Lecture 13 - Systems Biology - George Mason University · 1 Lecture 13 Systems Biology Saleet Jafri...
Transcript of Lecture 13 - Systems Biology - George Mason University · 1 Lecture 13 Systems Biology Saleet Jafri...
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Lecture 13 Systems Biology
Saleet Jafri
What is Systems Biology?
In traditions science a reductionist approachis typically used with an individual system or subsystem is dissected and studied in detail
Systems biology integrates information from different sources to understand how larger more complex systems work.
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Systems Biology and Integration
• Molecule (Gene and Protein)• Organelle (cellular subsystem)• Cell• Organ• Organism• Environment
History of System Biology
• The Human Genome Project and modern biotechnology have created the ability to gather large amount of information about an organism.
• Due to the inherent complexity of biological systems, computational methods and models must be used to understand and integrate the data.
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Systems Biology Methods
• There are many methods used in systems biology and each has its strengths and weaknesses
• Much of what is called systems biology relates to modeling genetic networks and biochemical reaction networks, however they are not the only methods.
Systems Biology Methods
I will present an example from my own research that integrates biochemical, biophysical, and microstructuralinformation to explain the basic mechanisms that initiate contraction in the heart.
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M. Saleet Jafri
School of Computational Science
George Mason University
Modeling the Mechanism of Calcium Sparks in the Heart
Eric Sobie
Keith Dilly Jader Cruz
Jon Lederer
Co-workers
Hena Ramay
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Research Goals
What factors influence spark dynamics?
• What is the mechanism of spark termination?
• How can we account for the spatial spread of the spark?
Presentation Outline
1. Introduction
2. Spark Termination
3. Spatial Spread of Sparks
4. Conclusions
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MembraneCurrents
CalciumHandling
ForceGeneration
Basic Components ofCardiac E-C Coupling
ActionPotential
CalciumTransient
ForceTransient
Cardiac Ca2+-induced Ca2+ release
1) Controldiastole
systole
+40 mV
-80 mV50 ms
2) CICR disabled (caffeine)
3) No Ca2+ entry (Ba2+)
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What is a Ca2+ spark?
thanks to Andy Ziman for assistance
What is a Ca2+ spark?0.0 0.5 1.0 1.5 2.0 2.5 seconds
cell images at 0.5 sec per image
(from Cheng, Lederer & Cannell (1993), Science 262:740)
sparks
line-scan image at 2 ms per line
sparktime
location
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Why Study Calcium Sparks?
•Calcium sparks are the most elementary observed events in excitation contraction coupling
•Calcium sparks are thought to regulate vascular tone in vascular smooth muscle
•Calcium sparks provide a good example where cellular structure and the detailed biophysics of cellular components combine to observed experimental behavior
•Excitation contraction coupling is defective in certain diseases such as heart failure.
Heart Cell
(From L. Fernando Santana, unpublished)
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T-tubules and SR apposition
MZ-line
Modified from J. Frank (1990)
T-tubule
TT-SRjunction
SR RyRs
Elements of Ca2+ Spark Generation
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An array of RyRs
Junction between T-tubule and the sarcoplasmic reticulum
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Sequence of EC coupling
Ca2+
Action potential
Na+
Ca2+ ??
Ca2+
Presentation Outline
1. Introduction
2. Spark Termination
3. Spatial Spread of Sparks
4. Conclusions
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How do Ca2+ sparks terminate?
1) Depletion of SR Ca2+-- do Ca2+ sparks terminate because the SR runs out of Ca2+?This is ruled out because – a) There is still Ca available for release after a Ca2+ transient (Bassani et al., 1995; Trafford et al., 1997) and b) Ca2+ sparks can last a long time – up to seconds.
Three hypotheses have been proposed to explain the mechanism of Ca2+ spark termination:
long Ca2+ calcium sparks (ryanodine)
1 sec
(from Cheng, Lederer & Cannell (1993) Science 262:740)
If Ca2+ sparks terminate by "stochastic attrition", it is meant that termination happens when all of the RyR’s just happen to close at the same time.
This can occur if there is one or a just a few RyR's, but it is unlikely when the number of RyR’s in a cluster is large (e.g. 6 or more) (see analysis by Stern and others, starting with Stern, 1992). In adult heart cells the clusters of RyR's contain 30 or more.
3) Could Ca2+ sparks terminate because the RyRs "inactivate"? If not, could "adaptation" do the job?There are two problems:
• First, “simple inactivation” of RyRs has NOT been observed in planar lipid bilayer experiments.
• Second, adaptation ("complicated inactivation") of RyRs is too slow (100’s of ms to seconds). (Gyorke and Fill, 1993; Valdivia et al., 1995)
Recent experimental results suggested another hypothesis to us......
2) Stochastic attrition?
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Hypothesis
[Ca2+]lumen and RyR gating
from Gyorke & Gyorke (1998) Biophys J. 75:280
trans [Ca2+]=20 μM trans [Ca2+]=5 mM
Ca2+ sparks terminate because of the influence of three factors on RyR gating
2. SR lumenal [Ca2+]
3. Coupled gating of RyRs
Coupled gating of RyRs
Skeletal Muscle RyRs: Marx et al., (1998) Science 281:818.Heart RyRs: Gaburjakova et al. (2001) Biophys. J. 80:380A.
control
+ FK506
0
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RYR
'S
0
21
RYR
'S
1. Large number of RyRs (Franzini-Armstrong et al., 1998)
Experimental Results
0.5 F/F0
10 µm
100 ms
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Pooled Experimental Results
0.2
0.4
0.6
0.8ns
≥40ms<40 ms
fract
ion
of s
park
s
ns ****
****
controlFK506 (25 μM)rapamycin (20 μM)
Model: Conceptual Outline
ΣRyR
2) SR release flux
ms
pA
3) Ca2+ profile
μm
μM
4) Ca2+ spark image
diffusion, buffering optical blurring
1) RyR gating
C
O
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Model: “Sticky Cluster”Spatial organization
Model: “Sticky Cluster”RyR Gating
C Okopen
kclose
kclose = Const.*CFclose
kopen = Const.*CFopen
([Ca]ss)4
Km 4 +([Ca]ss)4
Km =f([Ca]lumen)
CFclose= kcoop*g(Nclosed,Nopen)
CFopen= h(Nclosed,Nopen)
[Ca2+]ss
k ope
n
high [Ca2+]lumen
low [Ca2+]lumen
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Model Equations
1
][341.0001.04
2
)][][(
)][]([1
)][]([1
2
22
8
1
22
22
−
−=
=
−=
−=
−=
∑=
++
++
RTVF
oRT
VF
CaDHPR
SS
openDHPRDHPR
SSJSRi
iopenRyRRyR
JSRNSRtr
tr
MyoSSxfer
xfer
e
CaeRT
VFPI
whereFV
DHPRJ
CaCaRyRJJ
CaCaJ
CaCaJ
I
τ
τ
1
22
2
2
2
)][(
][
1
][]][[
)(][
][
−
+
+
+
+
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
++=
+−=
−=
+++=
JSRCSQN
CSQN
total
JSR
offonbuffer
RyRSS
trJSRJSR
bufferxferRyRDHPRSS
CaKK
CSQN
andCaBkBCakJ
where
JV
VJ
dtCad
JJJJdt
Cad
myo
β
β
Model Solution• RyR open state calculated using a Monte Carlo Method
• Fluxes calculated to determine derivatives
• Differential equations solved using a Euler Method
• Programmed in Fortran 90 on a HP Unix Workstation
• Computation time for control 500 runs in 30 minutes
• Spark visualization determined by solving reaction-diffusion system for buffered diffusion and optical blurring using Matlab on a PC
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Simulated Ca2+ release: control conditions
1 pA
SR Ca2+ release flux
1
0
RyR open probability
[Ca2+]SR
10 ms
1000
500
0
μM
Peak [Ca2+]SS=~150 μM
[Ca2+]NSR=1000 μM
Simulated Ca2+ sparks: control conditionsCa2+ spark image
20 ms
1 μm
1
2
F/F0
Ca2+ spark time course
20 ms
0 µm0.25 µm0.5 µm
Ca2+ spark spatial profiles
5 ms10 ms20 ms50 ms
0.5 μm
0.5 F0
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Simulated Ca2+ sparks: effect of noiseRecorded noise
Ca2+ spark image
Simulated noise
+ noise =
Ca2+ spark time course
+ noise =
Spontaneous simulated Ca2+ sparks[Ca2+]i = 100 nM
[Ca2+]i = 150 nM
20 μm
1 second
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Spark Rate vs Subspace Ca2+ and SR Lumenal Ca2+
00.20.40.60.8
11.21.41.61.8
0 1 2 3
resting SR [Ca] (mM)
spar
k ra
te (s
park
/s)
0
5000
10000
15000
20000
25000
0 50 100 150resting SS [Ca] (μM)
spar
k ra
te (s
park
/s)
0
20
40
60
80
100
120
0 0.5 1 1.5resting SS [Ca]
spar
k ra
te (s
park
/s)
Simulated Ca2+ sparks: cluster size100 RyRs
Ca2+ release flux
Ca2+ spark
[Ca2+]SR
1 pA
1
2
F/F0
1000
500
0
μM
20 ms
1 μm
50 RyRs 20 RyRs 10 RyRs
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Simulated Ca2+ sparks: cluster size
0 20 40 60 80 1000
10
20
30
Efflu
x du
ratio
n (m
s)
#RyRs in cluster
2
3
Spar
k am
plitu
de (F
/F0)
0 20 40 60 80 100#RyRs in cluster
ms
0.1
0.2
frac
tion
of s
park
s
100 RyRs 20 RyRs 10 RyRs50 RyRs
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
Simulated Ca2+ sparks: no lumenal dependence
400 ms
400 ms
No lumenal dependence
Ca2+ release flux
Ca2+ spark
Ca2+ spark image
Control
1 pA
1
2
F/F0
50 ms
1 μm
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Simulated Ca2+ sparks: SR Load
0
5
10
15
20
25
30
0 500 1000 1500 2000 2500resting SR Ca (uM)
spar
k du
ratio
n (m
s)
0
50
100
150
200
250
300
0 500 1000 1500 2000 2500resting SR Ca (uM)
peak
SS
Ca
( μM
)
Simulated Ca2+ sparks: reduced couplingkcoop= 0.4
Ca2+ release flux
Ca2+ spark
Ca2+ spark image
kcoop= 1
1 pA
1
2F/F0
50 ms
1 μm
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Reduced coupling: population data
100
200
300
Rel
ease
dur
atio
n (m
s)
1.5 1.0 0.5kcoop (relative to control)
kcoop = 1
ms
0.1
0.2
frac
tion
of s
park
s
10 20 30 40
kcoop = 0.4
0.1
0.2
frac
tion
of s
park
s
200 400 600ms
Presentation Outline
1. Introduction
2. Spark Termination
3. Spatial Spread of Sparks
4. Conclusions
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Involvement of Multiple release sites
• Conventionally sparks are thought to originate from a signal release site• Parker et al suggest that sparks can originate from multiple release sites depending on
the proximity of the release site
MZ-line
T-T
TT-SR junction
SR RyRs
Electron micrograph of the t-tubule and SR junction
Source: J. Frank 1990
Schematic diagram of the model TT-SR junction
Model Layout and Method
• Model Layout– Two Functional Release Units
• 2 LCC• 32 RyR Channel
– Homogeneous NSR and Myoplasm
• Method– Explicit finite difference method
(Euler Method)• Time step of 10-7 s • Spatial step of 0.1 μm
– Monte Carlo method to determine RyR channel state
– No flux boundary conditions
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Calcium Dynamics in Functional Release Unit
Subspace [Ca2+] Vs Time
0
100
200
300
400
0 5 15 25 35 45 50
Time (ms)
[Ca2+
] (μM
)
[CaF] Vs Time
0
10
20
30
40
50
5 15 25 35 45
Time (ms)
[CaF
] μM
Junctional SR [Ca2+] Vs Time
0
200
400
600
800
1000
40 80 120 160 200 240 280
Time (ms)
[Ca2
+ ] (μ
M)
Undistinguished Calcium Spark Peaks
[CaF] [CaF] with Optical blurring
Simulated Spark
• Release from one site almost always triggers release from the adjacent site on the other side of the T-tubule consistent with the results of Parker et al. 1996.
• FWHM = 2.0 μm
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Spark from One Release Site
[CaF] [CaF] with Optical blurring
Simulated Spark
• One site is disables to show release from a single site • FWHM < 2.0 μm
SERCA Pump Distribution
SERCA Distribution
Smith et al. 1998
[CaF] Vs Time
0
10
20
30
40
50
10 20 30 40 50Time (ms)
[CaF
] μM
HeterogeneousHomogeneous
Distribution
• Periodic distribution predicted by Smith and co-workers
• Homogeneous and non-homogeneous SERCA pump distribution made little difference on spark duration
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SERCA Pump Activity
[CaF] Vs Time
05
101520253035404550
5 10 15 20 25 30 35 40 45Time (ms)
[CaF
] μM
ControlIncreased
Blocked
Activity• Increasing SERCA pump activity leads to decrease spark duration
• Blocking SERCA pump activity leads to an increase in spark duration similar to that observed by Gomez et al 1996.
Calsequestrin and Sparks
Terentyev et al., 2003
Control
Decreased CSQ
Increased CSQ
• Iperatoxin was addedtocardiac myocytes to increase spontaneous sparks from the same site.
• Decreased calsequestrinexpression increases spark frequency
• Increased calsequestrin expression decreases spark frequency.
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Spark Restitution[C
a2+ ]
(μM
)
0
100
200
300
400450
0 100 200 300 400 500 600
Subspace [Ca2+] Vs Time
Time (ms)
0
400
800
1200
1600
0 100 200 300 400 500 600
[Ca2
+ ] (μM
)
Junctional SR [Ca2+] Vs Time
Time (ms)
• Spark amplitude increases as interspark interval increases
• The lower spark amplitude is a result of the partially filled state of the SR
• Since Popen depends on [Ca2+]SR the iperatoxin results can be explained by a delay in refilling.
Simulated Effects of Calsequestrin
50
100
150
00 100 200 300 400 500 600
[Ca2
+ ] (μM
)
Time (ms)
Increased CSQ Simulation
Time (ms)
[Ca2
+ ] (μM
)
50
100
150
00 100 200 300 400 500 600
Decreased CSQ Simulation
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SR Buffer Data
38%
183%
27%100%
%Spark rate (Exp.)
27%170 ms156 μMCitrate
190 %18 ms120 μMDecreased CSQ expression
28%150 ms147 μMIncreased CSQ expression
100%24 ms128 μMControl
%Spark rate (Sim.)
Peak duration
Peak Amplitude
Condition
Terentyev et al., 2003
Presentation Outline
1. Introduction
2. Spark Termination
3. Spatial Spread of Sparks
4. Conclusions
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Summary/Conclusions
• Our “sticky cluster” model of a Ca2+ release unit can simulate Ca2+
sparks that terminate reliably. Termination occurs through coupled gating and the influence of lumenal calcium.
• Reducing coupling between RyRs increases Ca2+ spark duration, consistent with experimental effects of FK506.
• Ca2+ spark magnitude is only mildly sensitive to the number of RyR'sin the cluster and the Ca2+ spark duration is even less sensitive to this number.
• Release from adjacent sights might combine to give spark widths of 2 μm as observed experimentally.
• The spontaneous spark rate alteration due to SR buffers is likely due to their effect on refilling of the SR.
Current Work
• We have integrated the Ca2+ spark model into a model for whole cell Ca2+ dynamics of the cardiac myocyte to demonstrate that the summation of many sparks from different release sites give rise to the global Ca2+ transient.
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Cardiac Myocyte Results
AP curve Obtained from Natali et al. 2002
Cardiac Myocyte Results
Transient recordings by Bouchard et al. 1995
Simulated patch clamp experiments under normal conditions. 20,000 FRUs simulated.
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Cardiac Myocyte Results
SR transient recorded by Wang et al. 2004
Simulated patch clamp experiments under normal conditions. 20,000 FRUs simulated.
Cardiac Myocyte Results
Lumenal transient recorded by Brochet et al. 2005
Simulated patch clamp experiments under normal conditions. 20,000 FRUs simulated.
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Cardiac Myocyte ResultsGraded release
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
-50 -40 -30 -20 -10 0 10 20 30 40 50
Membrane potential (mV)
Peak
Rel
ease
(mM
/s)
Graded release
Release curve recorded by Wier et al. 1994Simulated patch clamp experiments under normal conditions. 20,000 FRUs simulated.
Cardiac Myocyte Results
Gain Function Plot
0
5
10
15
20
25
-40 -30 -20 -10 0 10 20 30 40 50
Membrane potential (mV)
Gai
n (J
sr/Ic
a)
Gain Experimentally generated gain plot from Wang et al. 2004Simulated patch clamp experiments under normal
conditions. 20,000 FRUs simulated.
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END
Ca2+ sparks activated during ramp-depolarization from -60 to -40
(from Cannell, Cheng & Lederer (1995), Science 268: 1045.)