Dynamical Relation of Poisson Spike Trains In Hodkin-Huxley Neural Ion Current Model and Formation of Non-Canonical Bases, Islands, and G-quadruplexes in DNA, mRNA, and RNA at or near the Transcription.
“Thousands of diseases are produced by genetic defects in channels, including many diseases of profound importance, like cystic fibrosis, epilepsy, atrial and ventricular fibrillation, and so on, as documented in many papers …. among thousands of others. Many of these diseases are caused by problems in the construction of channels, or the insertion of channels in the wrong places in the wrong cells, or in the regulation and control of channels.” (Bob Eisenberg “Crowded Charges in Ion Channels”).
Keywords:Kolmogorov-Chentsov continuity theorem, Fokker-Plank stochastic differential equation, translation and transcription, neural networks.
Ground breaking application of mathematics and biochemistry to explain formation of non-canonical bases, islands, G-quadruplex structures, and analog bases in DNA and mRNA at or near the transcription with connection to neural networks is implemented using statistical and stochastic methods apparatus with the addition of quantum principles. As a result the usual transience of Poisson spike trains (PST) becomes very instrumental tool for finding periodical type of solutions to Fokker-Plank (FP) stochastic differential equation (SDE). The present study develops new multidimensional methods of finding solutions to SDE. This is based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem (KCCT) that allows the stochastic processes with jumps under certain conditions to have -Holder continuous modification, which is used as basis for finding analogous parallels in neural networks and dynamics of formation of CpG and non-CpG islands (CpGI or non CpGI), non-canonical bases, and structures involving G-quadruplexes during DNA transcription.
2. M. Fundator. Multidimensional Time Model for PDF. In JSM Proceedings . 4029-4039.
3. M. Fundator. Testing Statistical Hypothesis in Light of Mathematical of Probability Pre.
4. M. Fundator. Various Extensions of Original Born-Kramers-Slater Model for Reactions Kinetics Based on Brownian Motion and Fokker-Plank Equation Including 1D, 2D, 3D, and Multi-dimensional …J. Chem 11, 90-94
5. M. Fundator. Application of mass spectrometry to analysis of applications of Fokker-Plank equation to the velocity of chemical reactions Abstracts of papers of the ACS 256
6. M. Fundator. Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions Applied and Computational Mathematics 7 (3), 89-93
7. M. Fundator. Geometrical, Algebraic, Functional and Correlation Inequalities Applied in Support of James-Stein Estimator for Multidimensional Projections ACM
8. M. Fundator. Applications of multidimensional time model for PDF applied to Fokker-Planck equation and multi-scale time analysis to the rate of transcription ACS 255
9. M. Fundator. Applications of multidimensional time model for PDF applied to Brownian motion on fractals to solution of different questions of equilibrium, depolarizati ACS 255
10. M. Fundator. Applications of Multidimensional Time Model for PDF to Model Permeability of Plasma Membrane and Transcription of DNA for vaccination trails.
11. M. Fundator. Applications of multidimensional time model for probability cumulative function to Brownian motion on fractals to kinetics of chemical reactions and ACS 254
12. M. Fundator Application Of Multidimensional Time Model For Probability Cumulative Function To Brownian motion on fractals in chemical reactions Academia Journal of Scientific Research (ISSN 2315-7712) DOI: 10.15413/ajsr.2016.0167
13. Michael Fundator Developments in Application of Multidimensional Time Model For Probability Cumulative Function to Brownian motion on fractals in chemical reactions Academia Journal of Scientific Research . In preparation for publication.
14. Michael Fundator Multidimensional Time Model for Probability Cumulative Function and Connections Between Deterministic Computations and Probabilities Journal of Mathematics and System Science 7 (2017) 101-109 doi: 10.17265/2159-5291/2017.04.001
15. Michael Fundator Applications of Multiple-scale Time Analysis and Different Pseudospectral Methods Along with MTM for CDF to Modeling, Estimation, Control, and Optimization of Large Scale Systems with Big Data SIAM Conferen on Control and Its Appl, Pittsburgh, Pennsylvania, July 10-12/17 in publication in Journal of Applied and Computational Mathematics.
16. Michael Fundator Novel application of Fokker- Planck equation to the rate of transcription or translation controlled by riboswitches following Kramers Model for the Rate of Chemical Reactions and recent applications to Hodgkin-Huxley ion channel model. 7th Cambridge Symposium on Nucleic Acids Chemistry and Biology, Cambridge, UK, September 3-6/17.
17. Michael Fundator Applications of Multidimensional Time Model for PDF to Model Permeability of Plasma Membrane and Transcription of Cytoplasmic DNA. 26th International Genetic Epidemiology Society (IGES) Annual Meeting September 09 – 11/ 17 at Queens College, Cambridge, UK.
18. Michael Shelley et al “An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex” PNAS May 18, 2004 101 (20) 7757-7762
19. Michel Loeve Probability Theory. Springer
20. Revuz, Yor Continious Martingales and Brownian Motion. Springer
21. Guiseppe Da Prato et al Stochastic Equations in Infinite Dimensions. Cambridge University Press
22. Richard Naud, et al Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press
23. A. N. Borodin, P. Salminen Handbook of Brownian Motion. Birkhuaser
24. Peter Morters et al Brownian Motion Cambridge University Press
25. E Platen et al Numerical Solutions Of Stochastic Differential Equations With Jumps in Finance Springer
26. Michael Fundator. Various types of quantum coherence in biological systems implies scale dependence of spatio-temporal coherance. American Chemical Society Northwest Regional Meeting Portland, Oregon June 16-19/2019
27. Hugh P. C. Robinson Stages of spike time variability during neuronal responses to transient inputs Phys. Rev. E 66, 061902 – Published 10 December 2002
28. A. V. Rangan, G. Kovačič, and David Cai Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train. March 2008 Physical Review E 77(4 Pt 1)
29. J. Whelan et al, Stress induced gene expression drives transient DNA methylation changes at adjacent repetitive elements.
30. Bird A.et al CpG islands and the regulation of transcription. Genes Dev. 2011;25(10):1010‐1022. doi:10.1101/gad.2037511
31. Romain Barres, Jie Yan, Brendan Egan, Jonas Thue Treebak, Morten Rasmussen, Tomas Fritz, Kenneth Caidahl, Anna Krook, Donal J. O’Gorman, and Juleen R. Zierath Acute Exercise Remodels Promoter Methylation in Human Skeletal Muscle.
32. J. S. Flier, et al, Adipose Tissue as an Endocrine Organ, The Journal of Clinical Endocrinology & Metabolism, Volume 89, Issue 6, 1 June 2004, Pages 2548–2556,
33. Kangaspeska, S., Stride, B., Metivier, R., Polycarpou-Schwarz, M., Ibberson, D., Carmouche, R. P., ... Reid, G. (2008). Transient cyclical methylation of promoter DNA.
34. N. F. Troje; Decomposing biological motion: A framework for analysis and synthesis of human gait patterns. Journal of Vision 2002;2(5):2
35. Fisher A., Halder R, et al. DNA methylation changes in plasticity genes accompany the formation and maintenance of memory. Nature Neuroscience. 2016 Jan;19(1):102-110.
36. Rutherford, Nicola J et al. “Length of normal alleles of C9ORF72 GGGGCC repeat do not influence disease phenotype.” Neurobiology of aging vol. 33,12 (2012).
37. Fay, Marta M et al. “RNA G-Quadruplexes in Biology: Principles and Molecular Mechanisms.” Journal of molecular biology vol. 429,14 (2017): 2127-2147.
38. Henderson, A. et al. “Detection of G-quadruplex DNA in mammalian cells.” Nucleic acids research vol. 42,2 (2014): 860-9.
39. Bochman, M. L et al. “DNA secondary structures: stability and function of G-quadruplex structures.” Nature reviews. Genetics vol. 13,11 (2012): 770-80.
40. Fundator M. Application of continuous modification of solutions of Fokker-Plank stochastic differential equations for flux rate to the Mathematics of Neural networks. #78 Biological Physics/Physics of Living Systems: A Decadal Survey
41. Fundator M. Various types of quantum coherence in biological systems implies scale dependence of spatio-temporal coherance. #79 Biological Physics/Physics of Living Systems: A Decadal Survey
42. Fundator M. Applications of Multidimensional Time Model for Probability Cumulative Function to model Biology, Chemical Dynamics, and Electrophysiology of Plasma Cell Membrane and for Topographic and Retinotopic Mapping. # 88White Paper for Biological Physics/Physics of Living Systems: A Decadal Survey
43. Fundator M. Applications of Multidimensional Time Model for PDF to Model Permeability of Plasma Membrane and Transcription of Cytoplasmic DNA. # 89 White Paper for Biophysics Decadal Survey
44. Fundator M. Applications of Multidimensional Time Model for Probability Cumulative Function to model simulations of single fiber vs. a bundle. #90 White Paper for Biophysics Decadal Survey