CN107609338A - A kind of Skeletal Muscle Contraction model based on metabolism physiology - Google Patents
A kind of Skeletal Muscle Contraction model based on metabolism physiology Download PDFInfo
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Abstract
The invention discloses a kind of Skeletal Muscle Contraction model based on metabolism physiology.Its step is：Step 1：Establish energetic supersession physiological mode of the human body in different time sections；Step 2：Process is produced based on human energy metabolism ATP, establishes the mathematical modeling that the contraction of bone cross bridge is activated to from cell electrophysiology action potential.The present invention is based on people's energy i (in vivo) metabolic process, provides rational explanation for motion consumed energy process, the research to people's energy i (in vivo) metabolism and contraction of muscle relation of the motions such as dash has theoretical directive function.
Description
Technical Field
The invention relates to a method for modeling contraction processes based on skeletal muscle metabolic physiology.
Background
At present, a plurality of skeletal muscle contraction models are researched, but most of the skeletal muscle contraction models are the researches from electrical stimulation to muscle contraction processes, and a membrane potential change model, a calcium circulation mathematical model and the like are integrated according to in vivo and in vitro data to obtain a muscle contraction model. However, in actual exercise, it is observed that the energy supply modes of muscle contraction in human bodies are obviously different in different exercise time periods, which results in that the finally output contraction force is obviously changed due to different exercise time periods, and the research on the influence of the energy metabolism in muscle cells on the contraction process of skeletal muscles in the exercise process is lacked in the existing model, and based on the above problem, the physiological mechanism of the energy metabolism of the muscle cells needs to be added into the model of the skeletal muscles contraction.
Disclosure of Invention
The invention provides a skeletal muscle contraction model based on metabolism physiology, which aims to solve the problem that the existing skeletal muscle contraction model cannot reflect the change process of energy metabolism in a human body in different movement time periods.
A skeletal muscle contraction model based on metabolic physiology is realized by the following steps:
the method comprises the following steps: establishing energy metabolism physiological mathematical models of human bodies in different motion time periods:
a when muscles contract during short periods of high intensity exercise (< 8 s) energy is supplied to the muscles mainly for the ATP-CP system;
b when the continuous vigorous exercise time is between (8 s-40 s), the energy is mainly provided for the muscles by glycolysis energy production;
c when the muscle movement is more than 40s, mainly providing energy for the muscle movement for aerobic respiration;
step two: based on the ATP production process of human energy metabolism, a mathematical model from the activation of cell electrophysiological action potential to the contraction of skeletal muscle transverse bridges is established.
The invention has the following effects:
the traditional skeletal muscle model rarely relates to energy metabolism mechanisms in human bodies, and the influence of different energy metabolism mechanisms of the human bodies in different movement time periods on the skeletal muscle contraction model is not distinguished. The invention introduces a skeletal muscle contraction model which can reflect different energy metabolism mechanisms in different movement time periods based on the energy metabolism process in a human body. Has theoretical guidance function on exercise training, weight reduction and the like.
Drawings
FIG. 1 is a schematic diagram of the exchange of substances in a two-domain model;
FIG. 2 is a flow chart of a skeletal muscle contraction model based on metabolic physiology.
Detailed Description
The first embodiment is as follows: a skeletal muscle contraction model based on metabolism physiology comprises the following steps
The method comprises the following steps: establishing energy metabolism physiological mathematical models of human bodies in different motion time periods:
a when muscles contract during short periods of high intensity exercise (< 8 s) energy is supplied to the muscles mainly for the ATP-CP system;
b when the continuous vigorous exercise time is between (8 s-40 s), the energy is mainly provided for the muscles by glycolysis energy production;
c when the muscle movement is more than 40s, mainly providing energy for the muscle movement for aerobic respiration;
step two: based on the ATP production process of human energy metabolism, a mathematical model from the activation of cell electrophysiological action potential to the contraction of skeletal muscle transverse bridges is established.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the specific process of establishing the energy metabolism physiological mathematical model of the human body in different time periods in the step one is as follows:
there are three major functional systems in the human body: the ATP-CP function system, glycolysis function system and aerobic respiration function system, because the ATP storage quantity in muscle is very low, if the ATP storage quantity is singly used for supplying energy, the duration is less than 1s, the energy supply depends on ATP regeneration, firstly, the intracellular high-energy phosphobond hydrolysis transfers the energy to ADP, ATP is generated, because the content of the phosphocreatine in the body can only be maintained for a few seconds, such as supplying energy for hectometer running, then, the energy is supplied by the anaerobic glycolysis of sugar, and long-time endurance exercise needs to supply energy by aerobic respiration.
The in vivo substance exchange model is based on a two-domain model comprising a blood domain and a tissue cell domain, wherein substances in each domain are completely mixed, and the substance exchange process in the two-domain model is shown in figure 1;
the blood domain comprises capillaries and interstitial spaces, and the mass balance equation of each substance in the blood domain is
Wherein V b 、V isf 、Q、C a 、C b 、The volume of distribution of the substance in venous blood, the volume of distribution of the substance in the interstitial space of the tissue, the blood flow, the concentration of the substance in the artery (known quantity), the concentration of the substance in the vein, the transport flux of the substance from the blood into the tissue cells, respectively;
the tissue cell domain comprises cytosol and mitochondria, and the mass balance equation of each substance in the tissue cell domain is
Wherein V c 、C c 、β c，p 、φ c，p 、φ c，u 、φ c，u Respectively representing the distribution volume of the substance in the cells, the concentration of the substance in the cells of the tissue, the corresponding stoichiometric coefficient of substance production, the reaction flux during the reaction of substance production, the corresponding stoichiometric coefficient of substance utilization, and the reaction flux during the reaction of substance utilization;
whereinEffective permeability surface area for substance transport from blood to tissue cells；
Determination of C from the formula (1) and the formula (2) c ；
The substances are subjected to enzymatic reaction in tissue cells to generate ATP to provide energy for muscle contraction;
the expression of the total reaction of the enzymes with metabolic reaction flux is
Wherein φ is the reaction flux, V max For maximum reaction speed, K m Is the mie constant of the reaction and,is the phenomenological mie constant for phosphorylation,to couple the phenomenological mie constants of phosphorylation and redox reactions,the ratio of the concentration of ATP (adenosine triphosphate) to that of ADP (adenosine diphosphate),as the ratio of NADH (reduced form of nicotinamide adenine dinucleotide) to NAD + (oxidized form of nicotinamide adenine dinucleotide) concentration,is the product of substrate concentration;
(1) When the muscle contracts in short-time high-intensity exercise (< 8 s), the ATP-CP system mainly provides energy for the muscle, and the chemical reaction equation of the reaction of the phosphocreatine and ADP to generate ATP is
PCR+ADP→CR+ATP (5)
Wherein PCR is creatine phosphate, CR is creatine, and the mathematical equation of reaction flux is
Wherein phi PCR→CR 、V PCR→CR 、K PCR→CR 、C PCR The reaction flux of the reaction of the creatine phosphate and the ADP to generate ATP, the maximum reaction speed of the reaction in the formula (5), the phenomenological Michaelis constant of the coupled phosphorylation and oxidation reduction reaction of the creatine phosphate and the ADP to generate ATP, the Michaelis constant of the reaction (5) and the concentration of PCR are respectively;
(2) When the continuous vigorous exercise time is between (8 s-40 s), the energy is mainly provided for muscles by glycolysis, and the chemical reaction equation of the glycolysis ATP production is as follows
GLC+2ATP+2ADP+2PI+2NAD + →2PYR+4ATP+2NADH+2H + +2H 2 O (7)
Wherein GLC is glucose, PYR is pyruvic acid, PI is inorganic phosphate, and the mathematical equation of reaction flux is
Wherein phi GLC→PYR 、V GLC→PYR 、K GLC→PYR 、C GLC 、C PI The flux of reaction for producing pyruvic acid from glucose, the maximum reaction rate of the reaction in formula (7), the phenomenological mie constant of coupling phosphorylation and redox reaction for producing pyruvic acid from glucose, the mie constant of reaction (7), the concentration of GLC, and the concentration of PI, respectively;
(3) When the muscle movement is more than 40s, the aerobic respiration mainly provides energy for the muscle movement, and the chemical reaction equation of the ATP generated by the aerobic expiration is
O 2 +6ADP+6PI+2NADH→2H 2 O+6ATP+2NAD + (9)
Wherein O is 2 、H 2 O represents oxygen molecules and water molecules respectively;
the mathematical equation of the reaction flux is
WhereinC PI The reaction flux of the aerobic respiration reaction, the maximum reaction rate of the reaction in (9), the phenomenological mie constants of the coupled phosphorylation and redox reaction of the aerobic respiration, the mie constant of the reaction (9), the concentration of oxygen, and the concentration of PI, respectively;
and solving the energy provided by different energy supply modes for muscle contraction in each movement time period through a chemical reaction equation and a mathematical equation of reaction flux in each time period based on the concentration of each nutrient in the human body.
The third concrete implementation mode: the difference between the first embodiment and the second embodiment is as follows: the specific process of establishing a mathematical model from activation of cell electrophysiological action potential to contraction of a skeletal muscle transverse bridge based on the ATP generation process of human energy metabolism in the step two is as follows:
step two is as follows: mathematical model for membrane potential variation
Describing potential changes of a muscle cell membrane and a T-tube membrane by adopting a Hodgkin-Huxley model, and activating a Reynolds channel to release calcium ions when a membrane voltage value is greater than a voltage threshold value;
step two: calcium cycle process mathematical model
(1) A two-compartment model was used to describe the calcium cycling process during skeletal muscle contraction, with process variables including Ca 2+ (calcium ion concentration), [ ATP](ATP concentration), mg 2+ (concentration of magnesium ions), calcium binding proteins, troponins, troponin, and calcium collectin, wherein the concentration of ATP affects the rate of calcium cycling, ATP is primarily consumed in the operation of the calcium pump and in the activation of the transverse bridges, and the equation for the change of ATP in the sarcoplasmic reticulum and sarcoplasmic reticulum is
Wherein [ ATP] 1 The ATP concentration in the final pool, [ ATP ]] 2 Is the ATP concentration in the muscle slurry, and the ATP concentration in the muscle slurry is the ATP concentration produced by energy metabolism,Mg 1 、Mg 2 、 V 1 、V 2 、τ ATP respectively is the concentration of calcium ions in the muscle pulp of the ultimate pond, the concentration of calcium ions in the muscle pulp, the concentration of Ca-ATP binding units in the muscle pulp, the concentration of magnesium ions in the muscle pulp, the concentration of Mg-ATP binding units in the muscle pulp, the rate of binding ATP by calcium ions, the rate of dissociating ATP by calcium ions, the rate of binding ATP by magnesium ions, the rate of dissociating ATP by magnesium ions, the volume of the ultimate pond, the volume of the muscle pulp excluding the ultimate pond and an ATP dissociation parameter;
step two and step three: transverse bridge dynamic model
The chemical energy of ATP hydrolysis is converted into the conformational energy of myosin and the mechanical energy of transverse bridge oscillation,
concentration of free troponin binding sites
Wherein T is tot 、D 0 、D 1 、D 2 、A 1 、A 2 The total concentration of troponin binding sites, the concentration of Ca-troponin binding units in the sarcoplasm, the concentration of Ca-Ca-troponin binding units in the sarcoplasm, the concentration of isolated active troponin-tropomyosin active units, the concentration of isolated active troponin-tropomyosin-Ca active units, the concentration of weak binding state cross bridges, the concentration of strong binding state cross bridges, respectively;
dA 1 /dt＝+f 0 D 2 -f p A 1 +h p A 2 -h 0 A 1 (17)
dA 2 /dt＝-h p A 2 +h p A 1 -g 0 A 2 (18)
whereinf 0 、f p 、g 0 、h 0 、h p The rate of binding of troponin by calcium ions, the rate of dissociation of troponin by calcium ions, the activation rate of troponin-tropomyosin units not bound by calcium ions, the dissociation rate of troponin-tropomyosin units not bound by calcium ions, the activation rate of troponin-tropomyosin units bound by calcium ions, the dissociation rate of troponin-tropomyosin units bound by calcium ions, the association rate of a cross bridge, the dissociation rate of a weak association state cross bridge, the dissociation rate of a strong association state cross bridge, the forward rate of a cross bridge power stroke, the reverse rate of a power stroke, and the number of cross bridge associations is directly related to the generation of force.
Claims (3)
1. A skeletal muscle model based on metabolic physiology, which is characterized in that the skeletal muscle model modeling method based on metabolic physiology comprises the following steps:
the method comprises the following steps: establishing energy metabolism physiological mathematical models of human bodies in different motion time periods:
in different exercise time periods, different substances in a human body carry out metabolic reaction to generate ATP to provide energy for muscle contraction;
a when the muscle contracts during short-time high-intensity exercise (< 8 s), the muscle is mainly provided with energy for an ATP-CP system;
b when the continuous vigorous exercise time is between (8 s-40 s), the energy is mainly provided for the muscles by glycolysis energy production;
c when the muscle movement is more than 40s, mainly providing energy for the muscle movement for aerobic respiration;
step two: based on the ATP production process of human energy metabolism, a mathematical model from the activation of cell electrophysiological action potential to the contraction of skeletal muscle transverse bridges is established.
2. The skeletal muscle model based on metabolism physiology according to claim 1, wherein the specific process of establishing the mathematical model of energy metabolism physiology of human body in different movement time periods in the first step is as follows:
the in vivo substance exchange model is based on a two-domain model comprising a blood domain and a tissue cell domain, with the substances in each domain being completely mixed;
the blood domain includes capillaries and interstitial spaces, and the mass balance equation of each substance in the blood domain is
Wherein V b 、V isf 、Q、C a 、C b 、The volume of distribution of the substance in venous blood, the volume of distribution of the substance in the interstitial space of the tissue, the blood flow, the concentration of the substance in the artery (known quantity), the concentration of the substance in the vein, the transport flux of the substance from the blood into the tissue cells, respectively;
the tissue cell domain comprises cytosol and mitochondria, and the mass balance equation of each substance in the tissue cell domain is
Wherein V c 、C c 、β c，p 、φ c，p 、β c，u 、φ c，u Respectively representing the distribution volume of the substance in the cells, the concentration of the substance in the cells of the tissue, the corresponding stoichiometric coefficient of substance production, the reaction flux during the reaction of substance production, the corresponding stoichiometric coefficient of substance utilization, and the reaction flux during the reaction of substance utilization;
whereinFor transporting substances from blood to groupEffective permeability surface area in the tissue cells;
determination of C from the formula (1) and the formula (2) c ；
The substances are subjected to enzymatic reaction in tissue cells to generate ATP to provide energy for muscle contraction;
the expression of the total reaction of the enzymes with metabolic reaction flux is
Wherein φ is the reaction flux, V max For maximum reaction speed, K m Is the mie constant of the reaction and,to be the phenomenological mie constant of phosphorylation,to couple the phenomenological mie constants of phosphorylation and redox reactions,is the ratio of ATP (adenosine triphosphate) to ADP (adenosine diphosphate) concentration,as the ratio of NADH (reduced form of nicotinamide adenine dinucleotide) to NAD + (oxidized form of nicotinamide adenine dinucleotide) concentration,is the product of substrate concentration;
(1) When the muscle contracts under short-time high-intensity exercise (< 8 s), the ATP-CP system is mainly used for supplying energy to the muscle, and the chemical reaction equation of the creatine phosphate and ADP for generating ATP is as follows
PCR+ADP→CR+ATP (5)
Wherein the PCR is creatine phosphate, the CR is creatine, and the mathematical equation of reaction flux is
Wherein phi PCR→CR 、V PCR→CR 、K PCR→CR 、C PCR The reaction flux of the creatine phosphate and ADP for generating ATP, the maximum reaction speed of the reaction in the formula (5), the phenomenological mie constant of the coupling phosphorylation and the oxidation reduction reaction of the creatine phosphate and ADP for generating ATP, the mie constant of the reaction (5) and the concentration of PCR are respectively;
(2) When the continuous vigorous exercise time is between (8 s-40 s), the energy is mainly provided for muscles by glycolysis, and the chemical reaction equation of the glycolysis ATP production is as follows
GLC+2ATP+2ADP+2PI+2NAD + →2PYR+4ATP+2NADH+2H + +2H 2 O (7)
Wherein GLC is glucose, PYR is pyruvic acid, PI is inorganic phosphate, and the mathematical equation of reaction flux is
Wherein phi GLC→PYR 、V GLC→PYR 、K GLC→PYR 、C GLC 、C PI The flux of reaction for producing pyruvic acid from glucose, the maximum reaction rate of the reaction in formula (7), the phenomenological mie constant of coupling phosphorylation and redox reaction for producing pyruvic acid from glucose, the mie constant of reaction (7), the concentration of GLC, and the concentration of PI, respectively;
(3) When the muscle movement is more than 40s, the aerobic respiration mainly provides energy for the muscle movement, and the chemical reaction equation of the aerobic expiration to generate ATP is as follows
O 2 +6ADP+6PI+2NADH→2H 2 O+6ATP+2NAD + (9)
Wherein O is 2 、H 2 O represents oxygen molecule and water molecule respectively;
the mathematical equation of the reaction flux is
WhereinC PI The reaction flux of the aerobic respiration reaction, the maximum reaction rate of the reaction in (9), the phenomenological mie constants of the coupled phosphorylation and redox reaction of the aerobic respiration, the mie constant of the reaction (9), the concentration of oxygen, and the concentration of PI, respectively;
based on the concentration of each nutrient in the human body, the energy provided by different energy supply modes for muscle contraction in each movement time period is solved through a chemical reaction equation and a mathematical equation of reaction flux in each time period.
3. A skeletal muscle model based on metabolism physiology according to claim 1, wherein the specific process of establishing the activation of cellular electrophysiological action potentials to the skeletal muscle transverse bridge contraction mathematical model in step (2) is as follows:
(1) Mathematical model of membrane potential variation: describing potential changes of a muscle cell membrane and a T-tube membrane by adopting a Hodgkin-Huxley model, and activating a Reynolds channel to release calcium ions when a membrane voltage value is greater than a voltage threshold value;
(2) Calcium cycle process mathematical model: a two-compartment model was used to describe the calcium cycling process during skeletal muscle contraction, with process variables including Ca 2+ (calcium ion concentration), [ ATP](ATP concentration), mg 2+ (concentration of magnesium ion), calcium binding protein, troponin, and calciumA protein collection, wherein the concentration of ATP affects the rate of calcium cycling, ATP is primarily consumed in the operation of the calcium pump and in the activation of the transverse bridges, and the equation of change of ATP in the sarcoplasmic reticulum and sarcoplasmic reticulum is
Wherein [ ATP] 1 Is the ATP concentration in the final pool, [ ATP] 2 Is the ATP concentration in the muscle slurry, and the ATP concentration in the muscle slurry is the ATP concentration produced by energy metabolism,Mg 1 、Mg 2 、 V 1 、V 2 、τ ATP respectively is the concentration of calcium ions in the muscle pulp of the ultimate pond, the concentration of calcium ions in the muscle pulp, the concentration of Ca-ATP binding units in the muscle pulp, the concentration of magnesium ions in the muscle pulp, the concentration of Mg-ATP binding units in the muscle pulp, the rate of binding ATP by calcium ions, the rate of dissociating ATP by calcium ions, the rate of binding ATP by magnesium ions, the rate of dissociating ATP by magnesium ions, the volume of the ultimate pond, the volume of the muscle pulp excluding the ultimate pond and an ATP dissociation parameter;
(3) Transverse bridge dynamic model:
the chemical energy of ATP hydrolysis is converted into the conformational energy of myosin and the mechanical energy of transverse bridge oscillation,
concentration of free troponin binding sites
Wherein T is tot 、D 0 、D 1 、D 2 、A 1 、A 2 The total concentration of troponin binding sites, the concentration of Ca-troponin binding units in the sarcoplasm, the concentration of Ca-Ca-troponin binding units in the sarcoplasm, the concentration of isolated active troponin-tropomyosin active units, the concentration of isolated active troponin-tropomyosin-Ca active units, the concentration of weak binding state cross bridges, the concentration of strong binding state cross bridges, respectively;
dA 1 /dt＝+f 0 D 2 -f p A 1 +h p A 2 -h 0 A 1 (17)
dA 2 /dt＝-h p A 2 +h p A 1 -g 0 A 2 (18)
whereinf 0 、f p 、g 0 、h 0 、h p The rate of binding of calcium ions to troponin, the rate of dissociation of calcium ions from troponin, and the rate of unbinding of calcium ions, respectivelyThe method comprises the following steps of (1) activating rate of troponin-tropomyosin units of calcium ions, dissociating rate of troponin-tropomyosin units of unbound calcium ions, activating rate of troponin-tropomyosin units of bound calcium ions, dissociating rate of troponin-tropomyosin units of bound calcium ions, transverse bridge association rate, weak-bound-state transverse bridge dissociation rate, strong-bound-state transverse bridge dissociation rate, forward rate of transverse bridge power strokes and reverse rate of power strokes, wherein the transverse bridge association number is directly related to the generation of force.
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| CN111948401A (en) * | 2019-06-26 | 2020-11-17 | 浙江大学 | Application of CHCHHD 10 in promotion of AChR subunit gene expression and maintenance of NMJ stability |
| CN112365985A (en) * | 2020-11-10 | 2021-02-12 | 哈尔滨理工大学 | Skeletal muscle multi-scale model modeling method based on sarcoplasmic reticulum environment |
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| CN108596333A (en) * | 2018-03-15 | 2018-09-28 | 江西理工大学 | A kind of cardiac Purkinje fibers memristor perturbation circuit design method based on Hodgkin-Huxley models |
| CN108596333B (en) * | 2018-03-15 | 2021-08-24 | 江西理工大学 | Heart purkinje fiber memristor perturbation circuit design method based on Hodgkin-Huxley model |
| CN111948401A (en) * | 2019-06-26 | 2020-11-17 | 浙江大学 | Application of CHCHHD 10 in promotion of AChR subunit gene expression and maintenance of NMJ stability |
| CN111341382A (en) * | 2020-02-20 | 2020-06-26 | 江南大学 | Macroscopic dynamics and cell metabolism flux coupling modeling method in lysine biological manufacturing |
| CN111341382B (en) * | 2020-02-20 | 2023-04-18 | 江南大学 | Macroscopic dynamics and cell metabolism flux coupling modeling method in lysine biological manufacturing |
| CN112365985A (en) * | 2020-11-10 | 2021-02-12 | 哈尔滨理工大学 | Skeletal muscle multi-scale model modeling method based on sarcoplasmic reticulum environment |
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