Adaptation in bacterial chemotaxis
Adaptation in bacterial chemotaxis Massimo Vergassola UCSD, Physics Department
Three meanings of adaptation 1) Evolutionary. Increase of fitness
3) Desensitization. Filtering of constant stimuli (Block ‘82; Segall ‘86)
2) Information processing. Adaptation to natural statistics
(Attneave ‘54; Barlow ‘61; Laughlin ’81, Atick ‘92; Brenner ‘00).
Three meanings of adaptation 1) Evolutionary. Increase of fitness
3) Desensitization. Filtering of constant stimuli (Block ‘82; Segall ‘86)
2) Information processing. Adaptation to natural statistics
(Attneave ‘54; Barlow ‘61; Laughlin ’81, Atick ‘92; Brenner ‘00).
Standard qualitative argument for adaptation Shown (H Berg et al., Nature & PNAS 2012) that the motor shifts its range by regulating the number of FliM components, i.e. the curve is less steep than below.
Bacterial motor response curve (Cluzel et al., Nature 2000)
Drifting away from the inflection point reduces sensitivity and brings the system onto the plateaux.
The absolute concentration does affect the response in spite of adaptation 0.6 0.5
activity
0.4 change in activity
0.3 0.2 0.1 0 0
2
4
6 time
Kalinin et al., Biophys J., ‘09
8
10
2-fold jump in stimulus
The absolute concentration does affect the response in spite of adaptation 0.6 0.5
activity
0.4 change in activity
0.3 0.2 0.1 0 0
2
4
6
8
10
2-fold jump in stimulus
time
Scaleinvariance in natural images (Field, ’87; Ruderman & Bialek, ‘94)
E. coli function is to sense and to run Decreasing CheY-p: the running time τ increases and sensitivity reduces. Yet, the mean drift increases with τ.The balance between these competing factors depends on numbers… A negative lobe in the response reduces the current (de Gennes, 2004) t
∞ 2 2
υ = u (τ + − τ − ) 2τ ≈ gu τ
∫e 0
υ = χ∇c
2D0 χ= 3στ
−t
dt ∫ dsK(τ (t − s))s 0
∞
∫ 0
e−σ t K (t)dt
σ=
6Dτ + 2 3τ
u2 D0 = 3σ
(Celani & MV, PNAS ‘10)
E. coli function is to sense and to run 0.06 0.05 0.04 0.03 0.02 0.01 0
υ = χ∇c
2D0 χ= 3στ
0 ∞
∫ 0
e−σ t K (t)dt
2
4
6
6Dτ + 2 σ= 3τ
8
10
u2 D0 = 3σ
(Celani & MV, PNAS ‘10)
Physiology of bacterial motility
Adler, Temperton, Microb. 1967,1972; Amsler et al., J. Bac. 1993; Staropoli, Alon, Biophys. J. 2000
Interbacterial distance in colonies can become O(running length)
Fluctuations and adaptation Ø Bacteria compete for scarce nutrients and chemical cues at the entry of the stationary phase. Ø The chemical environment is likely to be perturbed unpredictably and actively by the rest of the colony. MaxiMin
Line of minima
(Celani & MV, PNAS 2010)
Fluctuations and adaptation Adaptation (in the second sense), i.e.and thechemical pathway is Ø Bacteria compete for scarce nutrients cues shaped and responds to the statistics of the at the by entry of the stationary phase. Ø environment. The chemical environment is likely to be perturbed
unpredictably and actively by the rest of the colony.
MaxiMin
Line of minima
(Celani & MV, PNAS 2010)
The response to serine is not perfectly adapted (Masson et al, PNAS ‘12)
Chemoattractant aspartate Running time vs concentration
Chemoattractant serine Serine Aspartate
Speed-races in gradients of serine and aspartate (Wong-Ng et al.)
The channel spans the range where serine looses adaptation (100µm to 1mM)
No impairment of gradient climbing!
Speed-races in gradients of serine and aspartate (Wong-Ng et al.)
Progress of the first 10
Progress of the first 20
4500
4500
4000
4000
3500
3500
3000
3000
2500
2500
2000
Position
Aspartate Serine
Position
Position
Aspartate Serine
2000
1500
1500
1000
1000
500
500
The channel spans the range where serine looses adaptation (100µm to 1mM) 0
0
50 Time (minutes)
No impairment of gradient climbing!
100
0
0
50 Time (minutes)
100
Tar/Tsr receptors crosstalk and their role in adaptation
The methylation state is shared among members of allosteric clusters of receptors. Tsr and Tar receptors can reciprocally assist and avoid the saturation of their methyl groups (see Endres & Wingreen PNAS ’06; Lan et al., Mol. Syst. Biol. ‘11).
Adding a background (30 or 100 µM) of serine, loss of adaptation to aspartate is induced
If we induce loss of adaptation to aspartate…
climbing of its gradients is sped up (compare left to right)
Bridging the gap among different meanings of adaptation Ø Functional questions necessary to understand what pathways are doing, what is evolutionarily shaping them and to go beyond the list of their parts. Ø Chemotaxis has been around for many years and great work has been done on dissecting and characterizing the pathway. It is precisely thanks to this knowledge that we can concretely address functional issues, which are open.
A. Celani (ICTP)
JB Masson (Pasteur)
A. Melbinger (UCSD)
J. Wong-Ng (UCSD)
Relations to growth and metabolism Aminoacid consumptions in a trypton broth (Prüβ et al., J. Bac., ’94)
Serine
Aspartate
Strength of chemotactic responses (Hedblom & Adler J. Bac., ’83)
Tar/Tsr ratio vs colony OD (Salman & Libchaber, Nat. Cell Biol, ’07; Kalinin et al., J. Bac., ’10)
Non-invasive microfluidic method we used (Masson et al., PNAS 2012)
Attractant field detected by fluorescence. The resulting gradient is 10µM/mm. Swimming E. coli cells imaged using phase contrast microscopy .
Allosteric model for receptor activity Two-state model (active-inactive) With free energy difference
a(m, L) =
1 1+ e f (m,L )
f (m, L) = α (m0 − m) + N log
1+ L K off 1+ L K on
dm(t) = kr (1− a(m, L)) − kb a(m, L) dt
Koff≈5µM
Kon≈160µM
Three meanings of adaptation 1) Evolutionary. Increase of fitness
3) Desensitization. Filtering of constant stimuli (Block ‘82; Segall ‘86)
2) Information processing. Adaptation to natural statistics
(Attneave ‘54; Barlow ‘61; Laughlin ’81, Atick ‘92; Brenner ‘00).
Three meanings of adaptation 1) Evolutionary. Increase of fitness
3) Desensitization. Filtering of constant stimuli (Block ‘82; Segall ‘86)
2) Information processing. Adaptation to natural statistics
(Attneave ‘54; Barlow ‘61; Laughlin ’81, Atick ‘92; Brenner ‘00).
Standard qualitative argument for adaptation Shown (H Berg et al., Nature & PNAS 2012) that the motor shifts its range by regulating the number of FliM components, i.e. the curve is less steep than below.
Bacterial motor response curve (Cluzel et al., Nature 2000)
Drifting away from the inflection point reduces sensitivity and brings the system onto the plateaux.
The absolute concentration does affect the response in spite of adaptation 0.6 0.5
activity
0.4 change in activity
0.3 0.2 0.1 0 0
2
4
6 time
Kalinin et al., Biophys J., ‘09
8
10
2-fold jump in stimulus
The absolute concentration does affect the response in spite of adaptation 0.6 0.5
activity
0.4 change in activity
0.3 0.2 0.1 0 0
2
4
6
8
10
2-fold jump in stimulus
time
Scaleinvariance in natural images (Field, ’87; Ruderman & Bialek, ‘94)
E. coli function is to sense and to run Decreasing CheY-p: the running time τ increases and sensitivity reduces. Yet, the mean drift increases with τ.The balance between these competing factors depends on numbers… A negative lobe in the response reduces the current (de Gennes, 2004) t
∞ 2 2
υ = u (τ + − τ − ) 2τ ≈ gu τ
∫e 0
υ = χ∇c
2D0 χ= 3στ
−t
dt ∫ dsK(τ (t − s))s 0
∞
∫ 0
e−σ t K (t)dt
σ=
6Dτ + 2 3τ
u2 D0 = 3σ
(Celani & MV, PNAS ‘10)
E. coli function is to sense and to run 0.06 0.05 0.04 0.03 0.02 0.01 0
υ = χ∇c
2D0 χ= 3στ
0 ∞
∫ 0
e−σ t K (t)dt
2
4
6
6Dτ + 2 σ= 3τ
8
10
u2 D0 = 3σ
(Celani & MV, PNAS ‘10)
Physiology of bacterial motility
Adler, Temperton, Microb. 1967,1972; Amsler et al., J. Bac. 1993; Staropoli, Alon, Biophys. J. 2000
Interbacterial distance in colonies can become O(running length)
Fluctuations and adaptation Ø Bacteria compete for scarce nutrients and chemical cues at the entry of the stationary phase. Ø The chemical environment is likely to be perturbed unpredictably and actively by the rest of the colony. MaxiMin
Line of minima
(Celani & MV, PNAS 2010)
Fluctuations and adaptation Adaptation (in the second sense), i.e.and thechemical pathway is Ø Bacteria compete for scarce nutrients cues shaped and responds to the statistics of the at the by entry of the stationary phase. Ø environment. The chemical environment is likely to be perturbed
unpredictably and actively by the rest of the colony.
MaxiMin
Line of minima
(Celani & MV, PNAS 2010)
The response to serine is not perfectly adapted (Masson et al, PNAS ‘12)
Chemoattractant aspartate Running time vs concentration
Chemoattractant serine Serine Aspartate
Speed-races in gradients of serine and aspartate (Wong-Ng et al.)
The channel spans the range where serine looses adaptation (100µm to 1mM)
No impairment of gradient climbing!
Speed-races in gradients of serine and aspartate (Wong-Ng et al.)
Progress of the first 10
Progress of the first 20
4500
4500
4000
4000
3500
3500
3000
3000
2500
2500
2000
Position
Aspartate Serine
Position
Position
Aspartate Serine
2000
1500
1500
1000
1000
500
500
The channel spans the range where serine looses adaptation (100µm to 1mM) 0
0
50 Time (minutes)
No impairment of gradient climbing!
100
0
0
50 Time (minutes)
100
Tar/Tsr receptors crosstalk and their role in adaptation
The methylation state is shared among members of allosteric clusters of receptors. Tsr and Tar receptors can reciprocally assist and avoid the saturation of their methyl groups (see Endres & Wingreen PNAS ’06; Lan et al., Mol. Syst. Biol. ‘11).
Adding a background (30 or 100 µM) of serine, loss of adaptation to aspartate is induced
If we induce loss of adaptation to aspartate…
climbing of its gradients is sped up (compare left to right)
Bridging the gap among different meanings of adaptation Ø Functional questions necessary to understand what pathways are doing, what is evolutionarily shaping them and to go beyond the list of their parts. Ø Chemotaxis has been around for many years and great work has been done on dissecting and characterizing the pathway. It is precisely thanks to this knowledge that we can concretely address functional issues, which are open.
A. Celani (ICTP)
JB Masson (Pasteur)
A. Melbinger (UCSD)
J. Wong-Ng (UCSD)
Relations to growth and metabolism Aminoacid consumptions in a trypton broth (Prüβ et al., J. Bac., ’94)
Serine
Aspartate
Strength of chemotactic responses (Hedblom & Adler J. Bac., ’83)
Tar/Tsr ratio vs colony OD (Salman & Libchaber, Nat. Cell Biol, ’07; Kalinin et al., J. Bac., ’10)
Non-invasive microfluidic method we used (Masson et al., PNAS 2012)
Attractant field detected by fluorescence. The resulting gradient is 10µM/mm. Swimming E. coli cells imaged using phase contrast microscopy .
Allosteric model for receptor activity Two-state model (active-inactive) With free energy difference
a(m, L) =
1 1+ e f (m,L )
f (m, L) = α (m0 − m) + N log
1+ L K off 1+ L K on
dm(t) = kr (1− a(m, L)) − kb a(m, L) dt
Koff≈5µM
Kon≈160µM
