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Open AccessArticlePost Publication Peer ReviewVersion 2

Quantum Calcium-Ion Interactions with EEG (Version 2, Approved)

Lester Ingber Research, Ashland, OR, 97520, USA
Received: 13 November 2018 / Accepted: 27 November 2018 / Published: 21 March 2019
Peer review status: 2nd round review Read review reports

Reviewer 1 Amir Atiya Cairo University Reviewer 2 Logan T. Trujillo Department of Psychology, Texas State University
Version 1 Approved
Authors' response
Approved with revisions
Authors' response
Version 2 Approved
Version 2
Published: 21 March 2019
DOI: 10.3390/sci1010020
  |  
PDF [432 KB, uploaded 1 May 2019]
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Version 1
Published: 11 December 2018
DOI: 10.3390/sci1010007.v1
PDF [443 KB, uploaded 19 December 2018]

Abstract

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI. View Full-Text
Keywords: quantum mechanics; EEG; short term memory; astrocytes; neocortical dynamics; vector potential quantum mechanics; EEG; short term memory; astrocytes; neocortical dynamics; vector potential
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Review Reports

Reviewer 1

Sent on 16 Mar 2019 by Amir Atiya | Approved
Cairo University

Review of the Paper: "Quantum calcium-ion interactions with EEG", by Lester Ingber:

I suggest accepting the paper. It is a nice analysis of how statistical mechanics concepts are used
for analysis of neo-cortical interactions, the so-called SNMI. The author uses
the path integral algorithm to solve the complicated Lagrange equation. It is a method
that the author has developed for analysis of financial options, but is applicable here.
The quantum path integral is used for the analysis of Calcium channels. The author applies for
the optimization, and uses a supercomputer to solve the computational problem.
The paper is an interesting contribution, and improves our understanding on the
role of Calcium channels in the function of the brain, and how it manifests
itself on the EEG.
My suggestion is that the author expands a little in the Introduction section,
to add a paragraph to explain the role of Calcium ions in the functioning of the brain.

 

Response to Reviewer 1

Sent on 21 Jul 2019 by Lester Ingber

I have added a bit more detail in the Introduction on Ca waves in the brain, citing 2 important references from 2012 and 2019 that review this subject in more detail. I also have made some small changes as promised after the previous review, correcting the relationship between efficacy and impedance in Section 2.1 and emphasising the use of the Amplitude A to measure survival time in Section 5.4.1. I also have now used consistently named variables in Section 4.6.2.

Reviewer 2

Sent on 09 Feb 2019 by Logan T. Trujillo | Approved with revisions
Department of Psychology, Texas State University

Review for manuscript sci-01-00007-v3 “Quantum calcium-ion interactions with EEG” by L. Ingber.

            This manuscript reports a modeling study based on an existing theory of the statistical mechanics of neocortical interactions (SMNI) originally introduced by the author several decades ago. In this study, the theory is extended to include the quantum effects of calcium ions at tripartite neuron-glial-neuron synaptic junctions. The basic idea as I understand it is that waves of calcium ions couple with the electromagnetic vector potential of neural cells/cell columns to influence synchronous neural activity that is observed via electroencephalography (EEG). A model based in this extended theory is then used to fit empirical EEG data during a P300 attentional-modulation task. A couple of established analytical techniques were used in a novel way in order to accomplish this modeling, including adaptive simulated annealing (ASA) for global optimization and the use of N-dimensional path-integrals in the classical and quantum variables spaces of the model. The study found that the extended SMNI theory yielded improved fits to EEG data over the purely classical version of the theory, suggesting a potential role of calcium ion-mediated quantum effects in neocortical dynamics.

I found this study to be an extremely interesting extension of the SMNI theoretical approach to cortical dynamics, which I have been generally familiar with prior to this review from one of the author’s previous publications. Also, I think studies like this are important tests of the possibility for the role of quantum effects in the brain, which are highly controversial (as the author points out in the present manuscript) yet plausible in my opinion. Moreover, I think the novel application of the various analytical techniques used in the study is worthy of report in its own right, as this can then inform future uses of these techniques in neural modeling outside of the exploration of quantum brain effects.

That said, I do have several questions, comments, and concerns about the present study that, if addressed, could make the study’s overall conclusions and impact much stronger. These questions/comments/concerns are listed below:

 

p.2, Section 2. The description of the SMNI theory is fairly condensed, but one question I have that I could not find in this manuscript (or in the author’s previous papers describing the theory) is how one accounts for volume conduction of neuroelectric signals. It is well known that cortical signals are dispersed as they travel through the head to the scalp, a situation that may produce apparent statistical dependencies among EEG sensors. Yet it is not apparent to me how volume-conduction is accounted for in the SMNI theory when this theory is used to make predictions about macroscopic scalp-level EEG measurements. How does the SMNI model account for this, and if it does not, then how much can we trust the fitting results reported later in the manuscript (see Sections 2.6 and Section 5.3)? This is my main concern with the SMNI approach to modeling scalp-level EEG signals.

 

p.3, Section 2.1: The author writes “[Phi] is the “inter-neuronal” probability distribution, of thousands of quanta of neurotransmitters released at one neuron’s postsynaptic site effecting a (hyper-)polarization at another neuron’s presynaptic site, taking into account interactions with neuromodulators, etc.”  Are the words “postsynaptic” and “presynaptic” in reversed locations in this sentence? Neurotransmitters are released from presynaptic neurons and the resultant depolarization occurs for the postsynaptic neuron.

 

p.3, Section 2.1: The author writes “The efficacy is related to the inverse conductivity across synaptic gaps.” I am not sure how to interpret this statement because I would think that the greater the conductivity across a synaptic gap, the greater efficacy of that synaptic communication, yet this statement seems to suggest the opposite. Please clarify.

 

p. 4, Section 2.4. The author writes “Nearest-neighbor interactions among columns give dispersion relations that were used to calculate speeds of visual rotation”. What is meant by “speeds of visual rotation”, I could not find this phrase in the papers cited for this statement. Is the author referring to “mental rotation” of visual imagery?

 

p. 5, Section 2.6. The author writes “Using EEG data…SMNI was fit to highly synchronous waves (P300) during attentional tasks, for each of 12 subjects, it was possible to find 10 Training runs and 10 Testing runs”. I have two questions about this. First, typical P300 tasks involve a response to oddball stimuli (the P300) and also nonresponse trials (standard stimuli presented). I presume that only trials with the P300 were modeled here? What would the model predict for the other trials? Second, what do “training runs” and “testing runs” mean here? Is this referring to subject performance in the task or does it refer to training and testing the analytical model? If the latter, how long were each run in seconds or sample points? How many electrodes across the scalp were modeled? Were the runs concatenated or was the EEG data preprocessed or filtered? More detail needs to be given.

 

p. 6, Section 2.6. The author writes “This describes the “7 +/ 2” rule, as calculated by SMNI PATHINT in Figure 2”. The figure is interesting, assuming that each of the displayed firing patterns is equivalent to a "memory" pattern. However, Miller’s “magic number” of memory is just a limit and does not give any information about why more or less memory items will be held in memory for any given task or context. So what in this model accounts for such high-level memory selectional control (i.e. the actual items to be retained in memory for a given task or context)?

 

p. 7, Section 2.8.1 The author uses the conventional bold face “A” notation for the electromagnetic vector potential. However, this can be confusing given that the variable “A” is also use to represent synaptic efficacy in previous portions of the paper. I might suggest changing the latter notation to reduce confusion.

 

p. 8, Section 2.9. This section on Model of Models (MOM) provides an interesting discussion, but I am not sure why this is being broached here, as it is tangential to the main description of the SMNI approach. This would go better in the Discussion section of the manuscript.

 

p.12 Section 4.6.1 The author writes “Many real-world systems propagate in the presence of continual “shocks”. In SMNI, collisions occur via regenerative Ca2+ waves”. Can these shocks be used to model transient external stimulation of the brain?

 

p.13, Section 5. The author writes “Detailed calculations show that p of the Ca2+ wave packet and qA of the EEG field make about equal contributions to P”. Could the author provide a table reporting some of the results of this calculation?

 

p.14, Section 5.2. This section describing the supercomputer resources utilized by the study should go in the methods section of the paper, not the results.

 

p.14, Section 5.3. Again the author mentions “Training and Testing runs”. As I asked in an earlier question above, what are does training and testing mean in this context? It is unclear. Does one need to "train" the model first, like a neuronal network? What are the details of the training and testing procedure?

 

p.14, Section 5.3. The author used “effective action” as the cost function, with an explicit expression for this function. Yet the expression given is still unclear in terms of the practical steps needed to fit the empirical scalp-recorded data to signals modeled at the cortical level (see my earlier question above concerning how volume-conduction is modeled or accounted for in SMNI). Can the author describe more explicitly how the EEG measures enter into this cost function during the model fitting procedure? This is important for other modelers who may want to reproduce or extend the present findings, or apply these methods to other modeling problems.

 

p. 15, Section 5.4. The author is using the letter “A” now to represent yet another quantity, the survival time A(t). Again this can be confusing given that the variable “A” is also use to represent synaptic efficacy and the vector potential in previous portions of the paper.

 

p. 15, Section 5.4. The author found that the quantum-mechanical wave function of the wave packet “survived” overlaps after multiple collisions. Does this result have any relevance to the debate about if quantum-superposed states in the brain may also “survive” over long enough time periods to influence cognition or consciousness? Also, how might the present theory relate (if at all) to other quantum theories of the brain, such as Freeman’s theory that the brain’s information-processing capacity could be mediated, in part, by quantum fields in the brain’s ‘neuropil’ (e.g. Freeman & Vitiello, 2008. Journal of Physics A: Mathematical and Theoretical, 304042)?

 

p.16, Section 6.2. The discussion of Free Will is interesting, but cursory and can be extended a bit. In particular, a brief summary of the “Free Will Theorem” should be given so that the reader can properly evaluate the claim made in this section.

 


Response to Reviewer 2

Sent on 21 Jul 2019 by Lester Ingber

I appreciate the careful reading of this manuscript and the intent to improve it by this reviewer. I will address each of the queries below. p.2, Section 2. The description of the SMNI theory is fairly condensed, but one question I have that I could not find in this manuscript (or in the author’s previous papers describing the theory) is how one accounts for volume conduction of neuroelectric signals. It is well known that cortical signals are dispersed as they travel through the head to the scalp, a situation that may produce apparent statistical dependencies among EEG sensors. Yet it is not apparent to me how volume-conduction is accounted for in the SMNI theory when this theory is used to make predictions about macroscopic scalp-level EEG measurements. How does the SMNI model account for this, and if it does not, then how much can we trust the fitting results reported later in the manuscript (see Sections 2.6 and Section 5.3)? This is my main concern with the SMNI approach to modeling scalp-level EEG signals. Reply: In the fits to data, the model uses Spline-Laplacian development of the data prior to fitting. This is briefly mentioned in Section 2.6, and the reference following, [Ingber, J. Theor. Biol. 2016], is to a paper that gives more details on prior fits to the same data (without the explicit quantum calculations used here). That paper also give credit: "I thank Ramesh Srinivasan for giving me part of his Matlab code for spline-Laplacian scalp transformations." This is used by many (not all) researchers modeling EEG to take into account these effects of not being able to localize signals from the raw data. The Laplacian is a second derivative that essentially examines the difference of a point with respect to nearby neighboring points, effectively helping to localize the data. The Spline fits smooths out the data, since derivative operations on noisy data (like EEG) just about always introduces more noise. p.3, Section 2.1: The author writes “[Phi] is the “inter-neuronal” probability distribution, of thousands of quanta of neurotransmitters released at one neuron’s postsynaptic site effecting a (hyper-)polarization at another neuron’s presynaptic site, taking into account interactions with neuromodulators, etc.” Are the words “postsynaptic” and “presynaptic” in reversed locations in this sentence? Neurotransmitters are released from presynaptic neurons and the resultant depolarization occurs for the postsynaptic neuron. Reply: Yes, you are correct. This typo crept in while I was paraphrasing my previous papers to comply with plagiarism checks. p.3, Section 2.1: The author writes “The efficacy is related to the inverse conductivity across synaptic gaps.” I am not sure how to interpret this statement because I would think that the greater the conductivity across a synaptic gap, the greater efficacy of that synaptic communication, yet this statement seems to suggest the opposite. Please clarify. Reply: You are correct. Synaptic efficacy is a measure of ionic permeability, and an inverse measure of electrical impedance (as I reported in my first 1982-1983 SMNI papers). For a wire, impedance = electrical conductivity * length/area. The word "conductivity" will be replaced by "impedance". p. 4, Section 2.4. The author writes “Nearest-neighbor interactions among columns give dispersion relations that were used to calculate speeds of visual rotation”. What is meant by “speeds of visual rotation”, I could not find this phrase in the papers cited for this statement. Is the author referring to “mental rotation” of visual imagery? Reply: Yes, speed of '“mental rotation” of visual imagery' is intended. I have added the word "mental" in 3 places. This mental rotation has been experimentally linked to a diffusion-like process across neurons in minicolumns, and SMNI has calculated the speed of this diffusion process across columns. p. 5, Section 2.6. The author writes “Using EEG data…SMNI was fit to highly synchronous waves (P300) during attentional tasks, for each of 12 subjects, it was possible to find 10 Training runs and 10 Testing runs”. I have two questions about this. First, typical P300 tasks involve a response to oddball stimuli (the P300) and also nonresponse trials (standard stimuli presented). I presume that only trials with the P300 were modeled here? What would the model predict for the other trials? Second, what do “training runs” and “testing runs” mean here? Is this referring to subject performance in the task or does it refer to training and testing the analytical model? If the latter, how long were each run in seconds or sample points? How many electrodes across the scalp were modeled? Were the runs concatenated or was the EEG data preprocessed or filtered? More detail needs to be given. Reply: Yes, only trials with the P300 were modeled. I do not know what the results would be for for the nonreponse trials, but I presume from previous studies that there would not be any (large) signal to process by this SMNI model. Training versus Testing runs in this context refers only to a separation of data sets -- one set used to fit parameters in the SMNI model, and the other set (same subject) processed using the parameters from that fit. p. 6, Section 2.6. The author writes “This describes the “7 +/- 2” rule, as calculated by SMNI PATHINT in Figure 2”. The figure is interesting, assuming that each of the displayed firing patterns is equivalent to a "memory" pattern. However, Miller’s “magic number” of memory is just a limit and does not give any information about why more or less memory items will be held in memory for any given task or context. So what in this model accounts for such high-level memory selectional control (i.e. the actual items to be retained in memory for a given task or context)? Reply: The figure presents a nonlinear multi-peaked probability distribution. How that distribution is utilized by a subject (e.g., the number of peaks actually populated) is not measured by this fit. I assume that a more specific experimental paradigm would have to be invoked for that data to have a chance of being fit by SMNI. p. 7, Section 2.8.1 The author uses the conventional bold face “A” notation for the electromagnetic vector potential. However, this can be confusing given that the variable “A” is also use to represent synaptic efficacy in previous portions of the paper. I might suggest changing the latter notation to reduce confusion. Reply: The multiple usage of letters for various math symbols is unfortunate but necessary, as they are in common usage. Most often, (the number of) indices identifies a property, e.g., in Section 2.3, as is common that literature, drifts have 1 index, covariance matrix or its inverse metric have 2 indices, the determinant has no index. I have used $bold A$ to denote he magnetic vector potential (a 3-D vector) as is common in that literature, and italics-A 2 with indices for the synaptic efficacy as is commonly used by me and some other researchers. p. 8, Section 2.9. This section on Model of Models (MOM) provides an interesting discussion, but I am not sure why this is being broached here, as it is tangential to the main description of the SMNI approach. This would go better in the Discussion section of the manuscript. Reply: This section is placed at the end of Section 2, which introduces SMNI, because SMNI is still a model, not a completely verified "theory". This Section 2.9 puts this model into a context of its utility as a generic model that can be and has been applied to other disciplines. p.12 Section 4.6.1 The author writes “Many real-world systems propagate in the presence of continual “shocks”. In SMNI, collisions occur via regenerative Ca2+ waves”. Can these shocks be used to model transient external stimulation of the brain? Reply: In this context, I consider stimuli, especially the experimental stimuli giving tise to the EEG data, as "shocks". These comments are to demonstrate that "shocks" occur in many systems that are amenable to similar modeling paradigms. Yes, I do believe that such shocks, e.g., that cause nonlinear and/or time-dependent changes in the brain, can be properly modeled using these path-integral formulations. p.13, Section 5. The author writes “Detailed calculations show that p of the Ca2+ wave packet and qA of the EEG field make about equal contributions to P”. Could the author provide a table reporting some of the results of this calculation? Reply: These calculations have been presented in several papers since circa 2012. This is a straightforward numerical calculation, but involves more additional information that is properly referenced rather than repeated (e.g., involving experimental measurements of columnar dipoles). I have added a reference to a 2015 paper that gives that detail. p.14, Section 5.2. This section describing the supercomputer resources utilized by the study should go in the methods section of the paper, not the results. Reply: In this paper, I consider the methods to be the math-physics algorithms used. The very short subsection 5.2 that mentions the supercomputer resources is meant to simply convey the resources required for these calculations. p.14, Section 5.3. Again the author mentions “Training and Testing runs”. As I asked in an earlier question above, what are does training and testing mean in this context? It is unclear. Does one need to "train" the model first, like a neuronal network? What are the details of the training and testing procedure? Reply: As I replied above, Training versus Testing runs in this context refer only to a separation of data sets -- one set used to fit parameters in the SMNI model, and the other set (same subject) processed using the parameters from that fit. Yes, in this sense, this would be like fitting any other algorithm such as a neural network and then testing it on out-of-sample data. The terms "Training" and "Testing" are common in such literature. p.14, Section 5.3. The author used “effective action” as the cost function, with an explicit expression for this function. Yet the expression given is still unclear in terms of the practical steps needed to fit the empirical scalp-recorded data to signals modeled at the cortical level (see my earlier question above concerning how volume-conduction is modeled or accounted for in SMNI). Can the author describe more explicitly how the EEG measures enter into this cost function during the model fitting procedure? This is important for other modelers who may want to reproduce or extend the present findings, or apply these methods to other modeling problems. Reply: The effective action is defined in the text in the description of Table 1, appearing just before that Table: "Cost functions are the effective Action, A_eff , which is L DELTAt - log(prefactor), where the prefactor multiplier of the exponential arises from the normalization of the short-time conditional probability distribution and L DELTAt is the argument of the exponential factor." I have added to this: "Eq. (3) defines the Lagrangian $L$, and the normalization is defined in $DM$ in Eq. (11)." p. 15, Section 5.4. The author is using the letter “A” now to represent yet another quantity, the survival time A(t). Again this can be confusing given that the variable “A” is also use to represent synaptic efficacy and the vector potential in previous portions of the paper. Reply: As I stated above, the multiple usage of letters for various math symbols is unfortunate but necessary, as they are in common usage. Most often, (the number of) indices identifies a property, e.g., in Section 2.3, as is common that literature, drifts have 1 index, covariance matrix or its inverse metric have 2 indices, the determinant has no index. I have used $bold A$ to denote the magnetic vector potential (a 3-D vector) as is common in that literature, and italics-A 2 indices for the synaptic efficacy as is commonly used by me and some other researchers. The use of italics-A with no indices is another example of this. p. 15, Section 5.4. The author found that the quantum-mechanical wave function of the wave packet “survived” overlaps after multiple collisions. Does this result have any relevance to the debate about if quantum-superposed states in the brain may also “survive” over long enough time periods to influence cognition or consciousness? Also, how might the present theory relate (if at all) to other quantum theories of the brain, such as Freeman’s theory that the brain’s information-processing capacity could be mediated, in part, by quantum fields in the brain’s ‘neuropil’ (e.g. Freeman & Vitiello, 2008. Journal of Physics A: Mathematical and Theoretical, 304042)? Reply: Yes, the importance of calculating a survival time is important in any such context, here as well as in that paper, and in many other papers that calculations. p.16, Section 6.2. The discussion of Free Will is interesting, but cursory and can be extended a bit. In particular, a brief summary of the “Free Will Theorem” should be given so that the reader can properly evaluate the claim made in this section. Reply: I have added a few sentences explaining the possible relevance of quantum processing of information in the brain to the Free Will Theorem: "The essence of FWT is that, since quantum states cannot be cloned, a ${roman Ca} sup {2+}$ quantum wave-packet may not generate a state proven to have previously existed. As explained by the authors, experimenters have specific choices in selecting measurements, which are shared by (twinned) particles, including the choice of any random number generator that might be used to aid such choices. The authors maintain that their proof and description of quantum measurements used is general enough to rule out classical randomness, and that classical determinism cannot be supported by such processes as exist in the quantum world."

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