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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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Regulation Of Phosphatidic Acid Synthesis at The Exocytotic Site: Implication of GTPASES And Kinases

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Dr. Rishabh Pathak

Regulation of phosphatidic acid synthesis at the exocytotic site involves the intricate interplay of GTPases and kinases, which play crucial roles in modulating lipid metabolism and membrane dynamics during exocytosis. Here is an overview of how GTPases and kinases are implicated in the regulation of phosphatidic acid synthesis at the exocytotic site:


1.      GTPases in Phosphatidic Acid Synthesis:

o    Rab GTPases: Rab GTPases are key regulators of vesicle trafficking and membrane fusion during exocytosis. They control the spatial and temporal dynamics of membrane trafficking events.

o    Arf GTPases: Arf GTPases are involved in vesicle formation, cargo sorting, and vesicle budding at the Golgi apparatus and endosomes. They regulate membrane trafficking pathways that impact phospholipid metabolism.

o Rho GTPases: Rho GTPases play a role in actin cytoskeleton dynamics and membrane remodeling. They can influence lipid metabolism indirectly by modulating cytoskeletal organization and membrane curvature.

2.     Kinases in Phosphatidic Acid Synthesis:

o    PI3K (Phosphoinositide 3-Kinase): PI3Ks are key enzymes that phosphorylate phosphatidylinositol lipids, generating phosphoinositides that serve as signaling molecules. They regulate membrane trafficking and vesicle fusion events during exocytosis.

o    PLD (Phospholipase D): PLD enzymes catalyze the hydrolysis of phosphatidylcholine to generate phosphatidic acid. They are involved in membrane remodeling, vesicle trafficking, and exocytosis.

o    PKC (Protein Kinase C): PKC isoforms can phosphorylate and regulate enzymes involved in phosphatidic acid metabolism. They modulate membrane dynamics and protein interactions at the exocytotic site.

3.     Implications for Exocytosis:

o Membrane Fusion: GTPases and kinases regulate membrane fusion events by modulating lipid composition and membrane curvature at the exocytotic site.

o Vesicle Docking and Priming: These signaling molecules influence vesicle docking, priming, and fusion with the plasma membrane, essential steps in neurotransmitter release.

o  Regulation of SNARE Complexes: GTPases and kinases may impact the assembly and function of SNARE complexes, which are essential for vesicle fusion and neurotransmitter release.

4.    Integration of Signaling Pathways:

o    Cross-Talk: GTPases and kinases interact with multiple signaling pathways involved in exocytosis, including calcium signaling, cytoskeletal dynamics, and protein phosphorylation cascades.

o    Fine-Tuning Exocytosis: The coordinated action of GTPases and kinases allows for precise regulation of phosphatidic acid synthesis and membrane dynamics during exocytosis.

o    Neuronal Communication: Proper regulation of lipid metabolism at the exocytotic site by GTPases and kinases is essential for efficient neuronal communication and synaptic transmission.

Understanding how GTPases and kinases regulate phosphatidic acid synthesis at the exocytotic site provides insights into the molecular mechanisms underlying neurotransmitter release and synaptic function. Dysregulation of these signaling pathways may impact synaptic vesicle dynamics and neurotransmission, highlighting the importance of GTPases and kinases in maintaining proper neuronal function.

 

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