Downloaded 24 times
![Population-level dynamics
• Keller-Segel model for chemotaxis
• Advection velocity
• Chemotactic potential f[s] determines
response to attractant concentration s
• Keller-Segel (1971)
f[s]=log[s]
• Lapidus-Schiller (1976)
Receptor law
f[s]=s/(s+k), k constant
v(x) = c[s(x)]
ds(x)
dx
º
df[s(x)]
dx
Rhodobacter sphaeroides in oxygen gradient
Bacterial band
E. Coli chemotactic rings
¶r(x,t)
¶t
= D
¶2
r(x,t)
¶x2
-
¶
¶x
c[s(x)]
ds(x)
dx
r(x,t)
é
ëê
ù
ûú
Tindall, M. J., Maini, P. K., Porter, S. L., & Armitage, J. P. (2008). Bulletin of Mathematical Biology 70, 1570–1607
v(x)](https://image.slidesharecdn.com/giomettoslides-160628155919/75/A-generalized-receptor-law-governs-phototaxis-in-the-phytoplankton-Euglena-gracilis-Giometto-Altermatt-Maritan-Stocker-Rinaldo-6-2048.jpg)
![r(x) =
r(x)
r(-L)
= exp
f[I(x)]
D
é
ëê
ù
ûú
Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050
Stationary algal distribution
Keller-Segel-like phototaxis model
¶r(x,t)
¶t
= D
¶2
r(x,t)
¶x2
-
¶
¶x
df[I(x)]
dx
r(x,t)
é
ëê
ù
ûú
Population-level dynamics
f(I) = Dlog r[x(I)][ ]
Phototactic potential
v(x)
Measured
Measured](https://image.slidesharecdn.com/giomettoslides-160628155919/75/A-generalized-receptor-law-governs-phototaxis-in-the-phytoplankton-Euglena-gracilis-Giometto-Altermatt-Maritan-Stocker-Rinaldo-20-2048.jpg)
![Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050
Phototactic potential
Measured in the
experimentsTypical irradiance
at sea level
f(I) = Dlog r[x(I)][ ]
Lightintensity
r(x) =
r(x)
r(-L)
= exp
f[I(x)]
D
é
ëê
ù
ûú
Infer f from dataStationary algal distributions](https://image.slidesharecdn.com/giomettoslides-160628155919/75/A-generalized-receptor-law-governs-phototaxis-in-the-phytoplankton-Euglena-gracilis-Giometto-Altermatt-Maritan-Stocker-Rinaldo-21-2048.jpg)
![Generalized Receptor Law
f(I) = aI
Ic - I
Ir + I
Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050
Phototactic potential
r(x) =
r(x)
r(-L)
= exp
f[I(x)]
D
é
ëê
ù
ûú
v(x) = c[s(x)]
ds(x)
dx
º
df[s(x)]
dx
f(I) = Dlog r[x(I)][ ]](https://image.slidesharecdn.com/giomettoslides-160628155919/75/A-generalized-receptor-law-governs-phototaxis-in-the-phytoplankton-Euglena-gracilis-Giometto-Altermatt-Maritan-Stocker-Rinaldo-22-2048.jpg)
![Phototactic potential
Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050
r(x) =
r(x)
r(-L)
= exp
f[I(x)]
D
é
ëê
ù
ûú
Generalized Receptor Law
f(I) = aI
Ic - I
Ir + I](https://image.slidesharecdn.com/giomettoslides-160628155919/75/A-generalized-receptor-law-governs-phototaxis-in-the-phytoplankton-Euglena-gracilis-Giometto-Altermatt-Maritan-Stocker-Rinaldo-23-2048.jpg)
Uploaded byLake Como School of Advanced Studies
A generalized receptor law governs phototaxis in the phytoplankton Euglena gracilis - Giometto, Altermatt, Maritan, Stocker, Rinaldo
The document discusses a study that found a generalized receptor law governs phototaxis in the phytoplankton Euglena gracilis. The study used experiments and modeling to determine that phototactic behavior in Euglena gracilis follows a generalized receptor law, where phototactic potential is determined by a function of light intensity divided by a constant plus intensity. This receptor law provided good agreement with measured distributions of algae in experiments with different light intensities and qualities.
A generalized receptor law governs phototaxis in the phytoplankton Euglena gracilis - Giometto, Altermatt, Maritan, Stocker, Rinaldo
- 1. A generalized receptorlaw governs phototaxis in the phytoplankton Euglena gracilis Giometto, Altermatt, Maritan, Stocker, Rinaldo © Micronaut, Martin Oeggerli
- 2. Phytoplankton • Primary producersin aquatic habitats • Major sink for atmospheric carbon dioxide • Inhabit the photic zone of the water column © ESA, 2012
- 3. Active movement Cilia /flagella Buoyancy control Response to environmental cues Chemotaxis Gravitaxis Phototaxis Phytoplankton movement Donat P. Häder
- 4. Phototactic algae: typicalfeatures • Photopigments • Stigma • Spiral swimming Euglena and Chlamydomonas sketches from: Jékely, G. (2009). Phil Trans R Soc B 364, 2795-2808 Video from: J. Vidyadharan and K. Foster, http://fosterlab.syr.edu
- 5. Volvox carteri Drescher, K.,Goldstein, R. E., & Tuval, I. (2010). PNAS, 107, 11171–11176
- 6. Population-level dynamics • Keller-Segelmodel for chemotaxis • Advection velocity • Chemotactic potential f[s] determines response to attractant concentration s • Keller-Segel (1971) f[s]=log[s] • Lapidus-Schiller (1976) Receptor law f[s]=s/(s+k), k constant v(x) = c[s(x)] ds(x) dx º df[s(x)] dx Rhodobacter sphaeroides in oxygen gradient Bacterial band E. Coli chemotactic rings ¶r(x,t) ¶t = D ¶2 r(x,t) ¶x2 - ¶ ¶x c[s(x)] ds(x) dx r(x,t) é ëê ù ûú Tindall, M. J., Maini, P. K., Porter, S. L., & Armitage, J. P. (2008). Bulletin of Mathematical Biology 70, 1570–1607 v(x)
- 7. Tindall, M. J.,Maini, P. K., Porter, S. L., & Armitage, J. P. (2008). Bulletin of Mathematical Biology 70, 1570–1607
- 8. Tindall, M. J.,Maini, P. K., Porter, S. L., & Armitage, J. P. (2008). Bulletin of Mathematical Biology 70, 1570–1607
- 9. © Micronaut, MartinOeggerli Phototactic potential? Euglena gracilis Eyespot absorption spectrum B R Strother, G., and Wolken, J. (1961) J. Protozool. 8
- 10. Giometto, A., Altermatt,F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050
- 11. Red LED RedLED Red light Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 12. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 13. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 14. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 15. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 16. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 17. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 18. Blue light Blue LED Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Algaldensity (re-normalized)
- 19. Giometto, A., Altermatt,F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050
- 20. r(x) = r(x) r(-L) = exp f[I(x)] D é ëê ù ûú Giometto,A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Stationary algal distribution Keller-Segel-like phototaxis model ¶r(x,t) ¶t = D ¶2 r(x,t) ¶x2 - ¶ ¶x df[I(x)] dx r(x,t) é ëê ù ûú Population-level dynamics f(I) = Dlog r[x(I)][ ] Phototactic potential v(x) Measured Measured
- 21. Giometto, A., Altermatt,F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Phototactic potential Measured in the experimentsTypical irradiance at sea level f(I) = Dlog r[x(I)][ ] Lightintensity r(x) = r(x) r(-L) = exp f[I(x)] D é ëê ù ûú Infer f from dataStationary algal distributions
- 22. Generalized Receptor Law f(I)= aI Ic - I Ir + I Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Phototactic potential r(x) = r(x) r(-L) = exp f[I(x)] D é ëê ù ûú v(x) = c[s(x)] ds(x) dx º df[s(x)] dx f(I) = Dlog r[x(I)][ ]
- 23. Phototactic potential Giometto, A.,Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 r(x) = r(x) r(-L) = exp f[I(x)] D é ëê ù ûú Generalized Receptor Law f(I) = aI Ic - I Ir + I
- 24. Giometto, A., Altermatt,F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Temporal dynamics
- 25. • Modeling verticaldistribution of phytoplankton • Harvesting in photobioreactors • Transport of colloidal particles Giometto, A., Altermatt, F., Maritan, A., Stocker, R., and Rinaldo, A., (2015) PNAS 112:7045-7050 Possible applications
- 26. Coauthors Amos Maritan, RomanStocker, Florian Altermatt, Andrea Rinaldo Funding Eawag Discretionary Funds Swiss National Science Foundation Thank you!
- 30. Euglena picture: http://www.dr-ralf-wagner.de/ Absorptionspectra: Strother, G., and Wolken, J. (1961) J. Protozool. 8 Eyespot absorption spectrum Chloroplast absorption spectrum B B R R Study species: Euglena gracilis 30
Editor's Notes
- #3 Very important organisms because they play a HUGE ROLE IN THE CYCLING OF CARBON DIOXIDE from the atmosphere to the biosphere and back, and this cycling helps to control Earth’s climate. PHOTOSYNTESIZE, sink for carbon dioxide (estimated 100 Gt C / year) Even though they account for less than 1% photosynthetic biomass on Earth, they contribute HALF OF THE WORLD'S TOTAL PRIMARY PRODUCTION--- as important as all the world's land plants combined. BLOOMS, BIOLOGICAL PUMP. Great blooms of oceanic algae are great sinks for carbon dioxide. Much of which is then TAKEN DEEP INTO THE OCEAN with them when they die (15% of organic material produced in the sunlit layer is pumped to the deep sea). Their fossilized remains, buried and compressed by geological forces, are transformed into oil, the dense liquid of carbon that we use to fuel our cars. Oxygen-producing photosynthesis only occurs in organisms that have CHLOROPHYLL A. This pigment enables the PHYTOPLANKTON TO ABSORB BLUE LIGHT, which would otherwise be scattered by the sea water. The more phytoplankton there are in an area of ocean, the more chlorophyll a there is and the darker the area appears from space. A special group of plankton are coccolithophores. These tiny organisms generate very thin plates of calcium carbonate known as coccoliths. Coccoliths reflect light in a unique way turning the color of the water into a bright, milky aquamarine during intense blooms, which can be seen from space. BASIS OF MARINE FOOD WEB, food for primary consumers (zooplankton). Phytoplankton PROVIDE ORGANIC MATTER for the organisms that comprise the vast majority of marine life. Inhabit TOP SUNLIT LAYER of the ocean.
- #4 Some dinoflagellates travel 35m every day Buoyancy: oil droplets, gas vacuoles Optimization of photosyntesis Avoidance of photodamage OPPOSING GRADIENTS OF LIGHT AND NUTRIENTS
- #5 Essential features: SPIRAL SWIMMING Body rotates on its longitudinal axis PHOTOPIGMENTS Generate ion currents, influx of ions to flagellum STIGMA A shading body in the cell will result in the periodic illumination of the photopigments (located in the vicinity) in one part of the cell and trigger periodic signalling during axial rotation Unicellular algae compare light intensity signals at different points in time DESPITE THE IMPORTANCE OF PHOTOTAXIS FOR THE POSITIONING OF PHYTOPLANKTON IN THE WATER COLUMN, IT HAS NOT BEEN STUDIED VERY MUCH ESPECIALLY FROM THE BEHAVIORAL POINT OF VIEW
- #6 Colonial alga made of many autonomous cells that are capable of colony-level coordination. They showed that individual cells adapt the beating frequency in response to light and the colony needs to rotate to perform accurate phototaxis. In particular, the response kinetics and the natural spinning frequency of the colony appear to be tuned to give accurate phototactic behavior (demonstrated experimentally by reducing the colony spinning frequency by increasing fluid viscosity). Spinning is desirable in the presence of adaptation. In fact, the cells on the surface may become adapted before the cell is oriented towards light. Spinning allows a continuous refinement of the swimming direction
- #7 We neglect growth of the population and consumption of the attractant S: attractant concentration Rho: density D: diffusion coefficient Phi: chemotactic potential Xi: Chemotactic coefficient Usually there is an equation for s[x,t] (diffusion and uptake by bacteria) in the case of chemoattractants This form of the chemotacticpotential embeds the fact that the response declines at low chemical concentrations and saturates at high concentrations The bacterial response of Rhodobacter sphaeroides to an oxygen gradient (aerotaxis) (Romagnoli, 2002). The bands of bacteria (marked by the arrow) can be seen on the left of the photo as they move toward an optimal oxygen concentration away from the miniscus of the capillary (and the oxygen source) on the right. Here the tip of the arrow head is 1.3 mm away from the bottom (left hand edge) of the meniscus. (b) Swarm plates of E. coli showing the formation of concentric bacterial rings (Armitage Laboratory). The petri dish has a diameter of 90 mm.and The effects that the functional form of the bacterial chemotactic χ(s) and diffusion µ coefficients, and to some degree, the rate of nutrient consumption have on the bacterial distribution has been explored by a number of authors. Models of this kind have been proposed to describe phototaxis, but relied on unrealistic assumptions concerning the potential phi Receptor law assumes the chemotactic force to be proportional to the gradient of the relative occupation of membrane receptors and the corresponding time constants. K is a constant determined by the characteristic mean time of receptor occupation. If an anaerobically utilizable energy source such as galactose is present in excess over the oxygen, the first band consumes all the oxygen and a part of the sugar and the second band uses the residual sugar anaerobically. On the other hand, if oxygen is present in excess over the sugar, the first band oxidizes all the sugar and leaves behind unused oxygen, and the second band uses up the residual oxygen to oxidize an endogenous energy source. The essence of the matter is that the bacteria create a gradient of oxygen or of an energy source, and then they move preferentially in the direction of the higher concentration of the chemical. As a consequence, bands of bacteria (or rings of bacteria in the case of agar plates) form and move out. These results show that E. coli is chemotactic toward oxygen and energy sources such as galactose, glucose, aspartic acid, threonine, or serine
- #8 Tindall, M. J., Maini, P. K., Porter, S. L., & Armitage, J. P. (2008). Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations. Bulletin of Mathematical Biology, 70(6), 1570–1607. http://doi.org/10.1007/s11538-008-9322-5
- #12 To test that we didn’t have a confounding effects, we tested accumulation in the presence of red light
- #21 Vincent and Hill (1996): v(I)=v T(I), T(I) is a taxis response function. Williams and Bees, idem with v(I)=v/Ic (I-Ic) movement without light gradient!! Burkart Häder (1980) experiment with Phormidium uncinatum, v(I)=a log[b I(x)] no negative phototaxis! Movement without gradient! Torney and Neufeld (2008) v[dI/dx] = a dI/dx no negative phototaxi, no saturation
- #22 Vincent and Hill (1996): v(I)=v T(I), T(I) is a taxis response function. Williams and Bees, idem with v(I)=v/Ic (I-Ic) movement without light gradient!! Burkart Häder (1980) experiment with Phormidium uncinatum, v(I)=a log[b I(x)] no negative phototaxis! Movement without gradient! Torney and Neufeld (2008) v[dI/dx] = a dI/dx no negative phototaxi, no saturation
- #23 This form of the phototactic potential embeds the fact that the response declines at low light intensity, recheas a maximum at a preferred intensity and then there is a very strong negative response at higher intensities (harmful) I_c value of I that I consider as good as darkness and a combination of I_c and I_r gives the maximum of phi (the preferred I) The data allow to reject all assumptions that had been taken in the literature
- #26 Also AVOID BIOFOULING
- #32 Step-up in light intensity causes a decrease in flagellar activity on a very short timescale and a recovery to baseline activity on a longer time scale