European Journal of Biophysics
Volume 4, Issue 6, December 2016, Pages: 47-66
Received: Jan. 2, 2017;
Accepted: Jan. 10, 2017;
Published: Feb. 10, 2017
Views 3355 Downloads 126
Paul Levi, Institute for Parallel and Distributed Systems (IPVS), Faculty for Informatics, Electrical Engineering and Information Technology, University Stuttgart, Stuttgart, Germany
This article describes small neurotransmitters as particles of a spinless quantum field. That is, the particles are Bosons that e.g. can occupy equal energy levels. In addition, we consider the particles of the presynaptic region before exocytosis occur as elements of a grand canonical ensemble that is in a thermodynamic equilibrium. Thus, the particles obey the Bose-Einstein statistics, which also determines the corresponding information entropy and the corresponding density matrix. When the release of neurotransmitters occur, the equilibrium collapses and the Bose-Einstein distribution transfers to the Poisson distribution. Moreover, the particles transmit as wave packets, with quantized energies and momenta, through the chemical synapses, where we also describe the effects of the quantum fluctuations. We mark this symmetry braking process that corresponds to a non-equilibrium phase transition by a threshold, which mainly depends on the mean of the particles number, with defined quanta. We model the connections of synaptic neurons of a population to a network by Hamiltonians that include both Bosons and Fermions and their interactions. Bosons are the carriers of messages (information) and Fermions are the switches, which forward these messages, with a modified content. The effects we observe in such a neural circuitry reveals a strong dependence of the solutions from the initial values and, more relevant, solutions with chaotic behavior exist. These circuitry-based ramifications together with possible internal malfunctioning of particular neurons (e.g. intermitted flow) of the network cause a sustainable reduction of the synaptic plasticity.
Quantum Effects in Synaptic Neurons and Their Networks in the Brain, European Journal of Biophysics.
Vol. 4, No. 6,
2016, pp. 47-66.
Albers B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2008). Molecular Biology of the Cell. Fifth edition, New York, Garland Science.
Bear F B, Connors B W, Paradiso M A, (2015). Neuroscience: Exploring the Brain. Fourth edition, Philadelphia, Wolters Kluwer.
Beck F, Eccles J (2003). Quantum Processes in the Brain. Neural Basis of consciousness. Proc Natl. Acad. Sci. USA, Vol. 89, 11357-11361, December 1992 (49).
Bjorken J. and Drell S, (1965). Relativistic Quantum Fields. New York, McGraw–Hill.
Dyan P and Abbott L F (2005). Theoretical Neuroscience. Second edition, Cambridge, The MIT Press.
Fermi E (1936). Thermodynamics. New York, Dover Publications, INC.
Feynman R P and Hibbs A R (2005). Quantum Mechanics and Path Integrals. Emended edition, New York, Mc Graw-Hill.
Gerstner W and Kistler W. (2011). Spiking Neuron Models. Second edition, Cambridge, Cambridge University Press.
Gerstner W, Kistler W, Naud R, and Paninski L (2014). Neural Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge, Cambridge University Press.
Hagan Sc, Hameroff St, and Tuszynski J (2014). Quantum Computation in Brain Microtubules: Decoherence and biological Feasibility. Physical Review E 65.6 (2002): 061901.
Guckenheimer J, Holmes Ph (2002). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Heidelberg, Springer-Verlag.
Haken H (1985). Light and Matter II. Amsterdam, North Holland.
Haken H (2006). Information and Self-Organization. Third edition, Heidelberg, Springer.
Haken H, Levi P (2012). Synergetic Agents–Classical and Quantum. From Multi-Robot Systems to Molecular Robotics. Weinheim, Wiley-VCH.
Huelga S F, Plenio M B (2011). Quantum Dynamics of bio-molecular Systems in noisy Environments. Twenty-twoth Solvay Conference in Chemistry, Procedia Chemistry 00(2011), 1-10, www.sciencedirect.com.
Haynie D T (2001). Biological Thermodynamics. Cambridge, Cambridge University Press.
Job G and Herrmann F (2006). Chemical Potential–a quantity in search of recognition, Eur. J. Phys. 27, 353-371.
Kandel E R, Schwartz J H, Jessel Th M, Editors (2012). Principles of Neural Science. Fourth edition, New York, McGraw-Hill.
Kittel Ch (2005). Introduction to Solid State Physics. Eighth edition, New Jersey, John Wiley & Sons.
Lambert N, Chen YN, Li CM, Chen GY, Nori F (2013). Quantum Biology. Nature Physics 9, 10-18, doi: 10.138/nphys2474.
Levi P (2015). Molecular Quantum Robotics: Particle and Wave Solutions, illustrated by “Leg-over-Leg” Walking along Microtubules. Frontiers in Neurorobotics, May 2015, Vol. 9, 1-16. doi: 10.3389/fnbot.2015.00002.
Levi P (2016). A Quantum Field Based Approach to Describe the Global Molecular Dynamics of Neurotransmitter Cycles. European Journal of Biophysics, Vol. 4, No. 4, 22-41. doi: 10.11648/j.ejb.20160404.11.
Lodish H, Berk A, Zipursky S L, Matsudaira P, Baltimore D, Darnell J. Molecular Cell Biology (2000). Fourth edition, New York, Freeman and Company.
Lurié D (1968). Particles and Fields. New York, John Wiley & Sons.
Weinberg S (2005). The Quantum Theory of Fields, Vol. I, II, III. Cambridge, Cambridge University Press.
Weinberg S (2013). Lectures on Quantum Mechanics. Cambridge, Cambridge University Press.
Wiggins S (1990). Introduction to Applied Nonlinear Dynamical Systems and Chaos. Heidelberg, Springer-Verlag.
Zaslavsky G M (2007). The Physics of Chaos in Hamiltonian Systems. Second edition, London, Imperial College Press.