IMMOBILIZATION-INDUCED ADAPTATIONS IN SKELETAL MUSCLE: CONTRACTILE PROPERTIES AND CALCIUM DYNAMICS
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Transcript of IMMOBILIZATION-INDUCED ADAPTATIONS IN SKELETAL MUSCLE: CONTRACTILE PROPERTIES AND CALCIUM DYNAMICS
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111Equation Chapter 1 Section 1
IMMOBILIZATION-INDUCED ADAPTATIONS IN SKELETAL MUSCLE:
CONTRACTILE PROPERTIES AND CALCIUM DYNAMICS
Matthew J. Conaway!"
an# B$%an C. C&a$'!"!(
.
1Ohio Musculoskeletal and Neurological Institute (OMNI), 2Department of
Biomedical Sciences, and Department of !eriatric Medicine and !erontolog" at Ohio
#ni$ersit", %thens, Ohio &'1
%ddress for *orrespondence+
Dr Matthe- . *ona-a"
Ohio #ni$ersit"OMNI / the Dept of Biomedical Sciences, 220 Ir$ine all
%thens, O &'1
mcona-a"304gmailcom
ABSTRACT
5he purpose of this -ork -as to e6amine the intramuscular mechanisms of muscle -eakness 7"
8uantif"ing changes in e$oked muscle force9time cur$es follo-ing &9-eeks of cast
immo7ili:ation, and use mathematical models to predict muscle force generation 7ased on the
d"namics of *a2; descri7ed 7" a ) or a control
group (n>) Before and after a &9-eek inter$ention period stud" participants peak e$oked force
from suprama6imal dou7let electrical stimulation and the relati$e rates of e$oked force
mailto:mjconaway68@mailto:mjconaway68@ -
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de$elopment 7et-een 1 and &? and ' and @? of peak force (;d=Adt) -ere determined
along -ith the relati$e rate of force rela6ation 7et-een @ and '? of peak force (9d=Adt)
Mathematical modeling -as used to predict muscle force generation 7ased on the d"namics of
*a2;descri7ed 7" a
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to9dou7let force ratio), and results in a slo-ing in the rate of e$oked for de$elopment (&)
=indings of this nature suggest that disuse alters the ph"siological properties in$ol$ed in the
e6citation9contraction coupling process, 7ut our o$erall understanding of these changes in human
skeletal muscle is particularl" limited %ccordingl", the purpose of this -ork -as to e6amine the
intramuscular mechanisms of muscle -eakness 7" 8uantif"ing changes in e$oked muscle force9
time cur$es follo-ing four -eeks of cast immo7ili:ation, and use mathematical models to
predict muscle force generation 7ased on the d"namics of calcium (*a2;) descri7ed 7" a
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Cast Immobilization Procedures.Su7ects in the immo7ili:ation group -ere fitted -ith a
rigid -rist9hand cast on the non9dominant forearm (Model 111911, Orthomerica, Orlando,
=lorida) 5he casts -ere made of light-eight pol"eth"lene and e6tended from ust 7elo- the
el7o- all the -a" past the fingers 5his cast does not permit -rist fle6ionAe6tension mo$ements
nor does it permit finger usage (eg, 7ecause the cast e6tends -ell 7e"ond the fingers, holding a
glass -ith the immo7ili:ed fingers is not possi7le) *asts -ere remo$ed 2H timesA-eek under
super$ision to -ash the arm and inspect it for complications (eg, skin lesions, edema) e
ensured compliance of the casting protocol at all other times 7" securing athletic tape around the
cast and marking the e6terior la"ers -ith a custom signature stamp to allo- us to tell if the
su7ects attempted to remo$e the cast
Voluntary and Evoked Contractile Properties. 5o 8uantif" -rist fle6ion forces su7ects
-ere seated -ith the el7o- at @J, the hand pronated, and the forearm supported and restricted
-hile the head rested on a pad (Biode6 S"stem &, Biode6 Medical S"stems, Shirle", NK) 5he
-rist ointLs a6is of rotation -as aligned -ith the a6is of rotation of a tor8ue motor to -hich a
le$er arm -as attached 5he signal -as scaled to ma6imi:e its resolution (20 m per N9M
Biode6
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Electrical stimulation -as deli$ered viaa Digitimer high $oltage constant current
stimulator (model DS%) to the median ner$e in the 7icipital groo$e at the optimal stimulation
site identified -ith a handheld pro7e Su7se8uentl", suprama6imal stimulation -as deli$ered via
surface electrodes (%gH%g*l, 21' Nikomed 5race1, udson alle", F%) 5o identif" changes
in the functional properties of the -rist fle6or muscles, -e e$aluated the force9time cur$es
e$oked from an electrical dou7let (1 :) deli$ered once per second for a total of 1 e$oked
contractions Feak force, the relati$e rates of e$oked force de$elopment 7et-een 1 and &?
(initial phase) and ' and @? (latter phase) of peak force (;d=Adt) -ere calculated along -ith
the relati$e rate of force rela6ation 7et-een @ and '? of peak force (9d=Adt) -ere calculated
and a$eraged across all e$oked contractions
Mathematical Model Formulation. 5he model de$eloped 7" Ding et al proposed that
d"namic isometric muscle forces are go$erned 7" e8uations19 (0911, 191', ) 5his model
descri7es the transient 7eha$ior of the t-o state $aria7les, , the normali:ed amount of
*a2;9troponin comple6, and the isometric force produced 7" muscle stimulation 5he state
$aria7le 7eha$es as a Michaelis9Menten process (2) 5he $aria7les are go$erned 7" the
free parameters Cc,A, , C1, and C2 5he parameter Ccis the time constant that modulates C
5he parameter is the sensiti$it" of $oltage9gated channels to the change in *a2;current
5he parameter C1 is the time constant of the decline in force due to the a7sence of strongl" 7ound
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cross97ridges, and C2is the time constant of decline in force due to the e6tra friction 7et-een
actin and m"osin resulting from the presence of cross97ridges 5he parameterAis the scaled
gain
22P ME
P ME
&&P ME
E8uation 1 represents the time9$ar"ing change in de$eloped force as a function of the
time9$ar"ing *a2;9troponin 7inding throughout a contraction E8uation 2 represents the glo7al
summation of nonlinear acti$ation of indi$idual muscle fi7ers in response to an input train
E8uation represents the d"namics of *a2;9troponin 7inding, captured in the unitless $aria7le
and modulated 7" the time constant Cc, -hich 8ualitati$el" descri7es the rate9limiting
step 7efore the actin and m"osin mechanicall" translate across each other and generate force
(12)5o account for the nonlinear summation of *a2;transients in single muscle Q7ers
stimulated -ith dou7lets, Ding et al proposed the!9model in E8 2 (0), -hich -as 7ased on the
earlier -ork of Duchateau and ainaut -ho in$estigated the force summation from human
adductor pollicis muscles triggered 7" paired stimuli at different interpulse inter$als (IFIs)
ranging from '9ms to 29ms (1) 5he results sho-ed that the forces generated 7" the dou7let
trains -ere greater than the sum of t-o indi$idual t-itches =urthermore, the force enhancement
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from the second pulse -as highest -hen the IFI -as '9ms and declined e6ponentiall" -ith
increases of the IFI 5he enhanced force of the paired stimuli -as suggested to 7e due to the
enhanced release of di$alent *a2;7" the second pulse (@) Ding et al modiQed the t-o9step
model 7" adding a factor -here is a scaling term that accounts for the differences in the
degree of acti$ation 7" each pulse relati$e to the Qrst pulse of the train (0)5he magnitude of the
enhancement is characteri:ed 7" a scalar , and its duration is characteri:ed 7"
=urthermore, Ding et al suggest that
su7se8uent pulses in a stimulus train as a deca"ing process =urther, the
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su7set of fi6ed parameters -ith initial $alues, is gi$en Our model of muscle force -as $alidated
using suprama6imal dou7let stimuli In addition, the model -as sho-n to 7e ro7ust using force
data from immo7ili:ed and non9immo7ili:ed muscles in different su7ects
###ISE!$ $A%&E ' (E!E###
e used the Re$en7urg9Mar8uardt unconstrained optimi:ation algorithm to estimate
model parameters Model agreement -ith the data -as calculated 7" minimi:ing the residual
difference 7et-een the force predicted from the model and the force measured from test su7ects
5he %kaike =inal Frediction Error (=FE) criterion pro$ides a measure of model 8ualit" 7" testing
the model on different parameter sets %fter se$eral different models are computed, the" can 7e
compared using this criterion %ccording to theor", the most accurate model has the least =FE
5he %kaike =FE is thus defined 7" the follo-ing e8uation+
(3)
-here Vis the s8uared error loss function, dis the num7er of optimi:ed parameters, andis the
num7er of points in the data set 5he s8uared error loss function Vis defined 7" the follo-ing
e8uation+
()
-here represents the estimated parameters#sing the optimal parameter $alues determined for from the 7aseline testing data for each
su7ect and model, force train predictions -ere produced for the post9testing data 5he %kaike
=FE criterion pro$ides a measure of model 8ualit" 7" simulating the situation -here the model is
tested on different parameter sets %fter se$eral different models -ere computed, the" -ere
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compared using this criterion %ccording to theor", the most accurate model has the least =FE as
agreement, not correlation, 7et-een a model and e6perimental data is -hat is sought %ctual
numerical $alues of force are not important for this component of the stud" per se, 7ut rather the
8uestion to 7e ans-ered is o- -ell does a model agree -ith the e6perimentTLG -hich leads
to the 8uestion fundamental to this stud"+ hich model agrees 7est -ith e6perimentTL
%ccordingl", -e used the %kaike =FE from the M%5R%B 0 Optimi:ation 5ool7o6 (5he
Math-orks, Natick, M%) to e$aluate the fit of each optimi:ation of each model relati$e to the
e6periment for 7oth test states 5herefore, the %kaike =FE -as determined for each candidate
optimal parameter set against data from the post9testing session for 7oth groups In all cases, the
optimal parameter set is the one that generates the least %kaike =FE -hile returning the most
realistic parameter $alues e $alidated our model of muscle force 7ased on the e$oked force
from a suprama6imal 19: dou7let in 7oth immo7ili:ed and non9immo7ili:ed muscles
o7tained from preliminar" data from the e6perimental and control groups Optimi:ation of these
ten free parameters -ere su7se8uentl" used to calculate agreement 7et-een the model and data
Specificall", to compare 7eha$ior 7et-een groups o$er time, parameter $alues (Cc>2, C1>20,
C2>32, U1>0, U2>', a>', 7>2, c>'), -ere optimi:ed for the respecti$e groups and the
%kaike =FE -as used to identif" the optimal parameter set for each e6perimental condition as
-ell as for the entire series of e$oked contractions Farametric trends -ere ascertained from this
anal"sis
Statistical Analysis. 5-o9-a" mi6ed9model %NO% tests -ere used to compare
differences 7et-een groups o$er time (7et-een9su7ects factor+ group -ithin9su7ects factor+
time) =or all anal"ses a t-o9tailed preset alpha9le$el of significance e8ual to ' -as re8uired
for statistical significance, and Sidak post9hoc tests -ere used to in$estigate significant main
effects or interactions Eta9s8uared effect si:es (2) are also reported to pro$ide an estimate of
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the magnitude of an effect Data are presented as meanstandard de$iation 5he SFSS statistical
package ($ 1@ for Mac, *hicago, Illinois) -as used for data anal"sis
Re*,&t*
oluntar" muscle strength decreased &? in the immo7ili:ation group (23'@ to
1''@ Nm), 7ut did not change in the control group (2112 to 21212& Nm)
(group 6 time interaction p>2, 2>&) e o7ser$ed a significant group 6 time interaction
term for the latter phase ;d=Adt(p>2, 2>&1) indicating that the immo7ili:ation group
e6hi7ited a slight slo-ing in the latter phase ;d=Adtfollo-ing immo7ili:ation -hen compared to
the slightl" faster latter phase ;d=Adto7ser$ed in the control group at post9testing e did not
o7ser$e significant interaction terms for e$oked dou7let peak force (p>2, 2>1), or the
initial ;d=Adt(p>3&, 2>2) or Hd=Adt(p>1, 2>1) Data on changes in the contractile
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properties are pro$ided in ta7le 2
e o7ser$ed a significant group 6 time interaction term for Cc(=igure 1, p1, 2>2)
indicating that the immo7ili:ation group e6hi7ited a 2'? increase in this time constant -hen
compared to no change in the control group at post9testing e did not o7ser$e significant
interaction terms for the other modeled parameters (C1p>, 2>1 U1p>3&, 2>2 U2
p> , 2>1 a p>0@, 2> %kaike =FE p>&', 2>') Data on these modeled
parameters are pro$ided in ta7le
D%*,**%on
5he purpose of this -ork -as to e6amine the intramuscular mechanisms of muscle
-eakness 7" 8uantif"ing changes in e$oked muscle force9time cur$es follo-ing four -eeks of
cast immo7ili:ation, and use mathematical models to predict muscle force generation 7ased on
the d"namics of *a2;descri7ed 7" a
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reaction rates (Cc) follo-ing cast immo7ili:ation %dditionall", -e o7ser$ed a slo-ing in the
latter part of the relati$e rate of force de$elopment Belo- -e discuss these findings in further
detail
Our findings indicate that -hile four -eeks of cast immo7ili:ation results in a dramatic
reduction in $oluntar" muscle strength, the ma6imal dou7let force generating capacit" of the
muscular itself is relati$el" resistant to adaptation as -e did not o7ser$e an" change in the peak
dou7let e$oked force %dditionall", -e did not o7ser$e an" changes in the initial phase of e$oked
force de$elopment, the rate of rela6ation, or the maorit" of the modeled parameters Rikel"
similar to pre$ious modeling -ork in chronicall" paral":ed human soleus, the lack of difference
in the modeled parameters 7et-een the test states ma" 7e 7ecause the stimulation fre8uenc" is
less than ' pulses per second () Our o7ser$ation of the -rist fle6or muscles 7eing relati$el"
resistant to immo7ili:ation9induced adaptations is reasona7l" consistent -ith that reported 7"
=ugle$and and colleagues for the intrinsic hand musculature as -ell as Kue and colleagues for
the el7o- fle6or muscles (1@,1) In 7oth of these prior e6periments, it -as reported that 9'
-eeks of cast immo7ili:ation slightl" increased e$oked t-itch force -ithout altering the t-itch
contraction time Similarl", our findings are congruent -ith our pre$ious report on changes in the
e$oked contractile properties of the -rist fle6or muscles follo-ing three -eeks of cast
immo7ili:ation (2) In our prior -ork, -e noted no changes in e$oked dou7let force or the rate of
force rela6ation, 7ut -e did o7ser$e a slo-ing in the rate of e$oked force rela6ation -hen
a$eraged across the entire force de$elopment time inter$al %ccordingl", the collecti$e findings
from the present stud" suggest that health" human -rist fle6ion musculature is generall"
resistant to functional adaptation of the contractile properties -hen its use has 7een reduced for
four -eeks 7" immo7ili:ation o-e$er, it should 7e noted that -e o7ser$ed a dramatic decrease
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in $oluntar" muscle strength, -hich suggests that negati$e adaptations are occurring in the
neuromuscular force production path-a" that contri7ute to the de$elopment of muscle -eakness
Based on our prior -ork, -e speculate that a large proportion of the -eakness is associated -ith
impairments in $oluntar", neural acti$ation of the musculature (293) o-e$er, it should 7e
noted that -e did not o7tain e$oked tetanic forces, and immo7ili:ation has 7een sho-n to
dramaticall" reduce tetanic force (13) 5his suggests that prolonged high9fre8uenc" acti$ation of
muscle ma" 7e more impaired in comparison to e$oked t-itch or dou7let responses
5he finding of an altered Ccfollo-ing immo7ili:ation is interesting 5his parameter -as a
fi6ed parameter in the pre9test data, and -as estimated from the post9test data to optimi:e the
model according to the modelAerror trade9off that the %kaike =FE demands 5his increase in Cc
likel" e6plains our o7ser$ed slo-ing of the rate of e$oked force de$elopment during the latter
phase of contraction Specificall", a larger Ccis considered to indicate an increase in the 7inding
and dissociation times as -ell as sarcoplasmic aggregate of the *a2;9troponin comple6 (@, 11,
1&) In turn, increased 7inding and dissociation times ma" e6plain the mechanism of a slo-ing
in the rate of force de$elopment Our modeling findings suggesting a longer 7inding and
disassociation time of the *a2;9troponin comple6 could e6plain the recentl" reported reduction in
*a2;sensiti$it" in single skeletal muscle fi7ers follo-ing t-o -eeks of cast9immo7ili:ation (21)
Belo-, to facilitate a more complete understanding of our findings, -e discuss in further details
the de$elopment and conceptual 7asis of our force model
The Force Model.5he force model -as de$eloped 7" decomposing the contractile
response into distinct ph"siological steps+ *a2;release and rea7sorption 7" the sarcoplasmic
reticulum (S
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7inding process is usuall" considered to 7e a t-o9step reaction, e6ler et al onl" considered its
o$erall effect of the for-ard and 7ack-ard reaction rates () =rom 7asic chemical kinetics and
mem7rane transport, the t-o differential e8uations that descri7e the calcium transient in the
sarcoplasm and the *a2;9troponin 7inding processes are in the muscle In the first chemical
e8uation, the Qrst t-o terms represent the dissociation of *a2;9troponin comple6 (5a) and 7inding
of *a2;to troponin, respecti$el" 5he third term is the rate of concentration increase due to
diffusion from the S< and the fourth term corresponds to diffusion and rea7sorption of *a2;7ack
into the SC1;C2V5aWAV5W, -here C1is
the $alue of the time constant in the a7sence of cross97ridges and is the additional frictional
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component due to the actin9m"osin 7onds () Making additional su7stitutions for B and 7A
gi$es
d=Adt>V5aW(19=A=m)9=A(C1;C2V5aWAV5W)
Ding and colleagues decomposed the contractile response to account for the distinct
ph"siological step of cross97ridge acti$ation (0) 5o model cross97ridge acti$ation, it -as sho-n
that the force9prediction a7ilit" of the model is relati$el" insensiti$e to the speciQc cur$ature and
amplitude of the calcium and calcium9troponin comple6 transient 5his implied that the first t-o
steps in the earlier model () could 7e com7ined into one 7" the unitless factor, *N =rom the
follo-ing differential e8uation, the d"namics of *Nare modulated 7" the time constant, Cc, -hich
descri7es 8ualitati$e the rate9limiting step 7efore the actin and m"osin mechanicall" translate
across each other and generate force (0) Our force model structure is the first to incorporate
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prolonged compared to a t-itch (2) %t lo- fre8uencies that generate t-itches -ithout fusion,
staircase phenomena in 7oth mathematical directions ha$e 7een o7ser$ed (2) 5his implies a
facilitation or depression of the force profiles from successi$e inputs, as -ell as post9tetanic
potentiation of t-itches (2)
Since a larger Ccindicates an increase in the 7inding and dissociation times as -ell as
sarcoplasmic aggregate of the *a2;9troponin comple6 (@, 11,1&), this implies that muscle disuse
that results from immo7ili:ation ma" disrupt the processes of facilitation or post9tetanic
potentiation that occurs -hen additional pulses are applied #pon immo7ili:ation of a muscle,
disrupted facilitation and post9tetanic potentiation ma" slo- rates of force de$elopment Indeed,
such a disruption in the contractile process ma" underlie decreased pro7a7ilities of calcium
channel acti$ation as -ell as inacti$ation in single immo7ili:ed skeletal muscle fi7ers, and it
-ould 7e interesting for future -ork to in$estigate these potential changes as a function of
muscle stimulation fre8uenc" in the range of 1 to 1 pulses per secondLimitations of the Present Work and Conclusions.5here are se$eral limitations of this
stud", -hich should 7e noted =irst, the population studied -as a relati$el" small num7er of
"oung, health" indi$iduals, and the data is onl" from one muscle group (-rist fle6ors)
%ccordingl", care should 7e taken to not e6trapolate these findings to other cohorts (eg, the
interacti$e effects of immo7ili:ation -ith age could differ), other disuse andAor muscle -asting
conditions (eg, post9surger", cancer cache6ia, microgra$it", etc), and other muscle groups
%dditionall", our data are 7ased on a series of ten e$oked dou7lets hence, to ascertain more
generali:a7le d"namics of immo7ili:ed muscle, the modified Ding model needs to 7e
in$estigated using stimulated forces e$oked -ith higher fre8uencies Rastl", another limitation of
this stud" is that there is no demonstra7le modeling of the transition 7et-een pre9immo7ili:ed
and post9immo7ili:ed states -ithin a muscle In the present stud", muscle 7eha$ior has 7een
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calcium9troponin mechanism 7eing one likel" contri7utor =uture -ork is needed to 7etter
delineate the neural and muscular mechanisms of muscle -eakness associated -ith models of
disuse as -ell as -eakness associated -ith disease states so that targeted effecti$e inter$entions
to promote muscle function can 7e de$eloped
9
ACKNO)LEDEMENT
5he e6tensi$e M%5R%B programming -ork of Mr
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*
B* *lark has recei$ed consulting fees from
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5a7le 1 Initial $alues of parameter sets for force models =ree parameters -ere estimated for the
post9testing data 7" Re$en7urg9Mar8uardt unconstrained optimi:ation
Model =i6ed Farameters
-ith Initial alues
=ree Farameters
Ding Cc>2 ms
3@
%, km, C1, C2
E6perimental Cc>2 ms km, C1, C2, U1, U2, a, 7, c
% is scaled
5a7le 2 *hanges in contractile properties 7efore and after &9-eeks of cast immo7ili:ation
(immo7ili:ation group) or 7efore and after a &9-eek period -ith no inter$entions (controlgroup)
Feak =orce
(Nm)
Initial Fhase
;d=Adt
(?Amsec)
Ratter Fhase;d=Adt
(?Amsec)
9d=Adt(?Amsec)
Fre Fost Fre Fost Fre Fost Fre Fost
Immo7ili:ation !roup
222
0
01
2'13
0
3@
1@
20
1@
2@
1&3
1&
10P
1
91&
&&
911
2
*ontrol !roup
22&
'
3
231@
1&
2'
2'
10
'@
1
@
1''
1
912
@
910
&
0 Initial Phase 4dF5dt6 !elative rate o1 evoked 1orce development bet7een '#89 o1 peak doublet 1orce.
&atter Phase 4dF5dt6 !elative rate o1 evoked 1orce development bet7een :#;9 o1 peak doublet 1orce.
#dF5dt6 !elative rate o1 evoked 1orce rela,ation bet7een ;#:9 o1 peak doublet 1orce.
*+roup , $ime Interaction p2.0< Eta0E11ect Size2.8'.
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5a7le No changes -ere o7ser$ed for the maorit" of muscle force model parameters 7efore
and after &9-eeks of cast immo7ili:ation (immo7ili:ation group) or 7efore and after a &9-eek
period -ith no inter$entions (control group) 5he one nota7le significant effect is illustrated in
=igure 1
C1 U1 U2 a %kaike =FEFre Fost Fre Fost Fre Fost Fre Fost Fre Fost
Immo7ili:ation
!roup
&2
@
&1@
10
1
@
2
@
2
'
'
203
2'
2
2@
2'
@
1&
2
21
1
*ontrol !roup
3&
13
&13
1&
3
0
1
2
3
1
2
&@
&@
2
1
21
3
'
10
1
1
1
12
1
2
APPENDI/:Rist of parameters for muscle force model
S"m7ol #nit Definition alue
*N Normali:ed amount of *a2;9troponin comple6 aries
= N Mechanical force aries
ti ms 5ime of the ith stimulation aries
N 5otal num7er of stimuli in the train 7efore time t aries
tp ms 5ime of the pth data point aries
t= ms 5ime of the 8th set of force model parameter set aries
Cc ms 5ime constant controlling the rise and deca" of *N 2
% NAms Scaling factor aries
C1 ms5ime constant of force decline at the a7sence of
strongl" 7ound cross97ridges
20
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C2 ms
5ime constant of force decline due to the e6tra
friction 7et-een actin and m"osin resulting from
the presence of cross97ridges
32
kmSensiti$it" of $oltage9gated calcium channels
to the change in calcium current
3
U1 ms91 Fro7a7ilit" that calcium channel -ill acti$ate 0
U2 ms91 Fro7a7ilit" that calcium channel -ill inacti$ate '
% *oefficient of k m '
B E6ponent of k m 1'
* Intercept of k m '
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