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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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From Basic Mechanisms to Therapeutic Targets in Huntington's Disease

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Dr. Rishabh Pathak

Huntington's disease (HD) is a devastating neurodegenerative disorder characterized by motor dysfunction, cognitive decline, and psychiatric symptoms. Understanding the basic mechanisms underlying HD pathology has led to the identification of potential therapeutic targets aimed at slowing disease progression and improving patient outcomes. Here is an overview of the journey from basic mechanisms to therapeutic targets in Huntington's disease:


1.      Basic Mechanisms of Huntington's Disease:

o    CAG Repeat Expansion: HD is primarily caused by an abnormal expansion of CAG repeats in the huntingtin (HTT) gene, leading to the production of mutant huntingtin protein (mHTT) with toxic properties.

o  Protein Aggregation: mHTT forms aggregates within neurons, disrupting cellular functions, impairing proteostasis, and triggering neurotoxicity.

o    Mitochondrial Dysfunction: HD is associated with mitochondrial abnormalities, including impaired energy metabolism, oxidative stress, and mitochondrial fragmentation, contributing to neuronal dysfunction and degeneration.

o Excitotoxicity and Calcium Dysregulation: Dysregulation of calcium homeostasis and excitotoxicity play a role in neuronal death in HD, leading to synaptic dysfunction and neurodegeneration.

2.     Therapeutic Targets in Huntington's Disease:

o    Targeting Protein Aggregation:

§  HSP90 Inhibition: Heat shock protein 90 (HSP90) inhibitors have shown promise in reducing mHTT aggregation and promoting protein clearance mechanisms [T11].

§Autophagy Modulation: Enhancing autophagy pathways through mTOR inhibition or activation of autophagy regulators can facilitate the clearance of mHTT aggregates and improve neuronal survival [T12].

o    Mitochondrial Protection:

§  Mitochondrial Biogenesis: Activating pathways involved in mitochondrial biogenesis, such as PGC-1α, can enhance mitochondrial function and protect neurons from HD-related mitochondrial dysfunction [T13].

§Antioxidant Therapy: Targeting oxidative stress with antioxidants or mitochondrial-targeted compounds may mitigate mitochondrial damage and reduce neuronal vulnerability in HD [T14].

o    Excitotoxicity and Calcium Regulation:

§  NMDA Receptor Modulation: NMDA receptor antagonists or modulators can help regulate calcium influx and excitotoxic signaling pathways implicated in HD pathogenesis [T15].

§  Calcium Channel Blockers: Inhibiting calcium channels or modulating calcium-binding proteins may offer neuroprotection by restoring calcium homeostasis in HD-affected neurons [T16].

3.     Emerging Therapeutic Strategies:

o Gene Silencing: RNA interference (RNAi) or antisense oligonucleotide (ASO) therapies targeting mHTT mRNA have shown potential for reducing mutant huntingtin levels and ameliorating HD symptoms [T17].

o  Epigenetic Modulation: HDAC inhibitors and other epigenetic modifiers are being explored for their ability to regulate gene expression, chromatin remodeling, and neuroprotection in HD [T18].

o    Neuroinflammation Targeting: Modulating neuroinflammatory responses through microglial activation inhibitors or anti-inflammatory agents may help mitigate neurodegeneration and disease progression in HD [T19].

In conclusion, the transition from understanding the basic mechanisms of Huntington's disease to identifying therapeutic targets has paved the way for the development of innovative treatment strategies aimed at addressing key pathological processes underlying HD. By targeting protein aggregation, mitochondrial dysfunction, excitotoxicity, and other disease mechanisms, researchers and clinicians are working towards improving outcomes for individuals affected by Huntington's disease.

 

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