1. 1 System physiology – on the design Petr Marsalek Class: Advances in biomedical engineering Graduate course, biomedical engineering

2. 2 Outline, part 1 What is systems physiology; Description levels: Mathematics level; Physics level; Biology level Design of the model; (Case study 1 - ODE solver in Matlab, block design); ? Problems of reverse engineering; Engineering design inspired by biology; (Biomimetic engineering; Neuromimetic engineering; Bionics;)

3. Outline, part 2 Case study 2: Internet atlas of physiology and pathological physiology, demo.

4. 4 Outline, part 3 Case study 3: Model of the flight control in Drospohila Melanogaster (fruit fly) Introduction to flight circuit; Known facts; Power muscles and steering muscles; Neural circuitry, schematics of reflex arcs; Why is feedback needed, the aerodynamics engineer's standpoint; Design of the model; (Methods - ODE solver in Matlab, block design); Model tuning – sensory neurons emit one spike per wing cycle; Left and right wing, amplitude and phase differences; Modeling the saccade; Exploring parameter space of one "linear" equation; Limited options for the feedback and its function; Towards comparison of model output with real data; Concluding remarks

5. 5 Neural sensori-motor circuits

6. 6 Known facts Neural circuits consist of neurons talking to each other through synapses. Thoracic ganglion is a part of fly brain. Sensory inputs are visual, mechanical and others (like odors etc.). Motor outputs are realized by muscles. Motoneurons are last neurons in the circuit. Most of the reflexes are fast (< 5 ms). Some of the reflexes are monosynaptic. Halteres – are a pair of club-shaped organs in a dipteran insect that are the modified second pair of wings and function as sensory flight stabilizers. Drosophila is an example of dipteran insect with one pair of wings and with halteres. Compare e.g. to dragonfly of odonata with two pairs of wings. Flies have two types of flight muscles: (1) power muscles and (2) steering muscles. Experiments: (1) limited kinematics experiments: tethered flight, single wing preparation; (2) behavioral experiments: free flight Description of reflex arcs is based on anatomy of neural circuits.

7. 7 flight forces flight flight trajectory wing haltere Neural sensori-motor circuits MN haltere muscle SN wing muscle SN descending visual input

8. 8 flight forces flight flight trajectory wing haltere Neural sensori-motor circuits MN haltere muscle SN wing muscle SN descending visual input Reflex arcs of halteres

9. 9 flight forces flight flight trajectory wing haltere Neural sensori-motor circuits MN haltere muscle SN wing muscle SN descending visual input Reflex arcs of wings

10. 10 Function of Sensory Input in Flight Control (Circuit) Sensory neuron Mechanoreceptor transduction Motoneuron Muscle Wing Mechanical coupling Delay Synapse Master pacemaker? No Mechanical Resonance? Yes Nonlinear oscillator? Yes Other inputs, visual, from halteres, etc.

11. Model: Introduction of Leaky Integrator (= RC circuit with threshold)

12. Model: Leaky Integrator and Spring Equations

13. Model: Reordered Equations 1. Although leaky integrator and spring equations are linear, threshold, adaptation and mechanoreceptor currents are nonlinear, making the whole DE set nonlinear. 2. Spring equation is rewritten to its normal form to be fed into a custom written fixed step Runge-Kutta numerical DE solver (in Matlab).

14. Wings Model Left and right wing is coupled through variable stiffness K(t) to an oscillator = oscillating power muscle [Vilfan and Duke] ___

15. Wing amplitudes and traces of leaky integrator

16. Wing amplitudes and phases

17. Feedback formula K L (t) is time varying stiffness, g F is gain of the feedback,  L is wing phase. This is the formula for the left wing (L) and analogous formula is for the right (R). [Tu and Dickinson, 96]

18. Variables of a saccade

19. 19 Saccade [Fry et al, 2003]

20. Investigating parameter values: without and with feedback

21. Investigating parameter values: wing mass M=1 and M=2

22. 22 From model to data

23. Function of Sensory Input in Flight Control (Wish list) Things to do, hypotheses, … Theory: perturbation of the neural circuit will alter flight maneuvers. Theory: test some of the popular hypotheses (eg. delay line in wing input). Theory: what entrains/ perturbs wing rhythm?, phase lock, contributions… Theory: minimal alterations of circuit, not possible in experiments. Theory… (Theory: any new ideas mostly sought and welcome…) Theory: in general should (ideally) suggest interesting experiments. Experiments: should (ideally) suggest interesting theoretical questions. Experiments: calcium levels recording in mechanoreceptors and neurons. Experiments: electrophysiological recording in mech.receptors and neurons. Experiments: flight recording in mutants, in other Drosophila species.

24. Function of Sensory Input in Flight Control (Wish list) Things to do, hypotheses, … Theory: perturbation of the neural circuit will alter flight maneuvers. Theory: test some of the popular hypotheses (eg. delay line in wing input). Theory: what entrains/ perturbs wing rhythm?, phase lock, contributions… Theory: minimal alterations of circuit, not possible in experiments. Theory… (Theory: any new ideas mostly sought and welcome…) Theory: in general should (ideally) suggest interesting experiments. Experiments: should (ideally) suggest interesting theoretical questions. Experiments: calcium levels recording in mechanoreceptors and neurons. Experiments: electrophysiological recording in mech.receptors and neurons. Experiments: flight recording in mutants, in other Drosophila species. V +- V +- X +- X +-

25. 25 Conclusions 1 The aim of the project is to understand the function of sensory input in Drosophila flight control. 2 Equilibrium reflexes are described in experiments. Their underlying circuitry is mostly unknown. 3 Current model: coupling of mechanoreceptors to spiking of their sensory neuron. Closing of feedback loop from motoneuron to sensory neuron. 4 We described the parameter space and key variables involved in feedback and saccades. 6 What remains to do: to describe effects of feedback and steering in terms of flight aerodynamics, which is the experimental description level. 7 We will analyze new experimental data in near future.