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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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Dynamics Interactions Underpinning Secretory Vesicle Fusion

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Dr. Rishabh Pathak

The dynamics of interactions underpinning secretory vesicle fusion are crucial for neurotransmitter release and synaptic communication. Here is an overview of the key molecular interactions involved in the process of secretory vesicle fusion at the synapse:


1.      SNARE Complex Formation:

o SNARE Proteins: Soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins, including syntaxin, synaptobrevin (VAMP), and SNAP-25, play a central role in mediating membrane fusion.

o    Complex Formation: SNARE proteins from the vesicle membrane (v-SNAREs) and the target membrane (t-SNAREs) form a stable SNARE complex, bringing the vesicle close to the plasma membrane for fusion.

2.     Synaptotagmin Interaction with Calcium:

o    Calcium Sensor: Synaptotagmin, a calcium-binding protein located on the vesicle membrane, senses the increase in intracellular calcium levels upon neuronal depolarization.

o Calcium Binding: Calcium binding to synaptotagmin triggers conformational changes that promote the interaction between the vesicle and the plasma membrane, facilitating membrane fusion.

3.     Complexin Regulation:

o  Complexin Binding: Complexin is a protein that binds to the SNARE complex and regulates the timing of membrane fusion by preventing premature fusion and ensuring synchronized release of neurotransmitters.

o    Fusion Promotion: Complexin interacts with the SNARE complex to facilitate the final steps of membrane fusion, leading to the release of neurotransmitters into the synaptic cleft.

4.    Munc18-1 and Munc13 Interaction:

o    Munc18-1: Munc18-1 is a protein that interacts with syntaxin and regulates SNARE complex assembly and vesicle fusion.

o Munc13: Munc13 is involved in priming vesicles for fusion by promoting the transition of vesicles to a fusion-ready state through interactions with SNARE proteins and other regulatory factors.

5.     Rab Proteins and Membrane Trafficking:

o    Rab GTPases: Rab proteins regulate vesicle trafficking, docking, and fusion by coordinating membrane dynamics and vesicle transport to specific subcellular locations.

o Membrane Fusion Regulation: Rab GTPases interact with tethering factors, SNARE proteins, and other regulatory molecules to orchestrate the fusion of secretory vesicles with the target membrane.

Understanding the intricate molecular interactions underlying secretory vesicle fusion is essential for elucidating the mechanisms of neurotransmitter release at synapses and synaptic communication. Dysregulation of these interactions can lead to synaptic dysfunction and neurological disorders characterized by impaired neurotransmission. Studying the dynamics of these interactions provides valuable insights into the fundamental processes governing synaptic function and offers potential targets for therapeutic interventions aimed at restoring proper synaptic vesicle fusion and neurotransmitter release in the brain.

 

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