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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 the Kinase Activity and Function of Cyclin-Dependent Kinase 5 In Postmitotic Neurons

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Dr. Rishabh Pathak

Cyclin-dependent kinase 5 (CDK5) is a crucial regulator of neuronal development, synaptic plasticity, and neuronal survival in postmitotic neurons. Here are some key points regarding the regulation of the kinase activity and function of CDK5 in postmitotic neurons:


1.      Regulation of CDK5 Activity:

o    Activators: CDK5 activity is dependent on its association with its regulatory subunits, p35 or p39. These activators bind to CDK5 and promote its kinase activity towards specific substrates involved in neuronal functions.

o Cyclin-Dependent Regulation: Unlike other CDKs that are regulated by cyclins, CDK5 is activated by p35 or p39, which do not exhibit cell cycle-dependent expression. This unique regulation allows CDK5 to function independently of the cell cycle in postmitotic neurons.

o    Phosphorylation: Phosphorylation of CDK5 at specific sites can modulate its activity and substrate specificity. Phosphorylation events mediated by upstream kinases can either activate or inhibit CDK5, fine-tuning its functions in neuronal processes.

2.     Function of CDK5 in Postmitotic Neurons:

o    Neuronal Migration and Differentiation: CDK5 plays a critical role in neuronal migration and differentiation during brain development. It regulates cytoskeletal dynamics, neuronal polarity, and axon guidance processes essential for proper neuronal circuit formation.

o    Synaptic Plasticity: CDK5 is involved in the regulation of synaptic plasticity, including long-term potentiation (LTP) and long-term depression (LTD). By phosphorylating synaptic proteins, CDK5 modulates neurotransmitter release, receptor trafficking, and dendritic spine morphology.

o Neuronal Survival: CDK5 promotes neuronal survival by regulating anti-apoptotic pathways and protecting neurons from stress-induced cell death. Dysregulation of CDK5 activity can lead to neuronal degeneration and contribute to neurodegenerative diseases.

3.     Implications in Neurological Disorders:

o Alzheimer's Disease: Aberrant activation of CDK5 has been implicated in the pathogenesis of Alzheimer's disease. Hyperphosphorylation of tau protein by CDK5 leads to the formation of neurofibrillary tangles, a hallmark of Alzheimer's pathology.

o    Parkinson's Disease: CDK5 dysregulation has also been linked to Parkinson's disease. In Parkinson's models, CDK5-mediated phosphorylation of specific substrates contributes to dopaminergic neuronal death and neuroinflammation.

o    Ischemic Stroke: CDK5 activity is altered in response to ischemic stroke, affecting neuronal survival and recovery. Modulating CDK5 function has shown potential therapeutic benefits in ischemic stroke models.

4.    Therapeutic Targeting of CDK5:

o  Drug Development: Targeting CDK5 activity has emerged as a potential therapeutic strategy for neurodegenerative disorders. Small molecule inhibitors and modulators of CDK5 activity are being explored for their neuroprotective effects in various neurological conditions.

o    Precision Medicine: Understanding the specific roles of CDK5 in different neurological disorders allows for precision medicine approaches tailored to target CDK5-related pathways in a disease-specific manner. Personalized treatments aimed at restoring CDK5 homeostasis could offer new avenues for disease management.

In summary, the regulation of CDK5 activity and function in postmitotic neurons is essential for neuronal development, synaptic plasticity, and neuronal survival. Dysregulation of CDK5 has implications in various neurological disorders, highlighting its potential as a therapeutic target for neuroprotection and disease intervention.

 

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