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Model predictions of myoelectrical activity of the small bowel

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Abstract

A mathematical model for the periodic electrical activity of a functional unit of the small intestine is developed. Based on real morphological and electrophysiological data, the model assumes that: the functional unit is an electromyogenic syncytium; the kinetics of L, T-type Ca2+, mixed Ca2+-dependent K+, potential sensitive K+ and Cl− channels determines electrical activity of the functional unit; the basic neural circuit, represented by a single cholinergic neurone, provides an excitatory input to the functional unit via receptor-linked L-type Ca2+ channels. Numerical simulation of the model has shown that it is capable of displaying the slow waves and that slight modifications of some of the parameters result in different electrical responses. The effects of the variations of the main parameters have been analyzed for their ability to reproduce various electrical patterns. The results are in good qualitative and quantitative agreement with results of experiments conducted on the small intestine.

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Abbreviations

C am :

capacitance of the nerve fiber

C p :

subsynaptic membrane capacitance

C m :

membrane capacitance (smooth muscle, SM)

R a :

membrane resistance (nerve fibre, NF)

R v :

resistance of the extrasynaptic structures

ϕ :

membrane potential (SM)

ϕ * :

membrane potential (NF)

ϕ p :

excitatory postsynaptic potential

ϕ rest :

resting potential (SM)

ϕ Na, ϕ K, ϕ Cl :

reversal potentials for Na+, K+ and Cl− currents (NF)

\(\tilde \varphi {\text{Ca}}\) :

reversal potential for fast Ca2+ current (SM)

\(\tilde \varphi {\text{K}}\) :

reversal potential for slow K+ current (SM)

\(\tilde \varphi {\text{Cl}}\) :

reversal potential for slow Cl− current (SM)

\(\tilde \varphi {\text{Ca}}\) :

calcium equilibrium potential (SM)

ϕ R :

resting potential of the synapse

ϕ o :

excitatory potential

ϕ *p :

threshold potential for L-type Ca2+ channels

g Na, g K, g Cl :

maximal conductances for Na+, K+ and Cl− currents (NF)

\(\tilde g_{{\text{Ca}}}^{\text{f}} ,{\text{ }}\tilde g_{{\text{Ca}}}^{\text{s}} \) :

maximal conductance of fast and slow Ca2+ channels, respectively (SM)

\(\tilde g{\text{K, }}\tilde g{\text{Ca - K}}\) :

maximal conductance of K+ and Ca2+ activated

K+ :

channels (SM)

\(\tilde g{\text{Cl}}\) :

maximal conductance of leak Cl− channels (SM)

m :

activation gating variable of Na+ current (NF)

h :

inactivation gating variable of Na+ current (NF)

\(\tilde m_I \) :

steady-state of activation gating variable of fast Ca2+ current (SM)

\(\tilde h\) :

inactivation gating variable of fast Ca2+ current (SM)

ñ :

activation gating variable of fast K+ current (SM)

αm, h, n :

activation time constants of Na+ and K+ channels (NF)

β m, h, n :

deactivation time constants of Na+ and K+ channels (NF)

\(\tilde \alpha _{{\text{m,h,n}}} \) :

activation time constants of fast Ca2+ and K+ channels (SM)

\(\tilde \beta _{{\text{m,h,n}}} \) :

deactivation time constants of fast Ca2+ and K+ channels (SM)

I fCa , I SCa :

fast and slow Ca2+ currents, respectively (SM)

I K :

potential sensitive K+ current (SM)

I lC :

leak current (SM)

ACh:

acetylcholine

AChc :

fraction of acetylcholine in the cleft

AChv :

vesicular acetylcholine

AChf :

free fraction of acetylcholine

AChp :

postsynaptic fraction of acetylcholine

R:

choline receptors

ACh-R:

acetylcholine-receptor complex

E:

acetylcholinesterase enzyme

AChE:

acetylcholine-enzyme complex

S:

products of chemical reactions

[...]:

concentration of the reacting components

[Ca2+]out :

external calcium concentration (synapse)

[Ca2+]:

internal calcium concentration (synapse)

\(\tilde Ca^{2 + } \) :

internal calcium concentration (SM)

k c :

affinity constant (synapse)

k d :

diffusion constant (synapse)

k + p :

diffusion velocity constant of acetylcholine on the subsynaptic membrane

k +,- :

constants of forward (+) "and backward (−) chemical reactions (synapse)"

a :

cross-section diameter of the axon

L :

length of the axon

L o :

length of the nerve terminal

Ω :

empirical constant of synapse

τx ca :

relaxation time constant of Ca2+ current (SM)

\(\tilde x_{{\text{ca}}} \) :

relaxation parameter for activation of intracellular Ca2+ current (SM)

α:

numerical parameter

λ :

Plant's factor

ϱ :

strength of the cellular Ca2+ buffering capacity (SM)

K c :

intracellular Ca2+ current constant (SM)

t :

time

t s :

time of excitation

s :

Lagrangian coordinate

References

  • Argemi J, Gola M, Chagneux H (1979) Qualitative analysis of a model generating long potential waves in Ba+-treated nerve cells. I. Reduced systems. Bull Math Biol 41:665–686

    Article  CAS  PubMed  Google Scholar 

  • Argemi J, Chagneux H, Ducreux C, Gola M (1984) Qualitative study of a dynamical system for metrazol-induced paroxysmal depolarization shifts. Bull Math Biol 46:903–922

    Article  CAS  PubMed  Google Scholar 

  • Baidan LV, Zholos AV, Wood JD (1992) Properties of calcium currents determined by patch clamp recording in myenteric neurons from adult guinea-pig small intestine. Digestive Disease Week, San Francisco, USA, May 10–13, 936

  • Benham CD, Bolton TB, Lang RJ, Takewaki T (1986) Calcium-activated potassium channels in single smooth muscle cells of rabbit jejunum and guinea pig mesenteric artery. J Physiol 185:45–67

    Google Scholar 

  • Carl A, McHale NG, Publicover NG, Sanders KM (1990) Participation of Ca2+-activated K+ channels in electrical activity of canine gastric smooth muscle. J Physiol 429:205–221

    CAS  PubMed  Google Scholar 

  • Carlson GM, Rudden RW, Hug CD, Bass P (1970) Effects of nicotine on gastric antral and duodenal contractile activity in the dog. J Pharm Exp Ther 172:367–376

    CAS  Google Scholar 

  • Chay TR (1990a) Bursting excitable cell models by a slow Ca2+ current. J Theor Biol 142:305–315

    CAS  PubMed  Google Scholar 

  • Chay TR (1990b) Electrical bursting and intracellular Ca2+ oscillations in excitable cell models. Biol Cybern 63:15–23

    Article  CAS  PubMed  Google Scholar 

  • Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic beta-cell Biophys J 42:181–190

    CAS  PubMed  Google Scholar 

  • Clapp LH, Vivadou MB, Walsh JV, Singer JJ (1987) Acetylcholine increases voltage-activated Ca2+ current in freshly dissociated smooth muscle cells. Proc Natl Acad Sci USA 84:2092–2096

    CAS  PubMed  Google Scholar 

  • Connor JA, Prosser CL, Weems WA (1974) A study of pacemaker activity in intestinal smooth muscle. J Physiol 240:671–701

    CAS  PubMed  Google Scholar 

  • Daniel EE, Berezin I (1992) Interstitial cells of Cajal: are they major players in control of gastrointestinal motility? J Gastrointest Mot 4:1–24

    Google Scholar 

  • Daniel EE, Sarna S (1978) The generation and conduction of activity in smooth muscle. Annu Rev Pharm Toxicol 18:145–166

    CAS  Google Scholar 

  • Daniel EE, Wachter BT, Honour AJ, Bogoch A (1960) The relationship between electrical and mechanical activity of the small intestine of dog and man. Can J Biochem Physiol 38:777–801

    CAS  PubMed  Google Scholar 

  • Droogmans G, Callewaert G (1986) Ca2+-channel current and its modification by the dihydropyridine agonist BAY K 8644 in isolated smooth muscle cells. Pfluegers Arch 406:259–265

    Article  CAS  Google Scholar 

  • El-Sharkawy TY, Daniel EE (1975) Electrical activity of small intestinal smooth muscle and its temperature dependence. Am J Physiol 229:1268–1276

    CAS  PubMed  Google Scholar 

  • FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1:445–466

    Google Scholar 

  • Fuji K, Inoue R, Yamanaka K, Yoshitomi T (1985) Effects of calcium antagonists on smooth muscle membranes of the canine stomach. Gen Pharmacol 16:217–221

    Google Scholar 

  • Honerkamp J, Mutschier G, Seitz R (1985) Coupling of a slow and a fast oscillator can generate bursting. Bull Math Biol 47:1–21

    Article  CAS  PubMed  Google Scholar 

  • Hukuhara T, Fukuda H (1968) The electrical activity of guinea-pig small intestine with special reference to the slow wave. Jpn J Physiol 18:71–86

    CAS  PubMed  Google Scholar 

  • Job DD, Griffing WJ, Rodda BE (1974) A possible origin of intestial gradients and their relation to motility. Am J Physiol 226:1510–1515

    CAS  PubMed  Google Scholar 

  • Karaki H, Weiss GB (1984) Calcium channels in smooth muscle. Gastroenterology 87:960–970

    CAS  PubMed  Google Scholar 

  • Kargacin G, Fay FS (1991) Ca2+ movement in smooth muscle cells studied with one and two-dimensional diffusion models. Biophys J 60:1088–1100

    CAS  PubMed  Google Scholar 

  • Kopell N, Ermentrout GB (1986) Subcellular oscillations and bursting. Math Biosci 78:265–291

    Article  Google Scholar 

  • Miftakhov RN, Wingate DL (1993a) Modelling of the enteric nervous network. II. Facilitation and inhibition of the cholinergic transmission. J Biomed Eng 16:67–73

    Google Scholar 

  • Miftakhov RN, Wingate DL (1993b) Modelling of the enteric nervous network. 2. Cholinergic neurone. J Med Phys Eng 16:311–319

    Google Scholar 

  • Miftakhov RN, Wingate DL (1993c) Numerical modelling of gastrointestinal motor function I. J Comput Inform 3:117–195

    Google Scholar 

  • Miftakhov RN, Wingate DL (1994a) Numerical simulation of electrochemical interaction between cholinergic and adrenergic neurones. In: Proc IEEE Int Conf Neural Networks, Orlando, USA June 28–July 2, 1994, pp 2258-2263

  • Miftakhov RN, Wingate DL (1994b) Biomechanics of small bowel motility. J Med Phys Eng 16:406–415

    CAS  Google Scholar 

  • Miftakhov RN, Wingate DL (1994c) Numerical simulation of the peristaltic reflex of the small bowel. Int J Biorheol 31:309–325

    CAS  Google Scholar 

  • Miftakhov RN, Wingate DL (1995) Modelling of the enteric nervous network. 5. Excitation propagation in a planar neural network. J Med Phys Eng 17:11–19

    CAS  Google Scholar 

  • Muraki K, Imaizumi Y, Watanabe M (1991) Sodium currents in smooth muscle cells freshly isolated from stomach fundus of the rat and ureter of the guinea-pig. J Physiol 442:351–375

    CAS  PubMed  Google Scholar 

  • Plant RE (1978) The effects of calcium+ + on bursting neurons. A model study. Biophys J 21:217–237

    CAS  PubMed  Google Scholar 

  • Plant RE, Kim M (1975) On the mechanism underlying bursting in the Aplasia abdominal ganglion R15 cell. Math Biosci 26:357–375

    Article  Google Scholar 

  • Rinzel J, Lee YS (1987) Dissection of a model for neuronal parabolic bursting. J Math Biol 25:653–675

    Article  CAS  PubMed  Google Scholar 

  • Sanders KM, Publicover NG (1989) Electrophysiology of the gastric musculature. In: Schultz S, Wood JD (eds) Handbook of physiology: the gastrointestinal system. Raven Press, New York, pp 187–216

    Google Scholar 

  • Sarna SK (1975) Models of smooth muscle electrical activity. In: Daniel EE, Paton DM (eds) Methods in pharmacology. Smooth muscle. Plenum, New York, pp 519–540

    Google Scholar 

  • Sarna SK, Daniel EE, Kingma YJ (1971) Simulation of slow-wave electrical activity of the small intestine. Am J Physiol 221:166–175

    CAS  PubMed  Google Scholar 

  • Shonnard P, Sanders KM (1988) Excitation of toad gastric muscles by ACh and substance P cannot be explained by decreased “M-current”. FASEB J 2:A758

    Google Scholar 

  • Szurszewski JH (1987) Electrical basis for gastrointestinal motility. In: Johnson LR (ed) Physiology of the gastrointestinal tract. Raven Press, New York, pp. 383–423

    Google Scholar 

  • Takenawa T (1982) Inositol phospholipids in stimulated smooth muscles. Cell Calcium 3:359–368

    Article  CAS  PubMed  Google Scholar 

  • Tsien RW, Ellinor PT, Home WA (1991) Molecular diversity of voltage-dependent Ca2+ channels. Trends Pharmacol Sci 145:349–354

    Google Scholar 

  • Walsh JV, Siger JJ (1983) Ca-activated K channels in vertebrate smooth muscle cells. Cell Calcium 4:321–330

    Article  CAS  PubMed  Google Scholar 

  • Weisbrodt NW, Christensen J (1972) Electrical activity of the cat duodenum in fasting and vomiting. Gastroenterology 63:1004–1010

    CAS  PubMed  Google Scholar 

  • Wood JD (1987) Neurophysiological theory of intestinal motility. Jpn J Smooth Muscle Res 23:143–186

    CAS  Google Scholar 

  • Yamamoto H, Breemen C van (1985) Inositol-1,4,5-triphosphate releases calcium from skinned cultured smooth muscle cells. Biochem Biophys Res Commun 130:270–274

    Article  CAS  PubMed  Google Scholar 

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Authors and Affiliations

  1. Department of Numerical Mathematics, Kazan University, 420008, Kazan, Russia

    R. N. Miftakhov & G. R. Abdusheva

  2. Gastrointestinal Science Research Unit, The London Hospital Medical College, University of London, E1 2AJ, London, UK

    D. L. Wingate

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  1. R. N. Miftakhov
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  2. G. R. Abdusheva
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  3. D. L. Wingate
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Miftakhov, R.N., Abdusheva, G.R. & Wingate, D.L. Model predictions of myoelectrical activity of the small bowel. Biol. Cybern. 74, 167–179 (1996). https://doi.org/10.1007/BF00204205

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