Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
The Big Squeeze
Why strain is so exciting to myocardium
Geoffrey A.M. Hunter
Department of Mathematics
University of Utah
IGTC Graduate Research Summit 2007
September 29, 2007
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Outline
Physiology overview:
Electrophysiological changes caused by strain.
How does regional ischemia lead to localized strain?
Identifying the protein subunit of the human stretch-activated channel
and its structure.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Outline
Physiology overview:
Electrophysiological changes caused by strain.
How does regional ischemia lead to localized strain?
Identifying the protein subunit of the human stretch-activated channel
and its structure.
Hypothesis
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Outline
Physiology overview:
Electrophysiological changes caused by strain.
How does regional ischemia lead to localized strain?
Identifying the protein subunit of the human stretch-activated channel
and its structure.
Hypothesis
Mathematical toolbox:
Hidden Markov model of a stretch-activated channel
Gillespie algorithm for single-channel simulations
Maximum Likelihood optimization for finding an optimal hidden Markov
model
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Outline
Physiology overview:
Electrophysiological changes caused by strain.
How does regional ischemia lead to localized strain?
Identifying the protein subunit of the human stretch-activated channel
and its structure.
Hypothesis
Mathematical toolbox:
Hidden Markov model of a stretch-activated channel
Gillespie algorithm for single-channel simulations
Maximum Likelihood optimization for finding an optimal hidden Markov
model
Future work & sideline interests
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Electrophysiological Changes from Strain
It’s well known that an electrical stimulus causes a mechanical response in the heart
(contraction), but mechanical stimuli can generate electrical responses as well.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Electrophysiological Changes from Strain
It’s well known that an electrical stimulus causes a mechanical response in the heart
(contraction), but mechanical stimuli can generate electrical responses as well.
The Good: Strain can explain the Frank-Starling Law whereby increased
diastolic volume leads to increased systolic contraction, which dynamically
maintains proper blood flow in the heart (i.e. rate in = rate out).
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Electrophysiological Changes from Strain
It’s well known that an electrical stimulus causes a mechanical response in the heart
(contraction), but mechanical stimuli can generate electrical responses as well.
The Good: Strain can explain the Frank-Starling Law whereby increased
diastolic volume leads to increased systolic contraction, which dynamically
maintains proper blood flow in the heart (i.e. rate in = rate out).
The Bad: A blunt impact to the chest during the refractory period of the action
potential can kill a healthy athlete immediately (Commodio Cordis).
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Electrophysiological Changes from Strain
It’s well known that an electrical stimulus causes a mechanical response in the heart
(contraction), but mechanical stimuli can generate electrical responses as well.
The Good: Strain can explain the Frank-Starling Law whereby increased
diastolic volume leads to increased systolic contraction, which dynamically
maintains proper blood flow in the heart (i.e. rate in = rate out).
The Bad: A blunt impact to the chest during the refractory period of the action
potential can kill a healthy athlete immediately (Commodio Cordis).
Changes to the action potential:
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Electrophysiological Changes from Strain
It’s well known that an electrical stimulus causes a mechanical response in the heart
(contraction), but mechanical stimuli can generate electrical responses as well.
The Good: Strain can explain the Frank-Starling Law whereby increased
diastolic volume leads to increased systolic contraction, which dynamically
maintains proper blood flow in the heart (i.e. rate in = rate out).
The Bad: A blunt impact to the chest during the refractory period of the action
potential can kill a healthy athlete immediately (Commodio Cordis).
Changes to the action potential:
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Electrophysiological Changes from Strain
It’s well known that an electrical stimulus causes a mechanical response in the heart
(contraction), but mechanical stimuli can generate electrical responses as well.
The Good: Strain can explain the Frank-Starling Law whereby increased
diastolic volume leads to increased systolic contraction, which dynamically
maintains proper blood flow in the heart (i.e. rate in = rate out).
The Bad: A blunt impact to the chest during the refractory period of the action
potential can kill a healthy athlete immediately (Commodio Cordis).
Changes to the action potential:
Figure courtesy of Dr. Frank B. Sachse
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Strain in the Border Zone
We tend to think of the genesis of localized strain as follows...
During regional ischemia, ischemic myocardium is known to contract slower and
generate less force than normal myocardium.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Strain in the Border Zone
We tend to think of the genesis of localized strain as follows...
During regional ischemia, ischemic myocardium is known to contract slower and
generate less force than normal myocardium.
Because of this inhomogeneity, the ischemic region bulges outward as it’s not
able to support the contractile load on the heart like the normal region is able to.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Strain in the Border Zone
We tend to think of the genesis of localized strain as follows...
During regional ischemia, ischemic myocardium is known to contract slower and
generate less force than normal myocardium.
Because of this inhomogeneity, the ischemic region bulges outward as it’s not
able to support the contractile load on the heart like the normal region is able to.
The border zone (see below) is an area where large gradients in strain are found
and is also where excitatory currents are generated.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Strain in the Border Zone
We tend to think of the genesis of localized strain as follows...
During regional ischemia, ischemic myocardium is known to contract slower and
generate less force than normal myocardium.
Because of this inhomogeneity, the ischemic region bulges outward as it’s not
able to support the contractile load on the heart like the normal region is able to.
The border zone (see below) is an area where large gradients in strain are found
and is also where excitatory currents are generated.
Some channels, called stretch-activated channels, are activated by strain and
the protein subunits of these channels were recently identified.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
Properties:
Small conductance
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
Properties:
Small conductance
∼ 0mV reversal potential
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
Properties:
Small conductance
∼ 0mV reversal potential
Permeable to cations only
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
Properties:
Small conductance
∼ 0mV reversal potential
Permeable to cations only
Strain in the cell membrane was sufficient
to activate TRPC1
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
Properties:
Small conductance
∼ 0mV reversal potential
Permeable to cations only
Strain in the cell membrane was sufficient
to activate TRPC1
Weak voltage dependence
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Identifying TRPC1
Maroto et al. 2005 used purified oocyte
membrane to identify TRPC1 as the protein
subunit of the human non-selective
stretch-activated channel.
Properties:
Small conductance
∼ 0mV reversal potential
Permeable to cations only
Strain in the cell membrane was sufficient
to activate TRPC1
Weak voltage dependence
Form homotetrameric channels
(Maroto et al. 2005)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Structure of TRPC1 Proteins & Channels
6 transmembrane spanning subunits with S5-S6 forming the pore
Known to associate with structural proteins (Cav-1, Homer-1, Ankyrin),
signalling molecules (Calmodulin), and other channels (IP3RI & IP3RII) but the
role of these relationships in myocardium is unknown.
Permeability ratios (PNa : PK : PCa ): 1:0.95:0.23
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Hypothesis: Role of stretch-activated channels
We suggest that the biphasic changes in conduction velocity can be explained
by the activation of stretch-activated channels.
Figure courtesy of Dr. Frank B. Sachse
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Hypothesis: Role of stretch-activated channels
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Hypothesis: Structure of border zone
The microscopic structure of the border zone is unknown (i.e. width, levels of ATP
and electrolytes, distribution of normal and ischemic cells), so we want to look at
different profiles of these factors in the border zone to see if there are significant
differences in action potential morphology, conduction velocity, and excitability.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Mathematical Tools
Our modelling work has utilized the following tools so far:
1
Hidden Markov model to model the stochastic behavior of a single
stretch-activated channel
2
Gillespie algorithm to make statistically and numerically accurate
simulations of single-channel behavior
3
Maximum Likelihood optimization to find the “best fit” model (i.e.
parameters and model topology)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Hidden Markov Model
TRPC1 forms homotetrameric channels that are activated by strain
α0
−→
α1
−→
α2
−→
α3
−→
k+
β1
β2
β3
β4
k−
→
C0 ←−C1 ←−C2 ←−C3 ←−C4 −
←−O
where βi+1 = (i + 1)b0 , αi = (4 − i)a(λ) for i = 0, ..., 3 with b0 , k− , and k+
constant and a(λ) is a function of membrane strain, λ.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Hidden Markov Model
TRPC1 forms homotetrameric channels that are activated by strain
α0
−→
α1
−→
α2
−→
α3
−→
k+
β1
β2
β3
β4
k−
→
C0 ←−C1 ←−C2 ←−C3 ←−C4 −
←−O
where βi+1 = (i + 1)b0 , αi = (4 − i)a(λ) for i = 0, ..., 3 with b0 , k− , and k+
constant and a(λ) is a function of membrane strain, λ.
This can be written in matrix-vector form as:
dx
dt
=
Ax
where
 
C0
C1 
 
 . 
x =  .. 
 
C 
4
O
A
=

−α0

 α0







Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
β1
−(α1 + β1 )
α1

..
.
..
.
..
.
..
..
.
.
k+
k−
−k−









Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
What’s “hidden” about it anyway?
Definition (Hidden Markov Model)
“A Markov model where the observation value is a probabilistic function of state.
These models have a doubly stochastic process where the underlying stochastic
process that is not observable can only be observed through another set of stochastic
processes that produce the sequence of observations.” (Rabiner 1989)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
What’s “hidden” about it anyway?
Definition (Hidden Markov Model)
“A Markov model where the observation value is a probabilistic function of state.
These models have a doubly stochastic process where the underlying stochastic
process that is not observable can only be observed through another set of stochastic
processes that produce the sequence of observations.” (Rabiner 1989)
This means that...
“...the underlying stochastic process that is not observable...”:
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
What’s “hidden” about it anyway?
Definition (Hidden Markov Model)
“A Markov model where the observation value is a probabilistic function of state.
These models have a doubly stochastic process where the underlying stochastic
process that is not observable can only be observed through another set of stochastic
processes that produce the sequence of observations.” (Rabiner 1989)
This means that...
“...the underlying stochastic process that is not observable...”:
“...set of stochastic processes that produce the sequence of observations.”:
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
What’s “hidden” about it anyway?
Definition (Hidden Markov Model)
“A Markov model where the observation value is a probabilistic function of state.
These models have a doubly stochastic process where the underlying stochastic
process that is not observable can only be observed through another set of stochastic
processes that produce the sequence of observations.” (Rabiner 1989)
This means that...
“...the underlying stochastic process that is not observable...”:
“...set of stochastic processes that produce the sequence of observations.”:
The likelihood of a model, θ, generating a sequence of observations is defined as:
Lik( θ)
≡
n
Y
P(Oi | θ)
i=1
where P(Oi | θ) = the probability observing Oi at
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
time ti given the model θ.
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
The Gillespie Algorithm
Numerical method for generating numerically and statistically accurate
single-channel data.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
The Gillespie Algorithm
Numerical method for generating numerically and statistically accurate
single-channel data.
Let aµ (t) dt be the propensity of the µ’th reaction, Rµ (i.e. a2 (t) = α1 (λ)C1 ).
You can show that the probability that the next reaction will occur in the
infinitesimal time interval (t + τ, t + τ + dτ ) given that the system is in state
Y = (C0 , C1 , . . . , C4 , O) at time t is:
P(τ, µ| Y, t) dτ
=
aµ (t + τ ) e−
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Rτ
0
aµ (t+τ 0 ) dτ 0
dτ
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
The Gillespie Algorithm
Numerical method for generating numerically and statistically accurate
single-channel data.
Let aµ (t) dt be the propensity of the µ’th reaction, Rµ (i.e. a2 (t) = α1 (λ)C1 ).
You can show that the probability that the next reaction will occur in the
infinitesimal time interval (t + τ, t + τ + dτ ) given that the system is in state
Y = (C0 , C1 , . . . , C4 , O) at time t is:
→
P(τ, µ| Y, t) dτ
=
F (T , µ| Y, t)
=
Rτ
aµ (t + τ ) e− 0 aµ (t+τ
Z T
P(τ, µ| Y, t) dτ
0
=
1 − e−
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
RT
0
aµ (t+τ 0 ) dτ 0
0
) dτ 0
dτ
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
The Gillespie Algorithm
Numerical method for generating numerically and statistically accurate
single-channel data.
Let aµ (t) dt be the propensity of the µ’th reaction, Rµ (i.e. a2 (t) = α1 (λ)C1 ).
You can show that the probability that the next reaction will occur in the
infinitesimal time interval (t + τ, t + τ + dτ ) given that the system is in state
Y = (C0 , C1 , . . . , C4 , O) at time t is:
→
P(τ, µ| Y, t) dτ
=
F (T , µ| Y, t)
=
Rτ
aµ (t + τ ) e− 0 aµ (t+τ
Z T
P(τ, µ| Y, t) dτ
0
) dτ 0
dτ
0
=
1 − e−
RT
0
aµ (t+τ 0 ) dτ 0
For each reaction, we set u = F (T , µ| Y, t) where u ∼ U(0, 1) and integrate
each equation until:
Z T +t
aµb (τ ) dτ = − ln(1 − u)
t
b for some µ
b and update the system
at time T
b. We update the new time to t + T
according to reaction µ
b (i.e. if µ
b = 2, then C1 → C1 − 1 and C2 → C2 + 1).
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Why use the Gillespie algorithm?
The random behavior of the channel is preserved with the Gillespie algorithm, while
the Master Equation produces the expected behavior.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
How do you find the “best fit” model?
We have to redefine our notion of “best fit” because the channel recording
data is...
...noisy from seal resistance, the electronic amplifier, and from Brownian motion
of the channel and the membrane.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
How do you find the “best fit” model?
We have to redefine our notion of “best fit” because the channel recording
data is...
...noisy from seal resistance, the electronic amplifier, and from Brownian motion
of the channel and the membrane.
...Markovian, so data will always be unique even in the absence of noise.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
How do you find the “best fit” model?
We have to redefine our notion of “best fit” because the channel recording
data is...
...noisy from seal resistance, the electronic amplifier, and from Brownian motion
of the channel and the membrane.
...Markovian, so data will always be unique even in the absence of noise.
...lost when sampled at a low sampling frequency and when it’s quantized.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
How do you find the “best fit” model?
We have to redefine our notion of “best fit” because the channel recording
data is...
...noisy from seal resistance, the electronic amplifier, and from Brownian motion
of the channel and the membrane.
...Markovian, so data will always be unique even in the absence of noise.
...lost when sampled at a low sampling frequency and when it’s quantized.
...sometimes non-stationary.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Maximum Likelihood Optimization
Can define “best fit” in the following two ways:
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Mathematical Toolbox
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Maximum Likelihood Optimization
Can define “best fit” in the following two ways:
1
A model that is most likely to reproduce the statistics of the data (i.e.
distributions of dwell times and conductances).
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Maximum Likelihood Optimization
Can define “best fit” in the following two ways:
1
A model that is most likely to reproduce the statistics of the data (i.e.
distributions of dwell times and conductances).
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Maximum Likelihood Optimization
Can define “best fit” in the following two ways:
1
A model that is most likely to reproduce the statistics of the data (i.e.
distributions of dwell times and conductances).
2
A model that is most likely to reproduce the sequence of data measured.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Maximum Likelihood Optimization
Can define “best fit” in the following two ways:
1
A model that is most likely to reproduce the statistics of the data (i.e.
distributions of dwell times and conductances).
2
A model that is most likely to reproduce the sequence of data measured.
Lik( θ)
≡
n
Y
P(Oi | θ)
i=1
→
d ln(Lik( θ))
=0
dθ
(Note: There are also other methods to define “best fit”)
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Conclusion
Future Work
Currently running Maximum Likelihood optimization on the model.
Hope to find a functional relationship between strain and αi (i.e Is αi (λ) ∝ λ or
is αi (λ) ∝ eηλ ).
Later we will integrate the TRPC1 model into single cell, 1-D chain, and 2-D
myocardium models then look at changes in action potential morphology,
conduction velocity, etc. in normal and ischemic myocardium.
Test different border zone profiles to see if there are any differences on the
macroscopic level
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Outline
Physiology Overview
Hypothesis
Quorum Sensing in Vibrio fischeri
The big picture (right) shows a soft
switch for how V.fischeri regulates
luminescence, but...
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Mathematical Toolbox
Conclusion
Outline
Physiology Overview
Hypothesis
Quorum Sensing in Vibrio fischeri
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Mathematical Toolbox
Conclusion
Outline
Physiology Overview
Hypothesis
Quorum Sensing in Vibrio fischeri
The big picture (right) shows a soft
switch for how V.fischeri regulates
luminescence, but...
... the small picture shows a hard
switch, so we want to know how a
hard switch turns into a soft switch.
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Mathematical Toolbox
Conclusion
Outline
Physiology Overview
Hypothesis
Mathematical Toolbox
Special Thanks To...
Dr. James Keener (keener@math.utah.edu): Supervisor
Dr. Frank B. Sachse (fs@cvrti.utah.edu): Thesis committee
Dr. Owen P. Hamill (ohamill@utmb.edu): hTRPC1 data
Geoffrey A.M. Hunter: IGTC Graduate Research Summit 2007
Conclusion