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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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Structure And Catalytic Mechanism Of NTPDases And E5NT In Purinergic Signaling

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Dr. Rishabh Pathak

Nucleoside triphosphate diphosphohydrolases (NTPDases) and ecto-5'-nucleotidase (e5NT) are key enzymes involved in purinergic signaling, regulating the extracellular levels of nucleotides and nucleosides. Here is an overview of the structure and catalytic mechanism of NTPDases and e5NT in purinergic signaling:


1.      Nucleoside Triphosphate Diphosphohydrolases (NTPDases):

o    Structure:

§NTPDases belong to the ectonucleoside triphosphate diphosphohydrolase family, with several isoforms identified in different tissues and cell types.

§The crystal structures of NTPDases reveal a conserved catalytic site with essential residues for nucleotide binding and hydrolysis.

o    Catalytic Mechanism:

§  NTPDases hydrolyze extracellular nucleoside triphosphates (e.g., ATP, ADP) to their respective nucleoside monophosphates (e.g., AMP) and inorganic phosphate.

§  The catalytic mechanism involves nucleophilic attack on the γ-phosphate of the nucleotide substrate, leading to the formation of a covalent enzyme-substrate intermediate that is subsequently hydrolyzed.

§  Metal ions, such as divalent cations (e.g., Mg2+), play a crucial role in coordinating the nucleotide substrate and stabilizing the transition state during hydrolysis.

2.     Ecto-5'-Nucleotidase (e5NT):

o    Structure:

§  e5NT, also known as CD73, is a glycosylphosphatidylinositol (GPI)-anchored enzyme located on the cell surface.

§  The crystal structure of e5NT reveals a catalytic domain with conserved residues involved in nucleotide binding and catalysis.

o    Catalytic Mechanism:

§  e5NT catalyzes the hydrolysis of extracellular AMP to adenosine and inorganic phosphate.

§ The catalytic mechanism involves the nucleophilic attack on the 5'-phosphate of AMP, leading to the formation of a covalent enzyme-AMP intermediate that is subsequently hydrolyzed to release adenosine.

§Metal ions, such as divalent cations, may also play a role in stabilizing the transition state during the catalytic reaction.

3.     Purinergic Signaling:

o    Role in Purinergic Signaling:

§NTPDases and e5NT play critical roles in regulating the extracellular levels of ATP, ADP, and adenosine, which act as signaling molecules in purinergic signaling pathways.

§ The balance between ATP release and its subsequent hydrolysis by NTPDases and e5NT influences purinergic signaling cascades, modulating various physiological processes such as neurotransmission, immune responses, and vascular function.

Understanding the structure and catalytic mechanisms of NTPDases and e5NT in purinergic signaling provides insights into the regulation of extracellular nucleotide and nucleoside levels, highlighting their importance in modulating purinergic signaling pathways and physiological responses. Further research on the enzymatic properties and regulatory mechanisms of NTPDases and e5NT may uncover novel therapeutic targets for manipulating purinergic signaling in health and disease.

 

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