Modeling multistable neural representations of knowledge as DNA annealing- denaturing non-linear dynamics.

The objective of the proposed work is to characterize and explain the multistable patterns of discharge using the well-developed non-linear dynamical framework that I have used to explain DNA annealing-denaturing during my doctoral work. This theoretical framework will be used to identify critical variables that control the neural dynamics, such as the possibility that temperature in that case of DNA is analogous to either overall neural
network excitation or inhibition. We will use this framework to further characterize the abnormal coordination, what is called “discoordination” that has been observed in place cell ensemble recordings from mouse models of autism.

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1. Modeling multistable neural representations of knowledge as DNA annealing- denaturing non-linear dynamics. Vanitha Collaborator : Andr´ e A Fenton, Professor, New York University, USA Co-director, Neural Systems and behavior MBL, WoodHole, MA 15 April 2016
2. Topic of Research Nonlinear dynamics. Outline Objective Nonlinear Dynamics of DNA Neuronal network simulation Model Hypothesis Summary
3. Objective To understand the coordination and discoordination mechanisms that arises in neural networks Eg. Mouse models of autism Inappropriately coordinated neural electrical activity within and between neural networks - Cognitive deficit Failures of coordination → uncoupling of excitation and inhibition → (DNA annealing-denaturing process) Temperature in that case of DNA is analogous to either overall neural network excitation or inhibition Tune the parameter values of the inhibition for stable states in neural network
4. Nonlinear Dynamics of DNA Physics of life DNA : Polymer, double helix Nucleotide: Made up of bases,sugar,phosphate. Purines : Adenine(A), Guanine (G) Pyrimidines: Thymine (T), Cytosine (C) Origin of coded instructions in DNA
5. DNA Dynamics Dynamic entity DNA Dynamics Fluctuations related to biological functions Large amplitude fluctuations Motions of bases: Translation, Longitudinal, Rotation, Twist etc. Small amplitude motion : Phonons Large amplitude motion : Soliton
6. DNA Dynamics Sketch of the base pair opening(Nonlinear) Transcription, Translation and Replication. DNA unwinds / “unzips” when the hydrogen bonds break. Genetic information is copied into mRNA.
7. Objective of my Ph.D thesis Numerical Study Analytical Study Continuum Chain Infinite lattice Short DNA segment Biological Process : Transcription, Replication, Drug binding etc Kink−antikink, Pulse soliton / Bubble and their Perturbations Generalized sine−Gordon and Nonlinear Schrodinger Equation DNA Internal Nonlinear Dynamics
8. Daniel’s Model Analogy : Ferromagnet system with DNA n+1 n n−1 n+1 n n−1 z s s’
9. A horizontal projection of the nth base pair in the xy- plane strength of the hydrogen bonds depends on the distance b/w them Hydrogen bond energy φn n n n ’ O P P ’ Φ ’ Q n n Q’ x y (a) O P n n P’ Qn n Q’ z θn θ ’ n (b)
10. A Generalized model for DNA internal Dynamics Distance b/w the complementary bases : D2 n = 2 + 4r2 + (zn − z′ n )2 + 2(zn − z′ n )(cos θn − cos θ′ n ) +2[sin θn sin θ′ n cos(φn − φ′ n ) − cos θn cos θ′ n ] −4r[sin θn cos φn + sin θ′ n cos φ′ n ]. Quasi spin operator: Sx n = sin θn cos φn, Sy n = sin θn sin φn, Sz n = cos θn, S′x n = sin θ′ n cos φ′ n , S′y n = sin θ′ n sin φ′ n , S′z n = cos θ′ n , D2 n = 2 + 4r2 + 2[Sx n S′x n + Sy n S′y n − Sz n Sz ′n ] − 4r[Sx n + S′x n ].
11. Total Hamiltonian in terms of rotational angles, Plane-base rotator model (θn = θ′ n = π 2 ) H = n I 2 ( ∂φn ∂t )2 + I′ 2 ( ∂φ′ n ∂t )2 − {Jxy fn + ˆ α(yn+1 − yn )} sin θn sin θn+1 cos(φn+1 − φn ) − {J′ xy f ′ n + ˆ α′(y′ n+1 − y′ n )} sin θ′ n sin θ′ n+1 cos(φ′ n+1 − φ′ n ) − Jz fn cos θn cos θn+1 −J′ z f ′ n cos θ′ n cos θ′ n+1 + {Jcgn + ˆ β(yn+1 − yn )} sin θn sin θ′ n cos(φn − φ′ n ) + J′ c gn cos θn cos θ′ n +h{sin2 θn sin2 θn+1 sin2(φn+1 − φn ) + q2 0 } +h′{sin2 θ′ n sin2 θ′ n+1 sin2(φ′ n+1 − φ′ n ) + q2 0 } + p2 n 2M + p′ n 2 2M + K(yn+1 − yn )2 + K′(y′ n+1 − y′ n )2
12. Dynamical Equation Dynamical Equations I = I′ = I I ∂2φn ∂t2 = (Jfn + ˆ α(yn+1 − yn )) sin(φn+1 − φn ) − (Jfn−1 +ˆ α(yn − yn−1 )) sin(φn − φn−1 ) + (Jcgn + ˆ β(yn+1 − yn )) sin(φn − φ′ n ) − 2hq0 {cos(φn+1 − φn ) − cos(φn − φn−1 )} I ∂2φ′ n ∂t2 = (Jfn + ˆ α(y′ n+1 − y′ n )) sin(φ′ n+1 − φ′ n ) − (Jfn−1 +ˆ α(y′ n − y′ n−1 )) sin(φ′ n − φ′ n−1 ) + (Jcgn + ˆ β(yn+1 − yn )) sin(φ′ n − φn ) − 2hq0 {cos(φ′ n+1 − φ′ n ) − cos(φ′ n − φ′ n−1 )}
13. Dynamical Equation Continued... M ¨ yn = 2K(yn+1 − 2yn + yn−1 ) − ˆ α[cos(φn+1 − φn ) − cos(φn − φn−1 )] + ˆ β[cos(φn+1 − φ′ n+1 ) − cos(φn−1 − φ′ n−1 )] M ¨ y′ n = 2K(y′ n+1 − 2y′ n + y′ n−1 ) − ˆ α[cos(φ′ n+1 − φ′ n ) − cos(φ′ n − φ′ n−1 )] + ˆ β[cos(φn+1 − φ′ n+1 ) − cos(φn−1 − φ′ n−1 )]
14. Solution: Base pair opening in terms of soliton : Local opening
15. Model Coordination in mouse models of Autism Place avoidance task in a rotating arena by a rodent Two spatial frames of positions, one stationary the other rotating Place the electrode in the hippocampus of rats → Record the action potential discharge Discharge of place cell ensembles alternate between at least two stable patterns, one signalling the stationary the other signalling rotating positions More relevant spatial frame was likely to be actively represented in ensemble discharge
16. Place cell activity
17. Functional Model
18. Model Dynamical patterns of neuronal activity Same cells are coactive in either representation Activation of both the representations at the same time results in catastrophic information loss Two alternate patterns of discharge, the cylinder and the chamber patterns are formally equivalent to the annealed
19. Analogy : Complete separation of helical strands Winner take all competitive network neurons compete with each other for activation
20. Winner take all competitive network Continued... Triangles: Excitatory, circles : Inhibitory, Red(room coding) : Strong, Blue(arena) :Weak Either the coactive red or the coactive blue subpopulation is active, but not both excitatory subpopulations of neurons (triangles) represent two correspondingly different kinds of information Inhibition control the network activity when inhibition relaxes due to relative inactivity of inhibitory neurons, the system has the opportunity to denature and renature or reanneal into an new stable state.
21. Winner take all competitive network Continued... Very weak or strong or mistimed inhibition or excitation will cause imbalances (discoordination) between and/or within the subnetwork of neurons discoordination manifests as a pathophysiology responsible for cognitive dysfunction Question ? How to restore the coordination needed for improved cognition Central aim of this project : winner-take-all competitive-network conceptualization → DNA annealing - denaturing process
22. Winner take all competitive network Continued... Hydrogen bond interactions : wij tuned intrinsic excitation wij tuned intrinsic inhibition wij place tuned extrinsic excitation Stacking interactions Inhibition and the corresponding oscillatory activity (θ, γ) Write the Hamiltonian
23. Questions that we are asking in our theory Continued... Stacking and base pairing Above interactions forced us to consider all the interactions in the neuronal network and to categorize all Activation and firing rate of the cell, presynaptic activity within the network, oscillating inhibitory activity, Inhibition and external input How stable the neural activity is ? Does it give the realistic dynamics ?
24. Selected References Andrei V. Olypher, Daniel Klement, and Andr´ e A. Fenton, Cognitive Disorganization in Hippocampus: A Physiological Model of the Disorganization in Psychosis, The Journal of Neuroscience, (2006), 26(1), 158. Andr´ e A. Fenton, Excitation-Inhibition Discoordination in Rodent Models of Mental Disorders, Biological Psychiatry, 2015. M. Daniel and M. Vanitha, Bubble solitons in an inhomogeneous, helical DNA molecular chain with flexible strands. Physical Review E, Vol. 84, 031928 (2011) [21 pages]. Also appeared in Vir. J. Bio. Phys. Res. Vol. 22, Issue 7, 2011.
25. Summary and Outlook To understand the dynamics of coordinated neural activity using an established non-linear dynamical framework Foundation for a missing theoretical framework Focus : To alter the drive and strength between the excitatory or inhibitory connections in the network to explain the underlying dynamics To bring in the coordinated activity in the neuronal network from a concept from molecular biology