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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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P2X Receptors in The Post-Structure Era

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Dr. Rishabh Pathak

P2X receptors are a class of ligand-gated ion channels activated by extracellular ATP, playing crucial roles in various physiological and pathological processes in the nervous system. Here is an overview of P2X receptors in the post-structure era, focusing on recent advancements and implications:


1.      Structural Insights:

oInitial Discoveries: Early structural studies using X-ray crystallography and cryo-electron microscopy provided insights into the overall architecture of P2X receptors, revealing trimeric assembly and ligand-binding sites.

o  Recent Advances: High-resolution structures of P2X receptors, such as P2X3 and P2X7, have elucidated the conformational changes upon ATP binding, ion permeation pathways, and allosteric modulation sites.

2.     Functional Diversity:

o Subunit Composition: P2X receptors are composed of seven subunits (P2X1-7), each exhibiting distinct pharmacological properties, ion selectivity, and expression patterns in different cell types.

o Functional Roles: P2X receptors mediate fast excitatory neurotransmission, synaptic plasticity, pain sensation, immune responses, and neuroinflammation, highlighting their diverse functions in health and disease.

3.     Allosteric Modulation:

o Allosteric Sites: Recent studies have identified allosteric modulatory sites on P2X receptors that can fine-tune channel activity, providing opportunities for developing subtype-selective modulators with therapeutic potential.

o Pharmacological Targeting: Allosteric modulators of P2X receptors offer novel strategies for modulating receptor function, potentially avoiding the limitations of orthosteric ligands and enhancing therapeutic specificity.

4.    Pathophysiological Implications:

o Neurological Disorders: Dysregulation of P2X receptors is implicated in neurological disorders such as chronic pain, migraine, epilepsy, and neurodegenerative diseases, making them attractive targets for drug development.

o    Immune Responses: P2X receptors play critical roles in immune cell activation, inflammation, and cytokine release, suggesting their involvement in immune-related pathologies and potential immunomodulatory interventions.

5.     Therapeutic Potential:

o Drug Development: Targeting P2X receptors with selective agonists, antagonists, or allosteric modulators holds promise for developing novel therapeutics for pain management, neuroprotection, and inflammatory conditions.

o    Precision Medicine: Understanding the structural and functional diversity of P2X receptors enables the design of personalized treatment strategies tailored to specific receptor subtypes and disease contexts.

In the post-structure era, advances in understanding the structural basis, functional diversity, allosteric modulation, and pathophysiological implications of P2X receptors have opened new avenues for exploring their roles in health and disease. Harnessing the therapeutic potential of P2X receptors through precise modulation and targeted drug development offers exciting opportunities for advancing neuropharmacology and personalized medicine.

 

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