CN107330275B - A kind of modeling method to skeletal muscle fast muscle fiber excitation-contraction process - Google Patents
A kind of modeling method to skeletal muscle fast muscle fiber excitation-contraction process Download PDFInfo
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Abstract
The invention discloses a kind of modeling methods to skeletal muscle fast muscle fiber excitation-contraction process, include the following steps：1) as unit of half sarcomere, skeletal muscle fast muscle fiber film electro physiology mathematical model is established；2) as unit of half sarcomere, the geometrical model of calcium ion cycle is established；3) the calcium ion mathematical model that Reynolds routing (RyR) discharges from terminal cistern is established；4) mathematical model that calcium ion in sarcoplasm, magnesium ion are combined respectively with ATP, parvalbumin is established；5) mathematical model of calcium binding troponin and cross-bridges dynamic mathematical model are established；6) the film Tiredness model generated during skeletal muscle fast muscle fiber excitation-contraction and metabolic Tiredness model are established.The present invention is to be based on skeletal muscle physiological structure, it is established that skeletal muscle fiber excitation-contraction process can more accurately be analyzed, simulate and be predicted to the mathematical model of links.The present invention can be diagnosed for skeletal muscle disease, rehabilitation medical provides theoretical direction.
Description
Technical field
The present invention relates to the modeling methods to skeletal muscle fast muscle fiber excitation-contraction process.
Background technology
At present there are many mathematical model of research skeletal muscle fiber excitation-contraction, but these models are largely bases
In experience, it is impossible to simulate the entire skeletal muscle excitation-contraction process as caused by electro photoluminescence, and have ignored skeletal muscle excitement receipts
The fatigue generated in compression process influences, and is not based on physiological Mechanism founding mathematical models, it is impossible to accurate simulation and prediction bone
Flesh muscle fibre excitation-contraction process.Based on problem above, it is necessary to establish completely, can describe to be pierced by electricity from physiological Mechanism
Entire skeletal muscle excitation-contraction process mathematical model caused by swashing.
Invention content
The present invention is in order to which solution must not simulate the entire skeletal muscle excitation-contraction process as caused by electro photoluminescence, and ignore
The fatigue generated during skeletal muscle excitation-contraction influences, and is not based on physiological Mechanism founding mathematical models, it is impossible to accurately
It simulates and predicts this problem of skeletal muscle fiber excitation-contraction process, and propose a kind of to skeletal muscle fast muscle fiber excitement receipts
The modeling method of compression process.
A kind of modeling method to skeletal muscle fast muscle fiber excitation-contraction process is realized according to the following steps：
1) as unit of half sarcomere, skeletal muscle fast muscle fiber film electro physiology mathematical model is established；
2) as unit of half sarcomere, the geometrical model of calcium ion cycle is established；
3) the calcium ion mathematical model that Reynolds routing (RyR) discharges from terminal cistern is established；
4) mathematical model that calcium ion in sarcoplasm, magnesium ion are combined respectively with ATP, parvalbumin is established；
5) mathematical model of calcium binding troponin and cross-bridges dynamic mathematical model are established；
6) the film Tiredness model generated during skeletal muscle fast muscle fiber excitation-contraction and metabolic Tiredness model are established.
Further：Mammalian bone flesh is described using Hodgkin-Huxley electrophysiological models in the step 1
Fast muscle fiber sarolemma and T periosteum curent changes, specifically include potassium ion inward rectifying current (IIR), potassium ion delayed rectifier current
(IDR), sodium ion electric current (INa), Cl-currents (ICl), sodium-potassium pump (INaK), the electric current on corresponding T pipes hasIt is balanced according to Donnan, chlorion is passively distributed in film both sides, using Goldman-
Hodgkin-Katz (GHK) driving force equations drive the transmembrane movement of ion；
Electric current (I at T tube inletsT)：
IT=(Vs-Vt)/Ra (1)
Wherein VsFor sarolemma voltage, VtFor T tube voltages, RaResistance constant for T tube inlets；
Sarolemma voltage is：
WhereinIt is sarolemma electric current, CmIt is membrane capacitance constant；
T tube voltages are：
WhereinIt is T tube currents, γ is T pipe surfaces product and sarolemma surface area ratio；
Sarolemma electric current is：
Wherein IappFor applied current density constant；
T tube currents are：
T periosteum voltages are calculated by above formula, thunder is activated when voltage is higher than dihydropyridine voltage sensor threshold value
Promise channel.
Further：Half sarcomere is divided into 5 sections (from Z-line to M lines) in the step 2；
Half sarcomere volume：
V=lxπR2(wherein lxFor half sarcomere length, R is muscle fibril radius) (6)
Sarcoplasmic reticulum (SR) volume：V1=5.5%V
Terminal cistern (TSR) volume：V2=3.5%V
External muscle fibril volume：V3=6%V
Muscle fibril volume comprising actin filament：
Muscle fibril volume not comprising actin filament：
By the Geometric Modeling of double of sarcomere, calcium ion cycle analysis will be carried out in the geometrical model built.
Further：Dihydropyridine receptor (DHPR) experiences T tube voltages V in the step 3t5 ryanodines are stimulated afterwards
The open and close of channel (RyR)；
Activation rate under Reynolds routing closed state：
kC=0.5 α1exp(Vt-V′/(8K)) (7)
Wherein α1, V ', K be Reynolds routing activation rate constant, unit is respectively ms-1、mV、mV；
Deactivation rate under Reynolds routing closed state：
Reynolds routing is closed C0Equation be：
Wherein kLRate constant, k are opened for Reynolds routingLmFor Reynolds routing shutdown rate constant；
Reynolds routing is in opening state O0Equation be：
Wherein f is ryanodine channel design allosteric factor constant；
Opening (the O of remaining four channel1、O2、O3、O4) with closing (C1、C2、C3、C4) state modeling method and C0、O0Class
Seemingly, by the control to ryanodine passage switching state, and then the release of calcium ion in sarcoplasmic reticulum is controlled.
Further：Calcium ions and magnesium ions are combined, and with ATP, parvalbumin site in sarcoplasm respectively in sarcoplasm in the step 4
Middle diffusion：
(1) mathematical model of calcium ion and binding site
Wherein S is ATP, parvalbumin site concentration, konIt is the association rate in calcium ion and site, koffCalcium ion with
The rate of departure in site；
(2) mathematical model of calcium ion and binding site
(3) diffusion mathematical model of each free ion in sarcoplasm
Wherein r is half sarcomere radial coordinate, and x is longitudinal coordinate, and D is free diffusing coefficient, and C is the dense of diffusion ion
Degree, F (C, t) is that the function that free ion concentration changes over time is calculated by (11), (12).
Further：Calcium ion is combined with troponin in the step 5, changes tropomyosin occurred conformation, from
It is detached on actin, exposes myosin binding site, cross-bridges activation；
(1) calcium ion with troponin is combined and former myogen occurred conformation variation carries out mathematical modeling
1. troponin (Tn) has 6 kinds of states：B1、B2、B3Represent that troponin does not have under interacting with tropomyosin
With reference to calcium ion, with reference to 1 calcium ion, with reference to 2 calcium ions；T1、T2、T3Represent that troponin detaches down with tropomyosin
Be not bound with calcium ion, with reference to 1 calcium ion, with reference to 2 calcium ions；
B1+B2+B3+T1+T2+T3=1 (14)
Wherein K1~K5, k-1~k-5It is adjustable parameter；
State during 2. tropomyosin (Tm) has 5：Wherein there are 3 state Bs Chong Die with troponin0、B1、B2, C is former
Myosin equilibrium state, M are tropomyosin and actin, myosin interacting state；
B0+B1+B2+ C+M=1 (20)
Wherein K '0k-0It is the positive rate of M deformation, α is the average quantity of target area cross-bridges, and n is target area original flesh
The number of globulin；
(2) cross-bridges dynamic mathematical model
Cross-bridges weak binding model in sarcoplasm
Wherein f0It is cross-bridges exposure rate, fpRate of departure when being cross-bridges weak binding, CTmIt is contained original in half sarcomere
The concentration of myosin, h0It is the positive rate of cross-bridges expansion stroke, hpIt is the reverse rate of cross-bridges expansion stroke, g0Cross-bridges is done
The rate of departure after the strong combination of work(stroke；
Calcium ion in sarcoplasm by calcium pump active transport to sarcoplasmic reticulum, being combined in sarcoplasmic reticulum with calsequestrin,
The lid of high concentration is stored, when calcium ion release channel is activated, is discharged into sarcoplasm by calcium channel, calcium is formed and follows
Ring.
Further：The slow inactivation of sodium-ion channel draws during skeletal muscle fast muscle fiber excitation-contraction in the step 6
Film fatigue is played, the phosphate that ATP hydrolysis generates during cross-bridge cycle causes metabolic fatigue；
(1) it establishes skeletal muscle fast muscle fiber excitation-contraction process and generates film fatigue mathematical model
S∞=1/ (1+exp ((Vs-VS∞)/AS∞)) (25)
τS=8571/ (0.2+5.65 (((Vs+Vτ)/100)2) (26)
Wherein VsFor membrane voltage, VSHalf of the ∞ for the slow inactivated channel maximum voltage of sodium ion, AS∞ slope factor constants,
VτIt is to τSThe half of maximum voltage value；
(2) phosphoric acid in the tired mathematical model sarcoplasm of skeletal muscle fast muscle fiber excitation-contraction process generation metabolism is established
(Pi)：
Wherein h0It is cross-bridges expansion stroke forward direction rate, hPIt is cross-bridges expansion stroke reverse rate, A1When being cross-bridges weak binding
Cross-bridges concentration, A2It is cross-bridges concentration, b when cross-bridges combines by forcePBe in sarcoplasm phosphoric acid reduce rate, kPIt is P in sarcoplasmiIt is transported to
The rate of sarcoplasmic reticulum (SR), V4+V5It is sarcoplasm volume；
Phosphoric acid (P in sarcoplasmic reticulum (SR)i)：
Wherein V1It is the volume of sarcoplasmic reticulum, APiIt is phosphoric acid and calcium binding rate in sarcoplasmic reticulum, PiPiIt is phosphoric acid meltage
Product,It is the concentration of calcium ion in sarcoplasmic reticulum, BPIt is the rate of phosphoric acid combination calcium ion dissolving；
The combination of phosphoric acid and calcium ion in sarcoplasmic reticulum：
It is calculated by formula (11), (12), (13), film fatigue reduces T periosteum voltage magnitudes, reduces calcium channel
Activation；(14), (15), (16) calculate, and reduce calcium ion and are discharged from sarcoplasmic reticulum, thereby reduce the quantity of cross-bridges activation,
Skeletal muscle fast muscle fiber shows as fatigue.
Invention effect：
(1) it based on physiological Mechanism, establishes and the complete mathematics of skeletal muscle fiber excitation-contraction process is caused by electro photoluminescence
Model.
(2) the film fatigue generated during skeletal muscle fast muscle fiber excitation-contraction and metabolism fatigue are considered, and is built
Corresponding mathematical model is found.
(3) it accurately can simulate and predict skeletal muscle fast muscle fiber excitation-contraction process.
It (4) can be as the theoretical direction of experiment.
Description of the drawings
Fig. 1 is sarolemma voltage and T tube voltage simplified model schematic diagrames；
Fig. 2 is half sarcomere Geometric Modeling schematic diagram；
Fig. 3 is the schematic diagram that calcium ion, magnesium ion are combined with each cushion in sarcoplasm；
Fig. 4 is 6 status diagrams of troponin；
Fig. 5 is 5 status diagrams of tropomyosin；
Fig. 6 generates process schematic for metabolism fatigue；
Fig. 7 is skeletal muscle fast muscle fiber excited process mathematical modeling flow chart.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawings and examples.
As shown in fig. 7, a kind of modeling method to skeletal muscle fast muscle fiber excitation-contraction process includes the following steps：
1) as unit of half sarcomere, skeletal muscle fast muscle fiber film electro physiology mathematical model is established；
2) as unit of half sarcomere, the geometrical model of calcium ion cycle is established；
3) the calcium ion mathematical model that Reynolds routing (RyR) discharges from terminal cistern is established；
4) mathematical model that calcium ion in sarcoplasm, magnesium ion are combined respectively with ATP, parvalbumin is established；
5) mathematical model of calcium binding troponin and cross-bridges dynamic mathematical model are established；
6) the film Tiredness model generated during skeletal muscle fast muscle fiber excitation-contraction and metabolic Tiredness model are established.
As shown in Figure 1, mammalian bone flesh is described using Hodgkin-Huxley electrophysiological models in the step 1
Fast muscle fiber sarolemma and T periosteum curent changes, specifically include potassium ion inward rectifying current (IIR), potassium ion delayed rectifier current
(IDR), sodium ion electric current (INa), Cl-currents (ICl), sodium-potassium pump (INaK), the electric current on corresponding T pipes hasIt is balanced according to Donnan, chlorion is passively distributed in film both sides, using Goldman-
Hodgkin-Katz (GHK) driving force equations drive the transmembrane movement of ion；
Electric current (I at T tube inletsT)：
IT=(Vs-Vt)/Ra (1)
Wherein VsFor sarolemma voltage, VtFor T tube voltages, RaResistance constant for T tube inlets；
Sarolemma voltage is：
WhereinIt is sarolemma electric current, CmIt is membrane capacitance constant；
T tube voltages are：
WhereinIt is T tube currents, γ is T pipe surfaces product and sarolemma surface area ratio；
Sarolemma electric current is：
Wherein IappFor applied current density constant；
T tube currents are：
T periosteum voltages are calculated by above formula, thunder is activated when voltage is higher than dihydropyridine voltage sensor threshold value
Promise channel.
As shown in Fig. 2, half sarcomere is divided into 5 sections (from Z-line to M lines) in the step 2；
Half sarcomere volume：
V=lxπR2(wherein lxFor half sarcomere length, R is muscle fibril radius) (6)
Sarcoplasmic reticulum (SR) volume：V1=5.5%V
Terminal cistern (TSR) volume：V2=3.5%V
External muscle fibril volume：V3=6%V
Muscle fibril volume comprising actin filament：
Muscle fibril volume not comprising actin filament：
By the Geometric Modeling of double of sarcomere, calcium ion cycle analysis will be carried out in the geometrical model built.
Dihydropyridine receptor (DHPR) experiences T tube voltages V in the step 3t5 Reynolds routings (RyR) are stimulated afterwards
Open and close；
Activation rate under Reynolds routing closed state：
kC=0.5 α1exp(Vt-V′/(8K)) (7)
Wherein α1, V ', K be Reynolds routing activation rate constant, unit is respectively ms-1、mV、mV；
Deactivation rate under Reynolds routing closed state：
Reynolds routing is closed C0Equation be：
Wherein kLRate constant, k are opened for Reynolds routingLmFor Reynolds routing shutdown rate constant；
Reynolds routing is in opening state O0Equation be：
Wherein f is ryanodine channel design allosteric factor constant；
Opening (the O of remaining four channel1、O2、O3、O4) with closing (C1、C2、C3、C4) state modeling method and C0、O0Class
Seemingly, by the control to ryanodine passage switching state, and then the release of calcium ion in sarcoplasmic reticulum is controlled.
As shown in figure 3, calcium ions and magnesium ions are combined, and with ATP, parvalbumin site in flesh respectively in sarcoplasm in the step 4
It is spread in slurry：
(1) mathematical model of calcium ion and binding site
Wherein S is ATP, parvalbumin site concentration, konIt is the association rate in calcium ion and site, koffCalcium ion with
The rate of departure in site；
(2) mathematical model of calcium ion and binding site
(3) diffusion mathematical model of each free ion in sarcoplasm
Wherein r is half sarcomere radial coordinate, and x is longitudinal coordinate, and D is free diffusing coefficient, and C is the dense of diffusion ion
Degree, F (C, t) is that the function that free ion concentration changes over time is calculated by (11), (12).
Such as Fig. 4, shown in 5, calcium ion is combined with troponin in the step 5, changes tropomyosin occurred conformation,
It is detached from actin, exposes myosin binding site, cross-bridges activation；
(1) calcium ion with troponin is combined and former myogen occurred conformation variation carries out mathematical modeling
1. troponin (Tn) has 6 kinds of states：B1、B2、B3Represent that troponin does not have under interacting with tropomyosin
With reference to calcium ion, with reference to 1 calcium ion, with reference to 2 calcium ions；T1、T2、T3Represent that troponin detaches down with tropomyosin
Be not bound with calcium ion, with reference to 1 calcium ion, with reference to 2 calcium ions；
B1+B2+B3+T1+T2+T3=1 (14)
Wherein K1~K5, k-1~k-5It is adjustable parameter；
State during 2. tropomyosin (Tm) has 5：Wherein there are 3 state Bs Chong Die with troponin0、B1、B2, C is former
Myosin equilibrium state, M are tropomyosin and actin, myosin interacting state；
B0+B1+B2+ C+M=1 (20)
Wherein K '0k-0It is the positive rate of M deformation, α is the average quantity of target area cross-bridges, and n is target area original flesh
The number of globulin；
(2) cross-bridges dynamic mathematical model
Cross-bridges weak binding model in sarcoplasm
Wherein f0It is cross-bridges exposure rate, fpRate of departure when being cross-bridges weak binding, CTmIt is contained original in half sarcomere
The concentration of myosin, h0It is the positive rate of cross-bridges expansion stroke, hpIt is the reverse rate of cross-bridges expansion stroke, g0Cross-bridges is done
The rate of departure after the strong combination of work(stroke；
Calcium ion in sarcoplasm by calcium pump active transport to sarcoplasmic reticulum, being combined in sarcoplasmic reticulum with calsequestrin,
The lid of high concentration is stored, when calcium ion release channel is activated, is discharged into sarcoplasm by calcium channel, calcium is formed and follows
Ring.
As shown in fig. 6, the slow inactivation of sodium-ion channel draws during skeletal muscle fast muscle fiber excitation-contraction in the step 6
Film fatigue is played, the phosphate that ATP hydrolysis generates during cross-bridge cycle causes metabolic fatigue；
(1) it establishes skeletal muscle fast muscle fiber excitation-contraction process and generates film fatigue mathematical model
S∞=1/ (1+exp ((Vs-VS∞)/AS∞)) (25)
τS=8571/ (0.2+5.65 (((Vs+Vτ)/100)2) (26)
Wherein VsFor membrane voltage, VSHalf of the ∞ for the slow inactivated channel maximum voltage of sodium ion, AS∞ slope factor constants,
VτIt is to τSThe half of maximum voltage value；
(2) it establishes skeletal muscle fast muscle fiber excitation-contraction process and generates the tired mathematical model of metabolism
Phosphoric acid (P in sarcoplasmi)：
Wherein h0It is cross-bridges expansion stroke forward direction rate, hPIt is cross-bridges expansion stroke reverse rate, A1When being cross-bridges weak binding
Cross-bridges concentration, A2It is cross-bridges concentration, b when cross-bridges combines by forcePBe in sarcoplasm phosphoric acid reduce rate, kPIt is P in sarcoplasmiIt is transported to
The rate of sarcoplasmic reticulum (SR), V4+V5It is sarcoplasm volume；
Phosphoric acid (P in sarcoplasmic reticulum (SR)i)：
Wherein V1It is the volume of sarcoplasmic reticulum, APiIt is phosphoric acid and calcium binding rate in sarcoplasmic reticulum, PiPiIt is phosphoric acid meltage
Product,It is the concentration of calcium ion in sarcoplasmic reticulum, BPIt is the rate of phosphoric acid combination calcium ion dissolving；
The combination of phosphoric acid and calcium ion in sarcoplasmic reticulum：
It is calculated by formula (11), (12), (13), film fatigue reduces T periosteum voltage magnitudes, reduces calcium channel
Activation；(14), (15), (16) calculate, and reduce calcium ion and are discharged from sarcoplasmic reticulum, thereby reduce the quantity of cross-bridges activation,
Skeletal muscle fast muscle fiber shows as fatigue.
Claims (1)
1. a kind of modeling method to skeletal muscle fast muscle fiber excitation-contraction process, which is characterized in that the skeletal muscle fast muscle is fine
The modeling method of dimension excitation-contraction process includes the following steps：
1) as unit of half sarcomere, skeletal muscle fast muscle fiber film electro physiology mathematical model is established；
2) as unit of half sarcomere, the geometrical model of calcium ion cycle is established；
3) the calcium ion mathematical model that Reynolds routing (RyR) discharges from terminal cistern is established；
4) mathematical model that calcium ion in sarcoplasm, magnesium ion are combined respectively with ATP, parvalbumin is established；
5) mathematical model of calcium binding troponin and cross-bridges dynamic mathematical model are established；
6) the film Tiredness model generated during skeletal muscle fast muscle fiber excitation-contraction and metabolic Tiredness model are established；
Mammalian bone flesh fast muscle fiber sarolemma is described using Hodgkin-Huxley electrophysiological models in the step 1)
With T periosteum curent changes, potassium ion inward rectifying current (I is specifically includedIR), potassium ion delayed rectifier current (IDR), sodium ion
Electric current (INa), Cl-currents (ICl), sodium-potassium pump (INaK), the electric current on corresponding T pipes hasIt is balanced according to Donnan, chlorion is passively distributed in film both sides, using Goldman-
Hodgkin-Katz (GHK) driving force equations drive the transmembrane movement of ion；
Electric current (I at T tube inletsT)：
IT=(Vs-Vt)/Ra (1)
Wherein VsFor sarolemma voltage, VtFor T tube voltages, RaResistance constant for T tube inlets；
Sarolemma voltage is：
WhereinIt is sarolemma electric current, CmIt is membrane capacitance constant；
T tube voltages are：
WhereinIt is T tube currents, γ is T pipe surfaces product and sarolemma surface area ratio；
Sarolemma electric current is：
Wherein IappFor applied current density constant；
T tube currents are：
T periosteum voltages are calculated by above formula, ryanodine is activated when voltage is higher than dihydropyridine voltage sensor threshold value
Channel；
Half sarcomere is divided into 5 sections from Z-line to M lines in the step 2)；
Half sarcomere volume：
V=lxπR2 (6)
Wherein lxFor half sarcomere length, R is muscle fibril radius；
Sarcoplasmic reticulum (SR) volume：V1=5.5%V
Terminal cistern (TSR) volume：V2=3.5%V
External muscle fibril volume：V3=6%V
Muscle fibril volume comprising actin filament：
Muscle fibril volume not comprising actin filament：
By the Geometric Modeling of double of sarcomere, calcium ion cycle analysis will be carried out in the geometrical model built；
Dihydropyridine receptor (DHPR) experiences T tube voltages V in the step 3)tOpening for 5 Reynolds routing (RyR) is stimulated afterwards
It opens and closes；
Activation rate under Reynolds routing closed state：
kC=0.5 α1exp(Vt-V′/(8K)) (7)
Wherein α1, V ', K be Reynolds routing activation rate constant, unit is respectively ms-1、mV、mV；
Deactivation rate under Reynolds routing closed state：
Reynolds routing is closed C0Equation be：
Wherein kLRate constant, k are opened for Reynolds routingLmFor Reynolds routing shutdown rate constant；
Reynolds routing is in opening state O0Equation be：
Wherein f is ryanodine channel design allosteric factor constant；
The opening state O of remaining four channel1、O2、O3、O4With closed state C1、C2、C3、C4Modeling method and C0、O0It is similar,
By the control to ryanodine passage switching state, and then control the release of calcium ion in sarcoplasmic reticulum；
Calcium ions and magnesium ions are combined with ATP, parvalbumin site respectively, and are spread in sarcoplasm in sarcoplasm in the step 4)；
(1) mathematical model of calcium ion and binding site
Wherein S is ATP, parvalbumin site concentration, konIt is the association rate in calcium ion and site, koffIt is calcium ion and site
The rate of departure；
(2) mathematical model of magnesium ion and binding site
(3) diffusion mathematical model of each free ion in sarcoplasm
Wherein r is half sarcomere radial coordinate, and x is longitudinal coordinate, and D is free diffusing coefficient, and C is the concentration of diffusion ion, F
(C, t) is that the function that free ion concentration changes over time is calculated by (11), (12)；
Calcium ion is combined with troponin in the step 5), changes tropomyosin occurred conformation, is divided from actin
From exposing myosin binding site, cross-bridges activation；
(1) calcium ion with troponin is combined and former myogen occurred conformation variation carries out mathematical modeling
1. troponin (Tn) has 6 kinds of states：B1、B2、B3Represent that troponin is not bound under interacting with tropomyosin
Calcium ion, with reference to 1 calcium ion, with reference to 2 calcium ions；T1、T2、T3Represent that troponin does not have under being detached with tropomyosin
With reference to calcium ion, with reference to 1 calcium ion, with reference to 2 calcium ions；
B1+B2+B3+T1+T2+T3=1 (14)
Wherein K1~K5, k-1~k-5It is adjustable parameter；
State during 2. tropomyosin (Tm) has 5：Wherein there are 3 state Bs Chong Die with troponin1、B2、B3, C is former flesh ball
Brotein equilibrium state, M are tropomyosin and actin, myosin interacting state；
B1+B2+B3+ C+M=1 (20)
Wherein K '0k-0It is the positive rate of M deformation, α is the average quantity of target area cross-bridges, and n is target area tropomyosin
White number；
(2) cross-bridges dynamic mathematical model
Cross-bridges weak binding model in sarcoplasm
Wherein f0It is cross-bridges exposure rate, fpRate of departure when being cross-bridges weak binding, CTmIt is contained tropomyosin in half sarcomere
White concentration, h0It is the positive rate of cross-bridges expansion stroke, hpIt is the reverse rate of cross-bridges expansion stroke, g0Cross-bridges expansion stroke
The rate of departure after strong combination；
Calcium ion in sarcoplasm is stored by calcium pump active transport to sarcoplasmic reticulum, being combined in sarcoplasmic reticulum with calsequestrin
The calcium ion of high concentration when calcium ion release channel is activated, is discharged by calcium channel in sarcoplasm, is formed calcium and is followed
Ring；
The slow inactivation of sodium-ion channel causes film fatigue during skeletal muscle fast muscle fiber excitation-contraction in the step 6), horizontal
The phosphate that ATP hydrolysis generates in bridge cyclic process causes metabolic fatigue；
(1) it establishes skeletal muscle fast muscle fiber excitation-contraction process and generates film fatigue mathematical model
τS=8571/ (0.2+5.65 (((Vs+Vτ)/100)2) (26)
Wherein VsFor membrane voltage,For the half of the slow inactivated channel maximum voltage of sodium ion,Slope factor constant, VτIt is pair
τSThe half of maximum voltage value；
(2) it establishes skeletal muscle fast muscle fiber excitation-contraction process and generates the tired mathematical model of metabolism
Phosphoric acid (P in sarcoplasmi)：
Wherein h0It is cross-bridges expansion stroke forward direction rate, hPIt is cross-bridges expansion stroke reverse rate, A1Cross-bridges when being cross-bridges weak binding
Concentration, A2It is cross-bridges concentration, b when cross-bridges combines by forcePBe in sarcoplasm phosphoric acid reduce rate, kPIt is P in sarcoplasmiIt is transported to myoplasm
The rate of net (SR), V4+V5It is sarcoplasm volume；
Phosphoric acid (P in sarcoplasmic reticulum (SR)i)：
Wherein V1It is the volume of sarcoplasmic reticulum, APiIt is phosphoric acid and calcium binding rate in sarcoplasmic reticulum, PiPiIt is multiplying for phosphoric acid meltage
Product,It is the concentration of calcium ion in sarcoplasmic reticulum, BPIt is the rate of phosphoric acid combination calcium ion dissolving；
The combination of phosphoric acid and calcium ion in sarcoplasmic reticulum：
It is calculated by formula (11), (12), (13), film fatigue reduces T periosteum voltage magnitudes, reduces swashing for calcium channel
It is living；(14), (15), (16) calculate, and reduce calcium ion and are discharged from sarcoplasmic reticulum, thereby reduce the quantity of cross-bridges activation, bone
Bone flesh fast muscle fiber shows as fatigue.
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