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

6

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

8

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

10

An array of RyRs

Junction between T-tubule and the sarcoplasmic reticulum

11

Sequence of EC coupling

Ca2+

Action potential

Na+

Ca2+ ??

Ca2+


1. Introduction



4. Conclusions

12

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

21

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

15

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

16

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


1. Introduction



4. Conclusions

23

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


1. Introduction



4. Conclusions

29

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.

30

Cardiac Myocyte Results

AP curve Obtained from Natali et al. 2002


Transient recordings by Bouchard et al. 1995

Simulated patch clamp experiments under normal conditions. 20,000 FRUs simulated.

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SR transient recorded by Wang et al. 2004



Lumenal transient recorded by Brochet et al. 2005


32

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.


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.)

lecture 13 - systems biology - george mason university · 1 lecture 13 systems biology saleet jafri...

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