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IEEE International Conference on Bioinformatics and Bioengineering (BIBE)

Neurogenesis as a Probability Amplitude Governed by Charges-Dependent Hamiltonian

Huber Nieto–Chaupis

Published Nov 1, 2022• 0 citations
Publisher

Abstract

Inspired on the idea of Mathew P. A. Fisher about the possibility that quantum mechanics is playing some basic roles on the biochemical processes in the brain, this paper has opted by develop a theory based on the description of neurogenesis by using the formalism and concepts of quantum mechanics. To accomplish this, it is assumed that each one of the main steps towards to the formation of neuron is done in a probabilistic manner, so that the probability amplitude is calculated. Concretely, the main steps: proliferation, migration and differentiation are expressed in terms of amplitudes. Also, the evolution operator depends only on electrical interactions fom the fact of abundance of ions so that attractive or repulsion forces might be crucial to the completion of subprocesses previous to maturation of neuron. Based on the quantum mechanics probabilities simulations are presented and discussed.

DOI
10.1109/bibe55377.2022.00076

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Inspired on the idea of Mathew P. A. Fisher about the possibility that quantum mechanics is playing some basic roles on the biochemical processes in the brain, this paper has opted by develop a theory based on the description of neurogenesis by using the formalism and concepts of quantum mechanics. To accomplish this, it is assumed that each one of the main steps towards to the formation of neuron is done in a probabilistic manner, so that the probability amplitude is calculated. Concretely, the main steps: proliferation, migration and differentiation are expressed in terms of amplitudes. Also, the evolution operator depends only on electrical interactions fom the fact of abundance of ions so that attractive or repulsion forces might be crucial to the completion of subprocesses previous to maturation of neuron. Based on the quantum mechanics probabilities simulations are presented and discussed.
Under the assumption that neurogenesis is a fully random process then some laws such as the ones belonging to quantum mechanics might be applied. In this paper, it is assumed that along the process of creation of new neurons, some phases such as proliferation and creation would consist in quantum coherent states in the sense that the formation of new neurons might be synchronized. Thus the ion-dependence formalism of quantum mechanics is employed, with a special emphasis to the usage of evolution operator Hamiltonian governed by Coulomb forces.
The process of synaptic transmission is projected onto the territory of quantum mechanics. Thus, the electric interactions are seen as probabilistic events more than a deterministic one. In this manner, the neurotransmitter would obey quantum laws and their dynamics is governed by the evolution operator. Thus, synapse seen as an action of propagation would encompasses well to that the spatial propagator or Green function that might model the dyanamics of neurotransmitters along the cleft. This turns out to be instantaneous in coherence to the concept of neural transmission. Indeed under the quantum mechnics scenario it is found that the eigenvalues of energies of Hamiltonian consist in electric potentials between electrically charged neurotransmitters and receptors at the ion channels.
A probabilistic model of Synapse is proposed. In concrete, synapse is proposed as a Bayesian probability that requires the quantum probabilities for both: the interaction of Calcium 2+ in axon area, and the releasing of neurotransmitters. In this way, all available interactions that are carry out at axon zone, are dictated by quantum events. Once neurotransmitters are released from synaptic vesicles, their dynamics might be dictated by quantum probabilities based in a Hamiltonian. The diverse scenarios and their respective distribution of probabilities are simulated. From proposed theory, it is suggested that synapse would have a notable dependence on the accumulation of electric charges before and after the pass of neurotransmitters from a neuron to adjacent one. From the results, it is possible to argue that synapse is more than a biological phenomenon, a multidisciplinary event, that emphasizes the importance of transporting of electric charges with a potential dependence on probabilities, more than trivial determinism.
If neural synapse is a probabilistic event, then one would expect that this is the result of a chain of subprocesses that takes place in axon. Thus, one can adjudicate probabilistic quantities to each one of event previous to the releasing of neurotransmitters from synaptic vesicles. Indeed, one can argue that electrical interactions are responsible of neurotransmitters dynamics before them pass to cleft. Because this, the present paper has employed the formalism of quantum probabilities. Thus, quantum mechanics would apply to describe the entire process of synapse. Finally, it was associated a set of conditional probabilities that would led to state that neural synapse is a kind of conjunction of quantum events and conditional probabilities. Finally, probabilities are estimated exhibiting a logic agreement to common knowledge of synapse.
Artificial intelligence (AI) has drawn significant inspiration from neuroscience to develop artificial neural network (ANN) models. However, these models remain constrained by the Von Neumann architecture and struggle to capture the complexity of the biological brain. Quantum computing, with its foundational principles of superposition, entanglement, and unitary evolution, offers a promising alternative approach to modeling neural dynamics. This paper explores the possibility of a neuro-quantum model of the brain by introducing a stochastic quantum approach that incorporates random fluctuations of neuronal processing within a quantum framework. We propose a mathematical formalization of stochastic quantum neural networks (QNNS), where qubits evolve according to stochastic differential equations inspired by biological neuronal processes. We also discuss challenges related to decoherence, qubit stability, and implications for AI and computational neuroscience.
Biological neuronal networks represent a fundamental component of complex systems, including the brain. Simulating these networks accurately and efficiently is a significant challenge, largely due to the intricate, non-linear interactions between neurons. Traditional simulation methods, often relying on numerical integration techniques like the Hodgkin-Huxley model, are computationally intensive, particularly when scaling to large networks. This paper proposes a novel approach to neuronal network simulation inspired by quantum mechanics, specifically leveraging concepts of superposition and entanglement. We introduce a framework that utilizes quantum-inspired algorithms to represent and evolve neuronal states, aiming to dramatically reduce computational overhead. The core idea involves mapping neuronal dynamics onto a quantum system, where neurons are represented by qubits, and synaptic connections are modeled as quantum gates. The simulation process then utilizes quantum algorithms to evolve the system, effectively capturing the parallel and interconnected nature of neuronal networks. We present a mathematical formulation of the simulation process, focusing on the evolution equation for neuronal states. We explore key concepts like wave function collapse and measurement in the context of neuronal network simulation, offering a potential pathway for more realistic and efficient modeling of biological neural systems. The ultimate goal is to provide a computationally tractable method for simulating large-scale neuronal networks, leading to improved understanding of brain function and potentially facilitating the development of advanced neurotechnologies. The presented framework offers a distinct alternative to conventional methods, promising significant advantages in terms of speed and scalability.