1

System physiology – on the design

Petr Marsalek

Class: Advances in biomedical engineering

Graduate course, biomedical engineering

2

Outline, part 1What is systems physiology;Description levels:Mathematics level;Physics level;Biology levelDesign 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;)

Outline, part 2

Case study 2:Internet atlas of physiology and pathological

physiology, demo.

4

Outline, part 3Case study 3: Model of the flight control inDrospohila 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

Neural sensori-motor circuits

6

Known factsNeural circuits consist of neurons talking to each other throughsynapses. Thoracic ganglion is a part of fly brain. Sensory inputs arevisual, mechanical and others (like odors etc.). Motor outputs are realizedby muscles. Motoneurons are last neurons in the circuit.Most of the reflexes are fast (< 5 ms). Some of the reflexes aremonosynaptic.

Halteres – are a pair of club-shaped organs in a dipteran insect thatare the modified second pair of wings and function as sensory flightstabilizers. Drosophila is an example of dipteran insect with one pairof wings and with halteres. Compare e.g. to dragonfly of odonata withtwo pairs of wings.

Flies have two types of flight muscles:(1) power muscles and (2) steering muscles.Experiments: (1) limited kinematics experiments: tethered flight, singlewing preparation; (2) behavioral experiments: free flightDescription of reflex arcs is based on anatomy of neural circuits.

7

flightforces

flight

flight trajectory

wing

haltere

Neural sensori-motor circuits

MN

MN

haltere muscle

SN

wing muscle

SN

descendingvisual input

8

flightforces

flight

flight trajectory

wing

haltere

Neural sensori-motor circuits

MN

MN

haltere muscle

SN

wing muscle

SN

descendingvisual input

Reflex arcs of halteres

9

flightforces

flight

flight trajectory

wing

haltere

Neural sensori-motor circuits

MN

MN

haltere muscle

SN

wing muscle

SN

descendingvisual input

Reflex arcs of wings

10

Function of Sensory Inputin Flight Control (Circuit)

Sensory neuron

Mechanoreceptor transduction

Motoneuron

Muscle

Wing

Mechanical coupling

DelaySynapse

Masterpacemaker? NoMechanicalResonance? YesNonlinear oscillator? Yes

Other inputs,visual, from halteres, etc.

50 52 54 56 58 60 62 64 66 68 70-80

-70

-60

-50

time [ms] t

right voltage [mV] V Rleft voltage [mV] V L

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

THL for )( VVVdttV

L VVdt

dV RC

IVVgdt

dVg )( LLL

1L

Rg

Model: Leaky Integrator and Spring Equations

IVVxNpVVhgVVgdt

dVg ))(()()( Na0KALLL

)(SS Vhhdt

dhh

Fxkdt

dx

dt

xdm MRC2

2

TkxkE

xp

B

MRC

02

exp1

1)(

slope ,

half,

SS

exp1

11)(

h

h

V

VVVh

)(LfF

THL for )( VVVdttV

Model: Reordered Equations

IVVxNpVVhgVVgdt

dVg ))(()()( Na0KALLL

)(SS Vhhdt

dhh

Fxkydt

dym MRC

ydt

dx

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).

THL for )( VVVdttV

Wings Model

RR

RRRHR

LL

LLLHL

H2H

2HHHHHH

HHH2H

2HHHHHH

)(

)(

)(

)()(

wx

xtKwxw

wx

xtKwxw

yyxByExFy

xtKxyxByFxEx

Left and right wing is coupled through variable stiffness K(t) to an oscillator =

oscillating power muscle[Vilfan and Duke]

___

___

50 52 54 56 58 60 62 64 66 68 70

-0.5

0

0.5

power oscillator x Hright amplitude x Rleft amplitude x L

50 52 54 56 58 60 62 64 66 68 70-80

-70

-60

-50

time [ms] t

right voltage [mV] V Rleft voltage [mV] V L

Wing amplitudesand traces of leaky integrator

50 52 54 56 58 60 62 64 66 68 70

-0.5

0

0.5

power oscillator x Hright amplitude x Rleft amplitude x L

50 52 54 56 58 60 62 64 66 68 70

-0.5

0

0.5

time t [ms]

right phase Rleft phase L

Wing amplitudes and phases

55 60 65 70 75 80 85 90 95

-0.5

0

0.5

1left amplituderight amplitudephase differenceamplitude difference

55 60 65 70 75 80 85 90 95

-0.4

-0.2

0

0.2

0.4

time [ms]

left stiffness, = 0.5 msright stiffness, = 5 msalpha function, = 0.5 msalpha function, = 5 ms

Feedback formula1LFL for ),6.0)(()( iii ttttgtK

KL(t) is time varying stiffness, gF 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]

50 60 70 80 90 100

-0.5

0

0.5 left amplitude, x L

right amplitude, x R

power oscillator, x H

50 60 70 80 90 100

-0.5

0

0.5 left phase, L

right phase, R

50 60 70 80 90 100

-0.5

0

0.5 left stiffness, K L

right stiffness, K R

50 60 70 80 90 100-80

-70

-60

-50 left voltage, V

L right voltage, V

R

50 60 70 80 90 1000

10

20left relative spike timingright relative spike timing

Variables of a saccade

19

Saccade

[Fry et al, 2003]

Investigating parameter values: without and with feedback

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

gain g F, stiffness K

Amplitude

(magenta) amplitude, with feedback, varying gain(red) amplitude, no feedback, varying K

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

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

No feedback, amplitude in dependence on stiffness

stiffness K

(blue) amplitude, mass M=2(green) amplitude, mass M=1

22

From model to data

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.

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

X

X+-

25

Conclusions1 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.