decision-making populations (hIN) and CPG neurons.
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