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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Highlighting the Molecular Basis of Purinergic Transmission

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Dr. Rishabh Pathak

Purinergic transmission is a fundamental signaling mechanism in the nervous system that involves the release and action of purines, such as adenosine triphosphate (ATP) and adenosine, as neurotransmitters. Here is an overview highlighting the molecular basis of purinergic transmission:


1.      Purinergic Receptors:

o P2X Receptors: Ligand-gated ion channels activated by ATP, leading to cation influx (e.g., Ca2+, Na+). P2X receptors play a role in fast excitatory neurotransmission.

o    P2Y Receptors: G protein-coupled receptors activated by ATP or other nucleotides, triggering intracellular signaling cascades. P2Y receptors are involved in modulating synaptic transmission and neuronal excitability.

o    Adenosine Receptors: A1, A2A, A2B, and A3 adenosine receptors are G protein-coupled receptors activated by adenosine. They regulate neuronal activity, synaptic plasticity, and neuroprotection.

2.     ATP Release Mechanisms:

o Exocytosis: ATP can be released from synaptic vesicles via exocytosis in a calcium-dependent manner, similar to classical neurotransmitters.

o    Non-vesicular Release: ATP can also be released through connexin hemichannels, pannexin channels, and other mechanisms in a calcium-independent manner, contributing to volume transmission.

3.     Enzymes and Transporters:

o  Ectonucleotidases: Enzymes like CD39 and CD73 regulate the extracellular levels of ATP and adenosine by hydrolyzing ATP to adenosine.

o    Equilibrative Nucleoside Transporters (ENTs): Facilitate the reuptake of adenosine into cells, regulating its extracellular concentration and signaling duration.

4.    Roles in the Nervous System:

o    Neurotransmission: ATP and adenosine act as neurotransmitters and neuromodulators, influencing synaptic transmission, plasticity, and neuronal excitability.

o Neuroprotection: Adenosine, through A1 receptors, can exert neuroprotective effects by reducing excitotoxicity and inflammation in the brain.

oPain Modulation: Purinergic signaling is involved in pain processing, with ATP acting as a pain mediator and adenosine as an analgesic agent.

5.     Pathophysiological Implications:

o    Neurological Disorders: Dysregulation of purinergic transmission is implicated in various neurological disorders, including epilepsy, neurodegenerative diseases, and chronic pain conditions.

o    Therapeutic Targets: Purinergic receptors and signaling pathways are potential targets for drug development in the treatment of neurological and neuropsychiatric disorders.

Understanding the molecular basis of purinergic transmission provides insights into the complex mechanisms underlying neuronal communication and synaptic function. By elucidating the roles of purinergic signaling in health and disease, researchers can uncover novel therapeutic strategies for targeting purinergic receptors and modulating purinergic transmission in neurological conditions.

 

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