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How do sperm find the egg? Cross-fertilization of
theory and experiment
Jan F. Jikeli1, Luis Alvarez1, Benjamin M. Friedrich2, Laurence G. Wilson3 1 CAESAR, Bonn 2 Max Planck Institute for the Physics of Complex Systems 3 University of York, Department of Physics
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How do sperm find the egg?
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The search environment matters
Internal fertilization
© Eisenbach lab
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The search environment matters
© Rene Pascal, CAESAR
10 cm
100 mm
Internal fertilization
External fertilization
© Eisenbach lab
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Idealization: sperm path are persistent random walks
Friedrich et al.: Physical Biology (2008)
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Given an initial target distance R0 and finite search time ts, there is an optimal persistence length lp*
Search along persistent random walks
Friedrich et al.: Physical Biology (2008)
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Autonomous motility control
[Kaupp et al. 2005]
XXX
motility
sensing
© Rene Pascal, CAESAR
Close to the egg, there is true navigation
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The egg releases chemical guidance cues
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Theory: Sperm from marine species steer along helical paths
Friedrich et al.: PNAS (2007) Friedrich et al.: NJP (2008) Friedrich et al.: PRL (2009)
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Measuring concentration = Counting molecules
Concentration sensing is subject to strong shot noise
time
detecting single molecules
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We showed that navigation is adapted to tolerate noise
noise-free steering response
response to signaling noise
noise-induced drift
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How to measure a gradient?
exploitation exploration
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Gradient sensing strategies are adapted to noise level
Alvarez, Friedrich, Gompper, Kaupp: Trends Cell Biol. (2014) Berg, Purcell: BPJ (1977)
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Tiny bacteria can keep their direction only for a few seconds
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Slow slime molds have sufficient time for spatial comparison
Berg, Purcell: BPJ (1977)
signal-to-noise ratio
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Navigation strategies of cells are adapted to noise level
Alvarez, Friedrich, Gompper, Kaupp: Trends Cell Biol. (2014) Berg, Purcell: BPJ (1977)
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Let’s consider the simpler 2d case
How does steering along circular paths work?
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Sperm swim along circular paths close to boundaries
BMF, I Riedel-Kruse, J Howard, F Jülicher, J exp Biol 213, 2010
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Theory: Sperm measure concentration along circular paths
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concentration stimulus
Theory: Sperm measure concentration along circular paths
swimming path
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concentration stimulus
A signalling system transfers the stimulus into steering
50 µm
swimming path
path curvature
minimal description
as adaptation module
signalling system
inside sperm flagellum
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Stimulus oscillations elicit curvature oscillations
swimming path
concentration stimulus path curvature
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Theory of sperm chemotaxis
Friedrich, Jülicher: PNAS (2007)
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Sperm measure concentration
along circular paths and dynamically
adjust their beat
in a precisely timed manner
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Steering feedback aligns helical paths with the gradient
Friedrich, Jülicher: PNAS (2007)
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How to test the theory?
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3D-tracking from 2D-holographic images
z
y
x 2D-diffraction pattern
coherent laser light
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Numerical reconstruction of 3D-light beam
z
y
x
Rayleigh Sommerfeld back-propagator
2D-diffraction pattern
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Sperm swim along helical paths
Jikeli*, Alvarez*, Friedrich*, …, Kaupp: Nature Comm 6, 2015 (*=equal contribution)
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How do sperm steer along helical paths?
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Using light to “print” 3D concentration gradients
Chemoattractant with chemical cage UV light removes cage
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Using light to “print” 3D concentration profiles
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We compute how the concentration evolves in time
calibrated light intensity quantum yield diffusion coefficient
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Tracking a sperm cell in a 3D concentration profiles
UB Kaupp
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Helical paths bend in the direction of the local gradient
Jikeli*, Alvarez*, Friedrich*, …, Kaupp: Nature Comm 6, 2015
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We can extract the sensory-motor transfer function
Phase-locked oscillations with phase-lag of 167°±35°, close to the optimum value 180°
Cross-correlation
stimulus path curvature
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Theory and experiment of helical steering
swimming path
concentration stimulus path curvature
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Experiments prompt an extension of the theory
Small-amplitude oscillations of flagellar asymmetry
gradual helix alignment
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Experiments prompt an extension of the theory
Small-amplitude oscillations of flagellar asymmetry
gradual helix alignment
Large amplitude modulations of flagellar asymmetry
sharp turns
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Sharp turns are used in emergencies
Experiment
Jikeli*, Alvarez*, Friedrich*, …, Kaupp: Nature Comm 6, 2015
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Experiment and theory of adaptive feedback
Experiment Theory
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Thank you for your attention !
The experimental team Jan Jikely Luis Alvarez Laurence Wilson
René Pascal Rèmy Colin Magdalena Pichlo Andreas Rennhack Christopher Brenker
U Benjamin Kaupp