Lecture 13 Systems Biology Saleet Jafri What is Systems Biology? In traditions science a reductionist approach is 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. 1
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. 2
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 microstructural information to explain the basic mechanisms that initiate contraction in the heart. 3
Modeling the Mechanism of Calcium Sparks in the Heart M. Saleet Jafri School of Computational Science George Mason University Co-workers Hena Ramay Jon Lederer Eric Sobie Keith Dilly Jader Cruz 4
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 5
Basic Components of Cardiac E-C Coupling Membrane Currents Calcium Handling Force Generation Action Potential Calcium Transient Force Transient Cardiac Ca 2+ -induced Ca 2+ release +4 mv 1) Control -8 mv diastole 5 ms systole 2) CICR disabled (caffeine) 3) No Ca 2+ entry (Ba 2+ ) 6
What is a Ca 2+ spark? thanks to Andy Ziman for assistance What is a Ca 2+ spark?..5 1. 1.5 2. 2.5 seconds cell images at.5 sec per image sparks line-scan image at 2 ms per line location time (from Cheng, Lederer & Cannell (1993), Science 262:74) spark 7
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) 8
T-tubules and SR apposition Z-line SR M RyRs T-tubule TT-SR junction Modified from J. Frank (199) Elements of Ca 2+ Spark Generation 9
An array of RyRs Junction between T-tubule and the sarcoplasmic reticulum 1
Sequence of EC coupling Action potential Ca 2+ Na + Ca 2+ Ca 2+?? Presentation Outline 1. Introduction 2. Spark Termination 3. Spatial Spread of Sparks 4. Conclusions 11
How do Ca 2+ sparks terminate? Three hypotheses have been proposed to explain the mechanism of Ca 2+ spark termination: 1) Depletion of SR Ca 2+ -- do Ca 2+ sparks terminate because the SR runs out of Ca 2+? This is ruled out because a) There is still Ca available for release after a Ca 2+ transient (Bassani et al., 1995; Trafford et al., 1997) and b) Ca 2+ sparks can last a long time up to seconds. long Ca 2+ calcium sparks (ryanodine) 1 sec (from Cheng, Lederer & Cannell (1993) Science 262:74) 2) Stochastic attrition? If Ca 2+ 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 3 or more. 3) Could Ca 2+ 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 (1 s of ms to seconds). (Gyorke and Fill, 1993; Valdivia et al., 1995) Recent experimental results suggested another hypothesis to us... 12
Hypothesis Ca 2+ sparks terminate because of the influence of three factors on RyR gating 1. Large number of RyRs (Franzini-Armstrong et al., 1998) 2. SR lumenal [Ca 2+ ] 3. Coupled gating of RyRs [Ca 2+ ] lumen and RyR gating Coupled gating of RyRs RYR'S 2 1 control + FK56 trans [Ca 2+ ]=2 μm trans [Ca 2+ ]=5 mm RYR'S 2 1 from Gyorke & Gyorke (1998) Biophys J. 75:28 Skeletal Muscle RyRs: Marx et al., (1998) Science 281:818. Heart RyRs: Gaburjakova et al. (21) Biophys. J. 8:38A. Experimental Results 1 µm.5 F/F 1 ms 13
Pooled Experimental Results fraction of sparks.8.6.4.2 ** ** ns ** ** ns control FK56 (25 μm) rapamycin (2 μm) <4 ms 4ms Model: Conceptual Outline 1) RyR gating O 3) Ca 2+ profile μm C μm ΣRyR diffusion, buffering optical blurring 2) SR release flux 4) Ca 2+ spark image pa ms 14
Model: Sticky Cluster Spatial organization Model: Sticky Cluster C RyR Gating k open O k close k close = Const.*CF close ([Ca] ss ) 4 k open = Const.*CF open K 4 m +([Ca] ss ) 4 K m =f([ca] lumen ) CF close = k coop *g(n closed,n open ) CF open = h(n closed,n open ) k open high [Ca 2+ ] lumen [Ca 2+ ] ss low [Ca 2+ ] lumen 15
Model Equations J J J J I xfer tr 1 2+ = ([ Ca ] τ 1 = ([ Ca τ RyR DHPR DHPR = where tr 8 i= 1 = xfer I = P J Ca RyR DHPR ] 2+ NSR RyR 2FV 2 VF 4 RT SS SS [ Ca [ Ca i open DHPR ([ Ca] open.1e ] ] 2+ Myo 2+ JSR JSR 2VF RT e ) ) [ Ca] 2VF RT.341[ Ca ] 1 SS ) o d[ Ca dt ] 2+ SS d[ Ca ] dt where J buffer and β JSR 2+ JSR = k = J = β on DHPR [ Ca JSR 2+ + J ( J V V ][ B] + k [ CSQN] total K = 1+ ( KCSQN + [ Ca tr RyR + J myo SS off xfer J RyR [ CaB] CSQN 2+ 2 ] JSR ) + J ) 1 buffer 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 9 on a HP Unix Workstation Computation time for control 5 runs in 3 minutes Spark visualization determined by solving reactiondiffusion system for buffered diffusion and optical blurring using Matlab on a PC 16
Simulated Ca 2+ release: control conditions 1 RyR open probability 1 ms SR Ca 2+ release flux Peak [Ca 2+ ] SS =~15 μm 1 pa 1 μm 5 [Ca 2+ ] SR [Ca 2+ ] NSR =1 μm Simulated Ca 2+ sparks: control conditions Ca 2+ spark image 1 μm Ca 2+ spark time course 2 µm.25 µm.5 µm 2 ms Ca 2+ spark spatial profiles F/F 1 2 ms.5 F 5 ms 1 ms 2 ms 5 ms.5 μm 17
Simulated Ca 2+ sparks: effect of noise Recorded noise Simulated noise Ca 2+ spark image + noise = Ca 2+ spark time course + noise = 2 μm Spontaneous simulated Ca 2+ sparks [Ca 2+ ] i = 1 nm 1 second [Ca 2+ ] i = 15 nm 18
Spark Rate vs Subspace Ca 2+ and SR Lumenal Ca 2+ spark rate (spark/s) 25 2 15 1 5 spark rate (spark/s) 12 1 8 6 4 2.5 1 1.5 resting SS [Ca] 5 1 15 resting SS [Ca] (μm) spark rate (spark/s) 1.8 1.6 1.4 1.2 1.8.6.4.2 1 2 3 resting SR [Ca] (mm) Simulated Ca 2+ sparks: cluster size 1 RyRs 5 RyRs 2 RyRs 1 RyRs 1 pa Ca 2+ release flux 1 μm 5 2 ms [Ca 2+ ] SR F/F 2 1 Ca 2+ spark 1 μm 19
Simulated Ca 2+ sparks: cluster size fraction of sparks.2.1 1 RyRs 5 RyRs 2 RyRs 1 RyRs 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 ms Spark amplitude (F/F ) 3 2 Efflux duration (ms) 3 2 1 2 4 6 8 1 #RyRs in cluster 2 4 6 8 1 #RyRs in cluster Simulated Ca 2+ sparks: no lumenal dependence Control No lumenal dependence 1 pa 4 ms Ca 2+ release flux 2 4 ms Ca 2+ spark F/F 1 1 μm 5 ms Ca 2+ spark image 2
Simulated Ca 2+ sparks: SR Load spark duration (ms) peak SS Ca (μm) 3 25 2 15 1 5 5 1 15 2 25 resting SR Ca (um) 3 25 2 15 1 5 5 1 15 2 25 resting SR Ca (um) Simulated Ca 2+ sparks: reduced coupling 1 pa k coop = 1 k coop =.4 Ca 2+ release flux 2 Ca 2+ spark F/F 1 5 ms Ca 2+ spark image 1 μm 21
Reduced coupling: population data.2 k coop = 1.2 k coop =.4 fraction of sparks.1 fraction of sparks.1 1 2 3 4 ms 2 4 6 ms Release duration (ms) 3 2 1 1.5 1..5 k coop (relative to control) Presentation Outline 1. Introduction 2. Spark Termination 3. Spatial Spread of Sparks 4. Conclusions 22
Involvement of Multiple release sites Z-line SR RyRs M T-T TT-SR junction Electron micrograph of the t-tubule and SR junction Source: J. Frank 199 Schematic diagram of the model TT-SR junction 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 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 1-7 s Spatial step of.1 μm Monte Carlo method to determine RyR channel state No flux boundary conditions 23
Calcium Dynamics in Functional Release Unit 4 Subspace [Ca 2+ ] Vs Time [Ca 2+ ] (μm) 3 2 1 Junctional SR [Ca 2+ ]Vs Time 1 5 15 25 35 45 5 Time (ms) [Ca 2+ ] (μm) 8 6 4 5 [CaF] Vs Time 2 [CaF] μm 4 3 2 4 8 12 16 2 24 28 Time (ms) 1 5 15 25 35 45 Time (ms) 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. μm 24
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. μm SERCA Pump Distribution Distribution SERCA Distribution Periodic distribution predicted by Smith and co-workers Smith et al. 1998 [CaF] μm 5 4 3 2 1 [CaF] Vs Time Heterogeneous Homogeneous Homogeneous and non-homogeneous SERCA pump distribution made little difference on spark duration 1 2 3 4 5 Time (ms) 25
SERCA Pump 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. [CaF] μm 5 45 4 35 3 25 2 15 1 5 Activity [CaF] Vs Time Blocked Control Increased 5 1 15 2 25 3 35 4 45 Time (ms) Calsequestrin and Sparks Control Decreased CSQ Increased CSQ Iperatoxin was addedto cardiac myocytes to increase spontaneous sparks from the same site. Decreased calsequestrin expression increases spark frequency Increased calsequestrin expression decreases spark frequency. Terentyev et al., 23 26
[Ca 2+ ] (μm) [Ca 2+ ] (μm) 45 4 3 2 1 16 12 8 4 Spark Restitution Subspace [Ca 2+ ] Vs Time 1 2 3 4 5 6 Time (ms) Junctional SR [Ca 2+ ] Vs Time 1 2 3 4 5 6 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 [Ca 2+ ] SR the iperatoxin results can be explained by a delay in refilling. Simulated Effects of Calsequestrin [Ca 2+ ] (μm) 15 1 5 Increased CSQ Simulation 1 2 3 4 5 6 Time (ms) 15 Decreased CSQ Simulation [Ca 2+ ] (μm) 1 5 1 2 3 4 5 6 Time (ms) 27
SR Buffer Data Condition Peak Amplitude Peak duration %Spark rate (Sim.) %Spark rate (Exp.) Control 128 μm 24 ms 1% 1% Increased CSQ expression 147 μm 15 ms 28% 27% Decreased CSQ expression 12 μm 18 ms 19 % 183% Citrate 156 μm 17 ms 27% 38% Terentyev et al., 23 Presentation Outline 1. Introduction 2. Spark Termination 3. Spatial Spread of Sparks 4. Conclusions 28
Summary/Conclusions Our sticky cluster model of a Ca 2+ release unit can simulate Ca 2+ sparks that terminate reliably. Termination occurs through coupled gating and the influence of lumenal calcium. Reducing coupling between RyRs increases Ca 2+ spark duration, consistent with experimental effects of FK56. Ca 2+ spark magnitude is only mildly sensitive to the number of RyR's in the cluster and the Ca 2+ 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 Ca 2+ spark model into a model for whole cell Ca 2+ dynamics of the cardiac myocyte to demonstrate that the summation of many sparks from different release sites give rise to the global Ca 2+ transient. 29
Cardiac Myocyte Results AP curve Obtained from Natali et al. 22 Cardiac Myocyte Results Simulated patch clamp experiments under normal conditions. 2, FRUs simulated. Transient recordings by Bouchard et al. 1995 3
Cardiac Myocyte Results SR transient recorded by Wang et al. 24 Simulated patch clamp experiments under normal conditions. 2, FRUs simulated. Cardiac Myocyte Results Simulated patch clamp experiments under normal conditions. 2, FRUs simulated. Lumenal transient recorded by Brochet et al. 25 31
Cardiac Myocyte Results Graded release 2 1.8 1.6 Peak Release (mm/s) 1.4 1.2 1.8.6.4.2-5 -4-3 -2-1 1 2 3 4 5 Membrane potential (mv) Graded release Simulated patch clamp experiments under normal conditions. 2, FRUs simulated. Release curve recorded by Wier et al. 1994 Cardiac Myocyte Results Gain Function Plot 25 2 Gain (Jsr/Ica) 15 1 5-4 -3-2 -1 1 2 3 4 5 Membrane potential (mv) Gain Simulated patch clamp experiments under normal conditions. 2, FRUs simulated. Experimentally generated gain plot from Wang et al. 24 32
END Ca 2+ sparks activated during ramp-depolarization from -6 to -4 (from Cannell, Cheng & Lederer (1995), Science 268: 145.) 33