APPLICATION OF MULTIDIMENSIONAL TIME MODEL TO DYNAMICAL RELATION OF POISSON SPIKE TRAINS IN NEURAL ION CURRENT MODELS AND FORMATION OF NON-CANONICAL BASES, ISLANDS, AND G-QUADRUPLEXES IN DNA, MRNA, AND RNA AT OR NEAR THE TRANSCRIPTION

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INTRODUCTION
"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".) Recent numerous applications of FP SDE for flux rate to the to describe the mathematics of neural networks were introduced more than 60 years ago [21]. FitzHugh's consideration of stochasticity in neural networks was based on earlier works including Hodkin's article after Kramers introduced FP SDE to the theory of rate of chemical reactions. He used notions of equilibrium, energy barrier, and memory friction. Focus on development of kinetic and dynamical theory for integrate and fire (I&F) neurons with application to simple (with inhibitory usually linear responses) and complex (characterized by strong cortical nonlinear and significant second harmonic responses excitation) cells (determined by balance between cortico-cortical input and lateral geniculate nucleus (LGN)) in visual cortex provided qualitative intuition for dynamic phenomena related to transitions to bistability and hysteresis, where system jumps back and forth between the two branches of stable states for different, critical values of some control parameter that can result in optical binding.

FOKKER-PLANK STOCHASTIC DIFFERENTIAL EQUATIONS FOR FLUX RATE
Large part of neural networks analysis consists of a study of reduction of infinite models to finite models that include different types of bifurcations. Bifurcations occurring in neural networks include double period bifurcations, Hopf bifurcations, saddle-node bifurcations, torus bifurcations, and homoclinic bifurcations. Thus, the analysis is related to numerous quantum theoretical assumptions.
For example in the visual cortex the kinetic equations for evolution of the probability density: to find a neuron at time t within the x th the coarse-grained (CG) patch that the cortex is tiled with and are sufficiently small for the cortical architecture not to change systematically across it, but are sufficiently large to contain many (hundreds) of neurons) with voltage (v, v+ dv) and conductance (g, g + dg) that in quantum theory could be considered probability current, involves writing of the FP SDE for the probability evolution process and flux rate equation: Where is the "leakage" time constant, is the time constant of the AMPA synapse (mediating transmission of electrical or chemical signal in Nervous System) , f is the synaptic strength from LGN connections, N is number of neurons, and S is the cortico-cortical coupling strength.
is the flux along ν, v 0(t) is the (temporally modulated) rate for the Poisson spike train from the LGN Is the population-averaged firing rate per neuron in the CG patch, determined by the J-flux at the threshold to firing with normalized, dimensionless potentials related to original Hodkin-Huxley model V T = 1, V R = 0, and V E = constant.
The evolution processes are certainly the stochastic processes with jumps [28], e.g. transitions between metastates and to bistability and hysteresis, Poisson spike train etc…, and only application of Kolmogorov-Chentsov continuity theorem [20,21,23,24] assures the existence of � sample continuous modification of stochastic processes with the same probability law: under the conditions of existence of the constants , , C for some metrics d; { ( , ) } ≤ C |t-s| 1+ for all 0 ≤ , ≤ T; (6) and the modified process � would be -Holder continuous for every 0 < < . The importance of Kolmogorov's continuity criterion for the whole theory of Brownian Motion Stochastic Calculus including stochastic differentiation and integration and Stochastic Differential Equations is emphasized in [20], where the authors used this criterion for the constriction of Brownian motion.
The Poisson spike train that was mentioned in the relation to initial conditions in Equations (3) and (4)  This could be explained by the argument of [22]. Simulation of the Hodgkin-Huxley model depending on the different steps increase in current produces outcomes such as: 1) Damped oscillation, 2) A single spike that is followed by a transient spike, and 3) Sustained firing.
Consideration of the case (2) can be applied to find solutions to many other examples of SDE with or without jumps. Because the spike is transient the following theorem for the multidimensional Brownian motion (BM) can be applied [20,24] 3. TRANSIENCE Theorem1. BM is Point recurrent in dimension d=1. For reference and discussion look [19]. Neighborhood recurrent, but not point recurrent in d=2. Transient in d ≥ 3. Proposition2. The continuous modification of the solution of FP SDE is a function of BM. Proposition3. The continuous modification of the solution of FP SDE is transient if BM is the multidimensional BM.

RULES FOR FINDING CONTINUOUS SOLUTIONS TO FOKKER-PLANK SDE [36-40].
Rule1. If there is a transient condition the solution should be sought in form of function of multidimensional BM.
Rule2. Jump processes are associated with Poisson processes [25]. If Poisson spike train is supposed to be terminated, then Rule1 should be applied. Otherwise, time interval could be divided into smaller intervals that would lead to m-dimensional time parameter t = (t1… tm) and modification of Kolmogorov's continuity criterion [23 p3]: { ( , ) } ≤ Ck |t-s| + for all 0 ≤ , ≤ T; (9) such that si, ti ≤ k, i = 1,…,m. Rule3. Many solutions of Hodkin-Huxley model look like periodical with period T. Then the solution is sought in form of product of sums of trigonometric functions with period T and Brownian bridge (BB) over time interval [0, T] from x to y. BB is a Gaussian process that can be described as [23]: ; Or dBt = − − dt + dWt ; 0 ≤ ≤ T, and B0 = x (11). It can be observed that this process is a solution to the above SDE and another remarkable property of BB is that it can be well approximated by simple combinations of multidimensional BMs.
In the above example (1)-(4) the application of FP SDE to neural networks implements reduction of dimensions to (1+1)D from originally used 3D or (2+1)D in neural networks [17] due to involvement of Poisson spike trains. Most, perhaps all CpGIs are usually related to the sites of transcription initiation, including thousands that are remote from currently annotated promoters [30].

DNA TRANSLATION AND TRANSCRIPTION AND HYPOTHESES 1 AND 2 [26, 36-40].
The addition of methyl groups to DNA is called DNA methylation, whereas deletion is called demethylation. Both processes are studied in cancer research and other genetic related diseases.
To understand the necessity of application of quantum type principles to proteins and further facilitate the discussion of what kind of principles should be applied, it would be appropriate to mention the following questions and problems in investigation of proteins, DNA, and RNA structures [26].
In contrast to RNA, DNA has a double helix structure under Watson-Crick base pairs model that identifies standard base pairs (e.g. A-T, G-C). Non-canonical base pairs contribute to disruption of double helix in DNA.
In the beginning of investigation it was supposed that the approach to structure or sequence of bases or other properties should be probabilistic or statistical because all the alternatives seemed to be equally possible. This led to some distribution assumptions about 70 years ago which were followed by careful experimental investigations until different authors became convinced that the sequences of the bases do not follow any known probability distribution function, even in the fragments of DNA. This resulted in additional investigation and served as guide to researchers until there were found two additional analog bases: 5 methylC (the fifth base analog) and 5 hydroxymethylC (the sixth base). However, the belief that the structure would be described by some Probabilistic or Statistical Mechanics Principals was still very disorienting. This situation caused some additional questions that were finally resolved with finding two more analog bases: 5-formylcytosine and 5 carboxylcytosine which are actually versions of cytosine that have been modified by Tet proteins, molecular entities that are thought to play a role in the DNA demethylation and stem cell reprogramming.
Much in contrast the dynamical approach makes the situation quite different, and certain quantum principles that were applied by Kramers during introduction of FP SDE to the theory of rate of chemical reactions suggest similar application of FP SDE to the rate of translation and transcription of different fragments of DNA and RNA. This in its turn would suggest that the formation of islands and informal pairs of bases, analog bases, or G-quadruplexes is a result of some multidimensional stochastic process involving a continuous modification of solutions of FP SDE to the rate of translation and transcription. Similarity in application of FP SDE to the rate of translation and transcription in DNA and to neural ions model with many other different facts from these theories implies that formation of islands and informal pairs of bases in DNA depends on spike trains and the like phenomena: 1) The process of transcription involves translation from certain parts of DNA that is double stranded to mRNA, where the fragments are modified and are bind to a small RNA. As a result, mRNAs bind metabolites with untranslated regions (UTR) of RNA, and then the modified parts are copied back to DNA. These parts and stages of translation and transcription and translation naturally serve as memory friction or viscosity in the formation of Fokker-Plank equation. There are also additional steps that make the process sufficiently complicated to consider application of stochastic analysis. However, as mentioned previously such considerations are insufficient, but 2) There are certain constraints in the transcription process that make it highly similar to the corresponding subject of the velocity of chemical reactions in the sense that the translation has to go through some kind of a barrier, as in the case of the particle that has to go over potential barrier. To make a partial list: • The steps accounting for primary transcription involve consist from multiple molecular interactions followed by the transcription of DNA. • Depending on cellular activity transcripts from DNA contribute to different RNA translations into functional proteins. • Sequences of DNA in their turn control initiation of RNA primary transcription.
The a. and b. constraints correspond to probability of escape barrier for the particle for reaction activation in the theory of the rate of chemical reactions, c. corresponds to the notion of equilibrium, besides that these constrains also contribute to the corresponding notion of memory friction that is included in operators For n-dimensional process ̇ based on multidimensional BM linear FP SDE as in above (7) [4][5][6][7][8][9][10][11][12][13][14][15][16][17] ∂p( ̇,t) ∂t For example, in 1D velocity of Brownian particle ̇ = (x,v) moving in U(x) potential is given by Langevin equation: Where x, v, and m are the position, velocity, and a mass of the particle and ( ) is noise, and is a coefficient of viscosity or memory friction. The Langevin equation after substitution into probability conservation equation would be written in form of FP SDE: Hypothesis 1 that can be viewed as explanation of Main Propositions 1, 2, and 3. The information transmitted by transient spike train is stored in the inside or surrounding human body systems and contributes to the memory friction coefficient in the process of transcription and translation, and the rate of transcription and translation can be described by multidimensional Fokker-Plank equation, based on multidimensional BM (Wt) ≥0 . This in its turn implies Hypothesis 2 The number of dimensions that are involved in formation of Fokker-Plank equations in ion channels model and in the processes of transcription and translation of DNA and RNA can be considered equal.

FACTS AND EXAMPLES SUPPORTING MAIN PROPOSITIONS1, 2, 3 AND HYPOTHESES 3 AND 4.
Most, perhaps all CGIs are usually related to the sites of transcription initiation, including thousands that are remote from currently annotated promoters [29]. This fact in combination with Main Propositions 1, 2, and 3, Notion 1 and Hypothesis 1 imply Hypothesis 3 The intensity of distribution of CpGIs around transcription initiation can be distributed according to some probability distribution, and, if found to follow some stochastic law, could help in further investigations.
DNA methylation in many instances is transient [29,32,33]. Recent studies suggest high impact of DNA methylation on memory [35]. DNA methylation depends on stress [29]. Contrary to the expected that the connectivity of organs would require biochemical similarity (see adipose tissue [32] in #4 in Applications of Main Propositions 1, 2, and 3), only some of the total possibility of genes are expressed in any given tissue. For example, a protein that is active in a nerve cell is not expressed in the liver. [33] The most profound examples to support the theory of CpG and GpC islands and non regular bases formation due to additional dimensions involvement in transcription and translation processes is the discrepancy of DNA methylation levels in twin children or astronauts under changing environmental conditions in questions if the changes are transient or long-lived.
Multidimensional approach to skeletal muscles and biological motion that contains information about actions, intentions, and emotions [34], and their effect through exercise on methylation process.
• Patients with amyotrophic lateral sclerosis or frontotemporal dementia develop from 500 to few thousands G4C2 repeats in contrast to a normal person that usually has below 8 G4C2s. As in the 1. • G4s tend to occur near end 3'. • Hypothesis 4. Ions that are found inside G4 structure imply ion currents which are hardly detectable, but depend as in Hypothesis 1 on different factors including the memory and the information transmitted by transient spike trains and was stored in the inside or surrounding human body systems and later contribute to the process of transcription and translation.

APPLICATIONS OF MAIN PROPOSITIONS 1, 2, AND 3 HYPOTHESES 1, 2, 3 AND 4
Theoretical approach based on multidimensionality of Brownian motion in formation of Fokker-Plank equations for ion channels model and rate of transcription and translation of DNA and RNA allows multiple applications: 1) During first stages of genetic diseases.
2) In palliative care and opens a new approach of computational study during palliative care.
3) DNA methylation can carry effective predictive functions, as in the different types of diabetes due to complex correlation of DNA methylation and insulin gene expression. 4) Provides access to multiple discoveries in the direction of tissue analysis. 5) Analysis of the above 3 applications suggests that the information from the transient spikes is stored in electro-magnetical or bioossilations contributing to atrial fibrillation and similar diseases and acts only after long period of time depending on different factors. For example adipose tissue is essential in regulating whole body energy metabolism and besides adipocytes, adipose tissue contains connective tissue matrix, nerve tissue, stromovascular cells, and immune cells, and under some conditions it contributes to suppression of genes transcription [31].

CONCLUSION
Translation and transcription of DNA and RNA through transience, hidden dimensional consideration, memory friction, and other factors can be highly connected to neural networks and this connection can be mathematically modeled.

SOURCES OF FUNDING
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

CONFLICT OF INTEREST
The author have declared that no competing interests exist.

ACKNOWLEDGMENT
The author is grateful to Yehuda Goldgur from Sloan Kettering Cancer Center for the initial review and very valuable suggestions about this article.