Compartment model of neuropeptide synaptic transport with impulse control | Biological Cybernetics Skip to main content

Advertisement

Springer Nature Link
Log in

Compartment model of neuropeptide synaptic transport with impulse control

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

In this paper a mathematical description of a presynaptic episode of slow synaptic neuropeptide transport is proposed. Two interrelated mathematical models, one based on a system of reaction diffusion partial differential equations and another one, a compartment type, based on a system of ordinary differential equations (ODE) are formulated. Processes of inflow, calcium triggered activation, diffusion and release of neuropeptide from large dense core vesicles (LDCV) as well as inflow and diffusion of ionic calcium are represented. The models assume the space constraints on the motion of inactive LDCVs and free diffusion of activated ones and ions of calcium. Numerical simulations for the ODE model are presented as well. Additionally, an electronic circuit, reflecting the functional properties of the mathematically modelled presynaptic slow transport processes, is introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adams PR, Jones SW, Pennefather P, Brown DA, Koch C, Lancaster B (1986) Slow synaptic transmission in frog sympathetic ganglia. J Exp Biol 124: 259–285

    PubMed  CAS  Google Scholar 

  • Ashby WR (1958) An Introduction to Cybernetics. Chapman & Hall Ltd, London

    Google Scholar 

  • Aristizabal F, Glavinovic MI (2004) Simulation and parameter estimation of dynamics of synaptic depression. Biol Cybern 90: 3–18

    Article  PubMed  CAS  Google Scholar 

  • Beal MF, Mazurek MF, Chattha GK, Svendsen CN, Bird ED, Martin JB (1986) Neuropeptide Y immunocreativity is reduced in cerebral cortex in Alzheimer’s disease. Ann Neurol 20: 282–288

    Article  PubMed  CAS  Google Scholar 

  • Beal MF, Clevens RA, Mazurek MF (2004) Somatostatin and neuropeptide Y immunoreactivity in Parkinson’s disease dementia with Alzheimer’s changes. Synapse 2(4): 463–467

    Article  Google Scholar 

  • Bertrand PP, Thomas EA, Kunze WAA, Bornstein JC (2000) A simple mathematical model of second-messenger mediated slow excitatory postsynaptic potentials. J Comput Neurosci 8: 127–142

    Article  PubMed  CAS  Google Scholar 

  • Bielecki A, Kalita P, Lewandowski M (2006a) Model of fast synaptic transmission. In: Proceedings of the 12th national conference on application of mathematics in biology and medicine. Kraków, Poland, pp 13–18

  • Bielecki A, Skomorowski M, Woźniak R (2006) Electronic neural networks modelling. In: Cader A, Rutkowski L, Tadeusiewicz R, Żurada J (eds) Artificial intelligence and soft computing. Series: challenging problems of science—computer science Bolc L (ed). Academic Publishing House EXIT, Warszawa, Poland, pp 8–14

    Google Scholar 

  • Bielecki A, Kalita P (2008) Model of neurotransmitter fast transport in axon terminal of presynaptic neuron. J Math Biol 56(4): 559–576

    Article  PubMed  Google Scholar 

  • Boyd IA, Martin AR (1956) The end-plate potential in mammalian muscle. J Physiol 132: 74–91

    PubMed  CAS  Google Scholar 

  • del Castillo J, Katz B (1954) Quantal components of the end-plate potential. J Physiol 124: 560–573

    PubMed  CAS  Google Scholar 

  • Donahue BS, Abercrombie RF (1987) Free diffusion coefficient of ionic calcium in cytoplasm. Cell Calcium 8: 437–448

    Article  PubMed  CAS  Google Scholar 

  • Friedman A, Craciun G (2005) A model of intracellular transport of particles in an axon. J Math Biol 51: 217–246

    Article  PubMed  Google Scholar 

  • Gabriel SM, Davidson M, Haroutunian V, Powchik P, Bierer LM (1996) Neuropeptide deficits in schizophrenia vs. Alzheimer’s disease cerebral cortex. Biol Psychiatry 39: 82–91

    Article  PubMed  CAS  Google Scholar 

  • Greengard P (2001) The neurobiology of slow synaptic transmission. Science 294: 1024–1030

    Article  PubMed  CAS  Google Scholar 

  • Han W, Ng YK, Axelrod D, Levitan ES (1999) Neuropeptide release by efficient recruitment of diffusing cytoplasmic secretory vesicles. Proc Natl Acad Sci USA 96: 14577–14582

    Article  PubMed  CAS  Google Scholar 

  • Harmon LD (1961) Studies with artificial neuron—properties and functions of an artificial neuron. Biol Cybern 1: 89–101

    CAS  Google Scholar 

  • Kalkstein JM, Magleby KL (2003) Augmentation increases vesicular release probability in the presence of masking depression at the frog neuromuscular junction. J Neurosci 24: 4127–4134

    Google Scholar 

  • Keener J, Sneyd J (1998) Mathematical physiology. Springer, New York

    Google Scholar 

  • Kruckenberg P, Sandweg R (1968) An analog model for acetylocholine release by motor nerve endings. J Theoret Biol 19: 327–332

    Article  CAS  Google Scholar 

  • Levitan ES, Lanni F, Shakiryanova D (2007) In vivo imaging of vesicle motion and release at the Drosophila neuromuscular junction. Nat Protocols 2: 1117–1125

    Article  CAS  Google Scholar 

  • Levitan ES (2008) Signaling for vesicle mobilization and synaptic plasticity. Mol Neurobiol 37(1): 39–43

    Article  PubMed  CAS  Google Scholar 

  • Magleby KL, Stevens CF (1972) A quantitative description of end-plate currents. J Physiol 223: 173–197

    PubMed  CAS  Google Scholar 

  • Masuo Y, Morita M, Oka S, Ishido M (2004) Motor hyperactivity caused by a deficit in dopaminergic neurons and the effects of endocrine disruptors: a study inspired by the physiological roles of PACAP in the brain. Regul Pept 123: 225–234

    Article  PubMed  CAS  Google Scholar 

  • Nagumo J, Arimoto S, Yoshizawa S (1964) An active pulse transmision line simulating nerve axon. Proc IRE 50: 2061–2070

    Article  Google Scholar 

  • Ng YK, Lu X, Gulacsi A, Han W, Saxon MJ, Levitan ES (2003) Unexpected mobility variation among indyvidual secretory vesicles produces an apparent refractory neuropeptide pool. Biophys J 84: 4127–4134

    PubMed  CAS  Google Scholar 

  • Oades RD, Daniels R, Rascher W (1998) Plasma neuropeptide—Y levels, monoamine metabolism, electro lyte excretion and drinking behavior in children with attention-deficit hyperactivity disorder. Psychiatry Res 80: 177–186

    Article  PubMed  CAS  Google Scholar 

  • Rall W (1969) Time constants and electronic length of membrane cylinders and neurons. Biophys J 9: 1483–1508

    Article  PubMed  CAS  Google Scholar 

  • Scott A (1995) Stairway to the mind. Springer, New York

    Google Scholar 

  • Scott R, Rusakov DA (2006) Main determinants of presynaptic Ca2+ dynamics at individual mossy fiber–CA3 pyramidal cell synapses. J Neurosci 26: 7071–7081

    Article  PubMed  CAS  Google Scholar 

  • Shakiryanova D, Tully A, Hewes RS, Deitcher DL, Levitan ES (2005) Activity-dependent liberation of synaptic neuropeptide vesicles. Nat Neurosci 8: 173–178

    Article  PubMed  CAS  Google Scholar 

  • Shakiryanova D, Tully A, Levitan ES (2006) Activity-dependent synaptic capture of transiting peptidergic vesicles. Nat Neurosci 9: 896–900

    Article  PubMed  CAS  Google Scholar 

  • Tadeusiewicz R (1994) Problems of biocybernetics. PWN, Warszawa (in Polish)

  • Virgo L, Humphries C, Mortimer A, Barnes T, Hirsch S, de Belleroche J (1995) Cholecystokinin messenger RNA deficit in frontal and temporal cerebral cortex in schizophrenia. Biol Psychiatry 37: 694–701

    Article  PubMed  CAS  Google Scholar 

  • Wong M, Shakiryanova D, Levitan ES (2008) Presynaptic ryanodine receptor-CamKII signaling is required for activity-dependent capture of transiting vesicles. J Mol Neurosci (to appear) doi:10.1007/s12031-008-9080-8

  • Waxman SG (1972) Regional differentation of the axon: a review with special reference to the concept of the multiplex neuron. Brain Res 47: 269–288

    Article  PubMed  CAS  Google Scholar 

  • Texas Instruments Incorporated (2006) Precision ADC and DACs with 8051 microcontroller and flash memory (Rev. F). http://focus.ti.com/docs/prod/folders/print/msc1211y2.html, Texas Instruments

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072, Kraków, Poland

    Andrzej Bielecki, Piotr Kalita & Marek Skomorowski

  2. Institute of Zoology, Jagiellonian University, Ingardena 6, 30-060, Kraków, Poland

    Marian Lewandowski

Authors
  1. Andrzej Bielecki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Piotr Kalita
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marian Lewandowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marek Skomorowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piotr Kalita.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bielecki, A., Kalita, P., Lewandowski, M. et al. Compartment model of neuropeptide synaptic transport with impulse control. Biol Cybern 99, 443–458 (2008). https://doi.org/10.1007/s00422-008-0250-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-008-0250-0

Keywords

Search

Navigation