Unavoidability and Functionality of Nervous System and Behavioral Randomness

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article titled "Unavoidability and Functionality of Nervous System and Behavioral Randomness" examines the role of inherent randomness in the nervous system's operations and its implications for behavior. It argues that the stochastic behavior of ionic channels and synaptic transmissions is functionally significant, enhancing the adaptability and flexibility of neural and behavioral responses. The study combines theoretical models and empirical data to assert that randomness is not merely noise but a foundational aspect of how the nervous system functions and adapts. This work contributes valuable insights into the complex dynamics of brain and behavior relationships. Here are some of my comments to further augment the quality of this article:

1.    The article heavily relies on theoretical models to draw conclusions about biological processes. There is a potential issue with how well these models are validated against empirical data. If the models are not adequately calibrated or validated with sufficient experimental data, the conclusions might not accurately reflect real biological phenomena.

2.  The premise that all neural variability can be attributed to randomness may overlook other deterministic or chaotic processes that could contribute to neural behavior. The differentiation between stochastic randomness and deterministic chaos is complex and not always clear-cut, which might lead to oversimplification in the interpretation of neural phenomena.

3.  The statistical methods used to analyze randomness and variability in neural processes need rigorous scrutiny. The use of certain distributions e.g., Gaussian, Poisson and their fit to the data should be critically evaluated, as the inappropriate use of these distributions could lead to incorrect conclusions about the underlying neural dynamics.

4.  The article may simplify the complexity of neurobiological systems by focusing predominantly on randomness. Neurobiological systems are influenced by a myriad of factors including genetic, environmental, and developmental aspects that interact in complex ways. By focusing mainly on randomness, other critical factors influencing neural behavior might be underrepresented.

5.  The generalizability of the findings across different types of neurons, synaptic configurations, and animal models may be limited. The behavior of ionic channels and their stochastic properties could vary significantly between different biological contexts, which may not have been fully accounted for in the study.

Author Response

This article titled "Unavoidability and Functionality of Nervous System and Behavioral Randomness" examines the role of inherent randomness in the nervous system's operations and its implications for behavior. It argues that the stochastic behavior of ionic channels and synaptic transmissions is functionally significant, enhancing the adaptability and flexibility of neural and behavioral responses. The study combines theoretical models and empirical data to assert that randomness is not merely noise but a foundational aspect of how the nervous system functions and adapts. This work contributes valuable insights into the complex dynamics of brain and behavior relationships. Here are some of my comments to further augment the quality of this article:

Thanks for your suggestions:

 

1. The article heavily relies on theoretical models to draw conclusions about biological processes. There is a potential issue with how well these models are validated against empirical data. If the models are not adequately calibrated or validated with sufficient experimental data, the conclusions might not accurately reflect real biological phenomena.

We agree with the reviewer, and by this reason we have included 4 different studies from our own group and quite a substantial number of references on the topic with theoretical and empirical results.

2. The premise that all neural variability can be attributed to randomness may overlook other deterministic or chaotic processes that could contribute to neural behavior. The differentiation between stochastic randomness and deterministic chaos is complex and not always clear-cut, which might lead to oversimplification in the interpretation of neural phenomena.

 

This is absolutely true and there is not clear cut to differentiate both of them. Please notice the comment included in the Ms. acknowledging this point:

 

For perception of ambiguous figures (in blue the new text):

“Lehky [26] also showed that the time series presented no autocorrelations and that this time series were not explained by a chaotic system. The demonstration of not being a chaotic system was based in correlation dimensions and in nonlinear forecasting of the time series, giving ground for a random process to govern the transitions of perceptual states.”

 

And in the discussion section:

 

The possible random behavior for ambiguous figures perceptual changes over chaotic deterministic dynamics has been previously explored [26], and for the ocular tremor and the psychometric function the compelling argument that the constituents of the model are random processes (inter-spike modelling and open and closing of ionic channels, respectively) suggest a random basis for these organismic phenomena. But of course, it does not discard other alternative models based in deterministic chaotic dynamics. For the case of IRT probability density functions have been fitted to the data and, no time dependence in the data time series has been found. Although these results suggest random behavior more compelling evidence, as this suggested by Lehky [26], would be needed.

 

 

 

3. The statistical methods used to analyze randomness and variability in neural processes need rigorous scrutiny. The use of certain distributions e.g., Gaussian, Poisson and their fit to the data should be critically evaluated, as the inappropriate use of these distributions could lead to incorrect conclusions about the underlying neural dynamics.

 

This comment is included in the discussion section for acknowledging the reviewer comment:

 

“With respect to probability density functions of the different variables presented in this review:  the perception of ambiguous figures [12] , IRTs [10 and 11] and, abducens nerve spike count [7] were all tested by chi squared and Kolmogorov-Smirnov test. However, for the simulation of the psychometric function [13] only and approximate graphical method was applied.”

 

4. The article may simplify the complexity of neurobiological systems by focusing predominantly on randomness. Neurobiological systems are influenced by a myriad of factors including genetic, environmental, and developmental aspects that interact in complex ways. By focusing mainly on randomness, other critical factors influencing neural behavior might be underrepresented.

 

Please see response to point 5.

 

5. The generalizability of the findings across different types of neurons, synaptic configurations, and animal models may be limited. The behavior of ionic channels and their stochastic properties could vary significantly between different biological contexts, which may not have been fully accounted for in the study.

 

This is absolutely true, and we are not dismissing the huge number of factors influencing the variability of behavior, but we are highlighting an aspect may be not so well represented in the literature, as it is neural noise.

 

Now in the discussion section:

 

“The phenotypical variability in life is huge for the organization levels presented in this review, but also in any other order of complexity level of life. We have tried only to highlight the influence of neural noise based in biophysical concepts on behavioral variability. Future studies should delimitate the relative importance of each of the factors influencing behavioral freedom of degrees in similar sensory contexts.”

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

You will find the report in the attached file.

Comments for author File: Comments.pdf

Author Response

Reviewer 2.

 

Report on the paper: \Unavoidability and functionality of nervous system and behavioral randomness" by C. M. Gomez, E. I. Rodriguez-Martínez & M.A. Altahona-Medina. In this article the authors discuss about the random nature of the physiological processes followed by the neurons and then taken to different levels, suggesting that the possible random variability at the microscopic level (modeled by geometric, Poisson and exponential distributions) are conserved

at the organismic level. That leads to the idea of the `unavoidable' random activity of the organisms at the behavioral level. The idea is very interesting but unfortunately it is neither new nor very surprising. Actually the article reviews many papers in which this topic is somehow studied, making it look more as a review than as a regular article. This is actually not a

disadvantage but it is the non-clear way in which it is written.

 

Yes, in fact this is a review paper, of four topics previously worked by the authors (please see the references 6,7,10,11,12,13) related to neural and behavioral noise, and now reviewed and put it in context, including more recent literature on this subject

 

I have found the paper well justified and it fits the scope of the journal. Also, the addressed question is interesting. The goal is explicitly stated as: to demonstrate that there are traces of random processes at the organismic level", however the study somehow stays at a speculation level, except possibly for the last case of the psychometric function in which the authors

analyze the random nature at different levels.

 

In our review following the recommendations of the reviewers we have tried to be more precise and acknowledge the limitation of the Ms. that we would like to indicate that it is a review paper from previous work of the authors.

 

I would like to suggest some modifications and clarifications, for instance, in the IRT Section, what would be the random nature detected at the organismic level that corresponds or that is “produced" by the fact that the IRT follow a Poisson distribution? Is has been even fitted a Poisson distributions for the IRT frequency distribution? I see the reference of Johnson & Kotz but it is not clearly explained in the paper.

 

Yes, the IRT follows a Poisson distribution, we forgot to cite our work demonstrating the fitting, Now cited (Gómez, C., Ruiz-Adán, A., Llosa, M. et al. Quantitative Analysis of IRT Variability During the First Training Stages of a Variable-Interval Schedule in Rats. Psychol Rec 42, 1992, 273–284. doi.org/10.1007/BF03399601). Now:

 

“Both distributions fitted the IRT values, although the Poisson distribution did it in a significant manner in a higher percentage of cases than gamma distribution (90% and 60% of cases, respectively) [10].”

 

There is of course a relationship between the responses of the animal and the schedule of reinforcement. For instance, in variable intervals schedules of 120 seconds, the animal is responding very frequently (mean of IRTs around 120s, see the reference above) but the computer randomly select the exact timing at which the unique response in the 120s would be reinforced. There is no in the literature any comment about which is the exact distribution of interreinforcemnt intervals, a different and much more sparse variable than the IRTs.

 

I  find that the Ocular Tremor Section is not self contained. It refers to the previous works of the authors, but there are no further details that might be useful to clearly understand what is going on.

 

As the objective of the review manuscript is to demonstrate that neural noise can influence behavior at the organismic level, we liked to demonstrate based in our previous work that ocular tremor is a physiological process  due to the random neural series of spike count in the abducens and oculomotor nerve, whose random behavior is produced by the randomness in the behavior of motoneurons, this has been clarified now in the paragraph:

 

“The purpose of this study [7] was to demonstrate that the statistical properties of the neural activity of the extraocular muscles was the cause of this movement, after filtering neural activity through the ocular mechanics. Taking in account the possible stochastic nature of the behavior of abducens motoneurons [6], and the fact that the statistical properties of the spikes count of abducens nerve [7] would then be also a random process due to the central limit theorem. The latter would imply a random behavior for the ocular tremor movement, a movement which is caused by the activity of extraocular muscles.”

 

 

In that section I have found confusing parts, for instance, the (eq. 4) it is said to be a second order differential equation model for the ocular mechanics, but then, from where does the random part come in? What does f stands for? (page 4 line 162).

 

In the original work of Robinson [24]  

 

Rm= 100 + 4 E + 0.95 E’ + 0.015 E’’

 

Where  Rm denotes the neural activity, and E the eye position. and E’ and E’’ first and second time derivatives of eye position.

 

 The problem to be solved in the equation above is the inverse to that presented in our previous work (Ref. 7, Gómez C, Quero JM, Escudero M. Computer simulation of the neural discharge carried by the abducens nerve during eye fixation in the cat. Int J Biomed Comput. 24(3). 1989, 207-15. doi: 10.1016/0020-7101(89)90031-7). Robinson approach was to predict the activity of motoneurons (Rm) from the eye position, velocity and acceleration recordings. Here we tried to predict the eye position from the simulated random global activity of the abducens nerve taking in account the random  behavior of motoneurons. We have changed f(t) by R(t) to eliminate confusion with other equations.

 

 

 

In general I find the explanations of the formulae (all along the paper) a bit confusing. For example, in (eq. 6), here there is another f(t) (different from (eq. 4)?) that is introduced as a frequency and as a duration time in the same line (page 6, line 214).

 

As indicated above, by changing the definition of the abducens nerve activity to RM, the term f(t) is reserved to the number of cases (frequency of cases) in which the perception duration is equal to t.

 

“Then, the frequency of cases in which a certain percept lasts a certain duration (f(t)): Duration Time) obtains a particular value between time 0 and time t is:

 

f (t) = (1-p)^(t-1) * p *N   (eq.6)

This equation implies that the frequency of cases in which a perception time obtains a particular value (f(t)), depends on how many times it wins the competition on a time scale between t = 1 and t. Equation 6 corresponds to the geometric probability density function (Fig. 5A) multiplied by the number of individual perceptions (N).”

 

 

 

 

 In that same equation p is a probability, that later is considered to be as a function of time and whose rule of evolution in given by (eq. 7), but it depends on p, so, it is a differential equation, thus (eq. 8) has a different meaning than (eq. 6). Here, there are no absolute values of probability p, but rates of change of that probability p’(t), so a further and clear explanation is needed.

 

Most of the possible confusion comes by our awkward selection of the term p’(t), while we only want to express that p changes with time, therefore we have suppressed the symbol prime (‘) which suggest the derivative of p.

 

We want to express that absolute probability is changing with time due to physiological processes as habituation, then p is in fact p(t), but is considered an absolute value, certainly we could consider the absolute value of p (function of time) as  p(t)=p(t)+∆p(t),   but given that we have an specific hypothesis derived from our previous work ([12] Gómez C, Argandoña ED, Solier RG, Angulo JC, Vázquez M. Timing and competition in networks representing ambiguous figures. Brain Cogn, 2. 1995, 103-14. doi: 10.1006/brcg.1995.1270.). We think the expression of equation 6 (now without the prime) define precisely p(t)

 

Please notice that we have changed all the expressions including p’(t) to p(t).

 

 

As I already mentioned, the section about Psychometric Function is, in my opinion, the clearest one, in which one can clearly identify the purpose of exhibit the random nature of the process at different levels. It would be improved if the authors consider the actual fits of the curves, and so they may propose a probabilistic model, that is, a geometrical model and the gaussian model for the distribution of the number of open channels, and so on.

 

The model is qualitatively suggested in the discussion, as a succession of Gaussian and then imposing a threshold, a geometric distribution, that by the central limit theorem becomes another Gaussian at a higher level of complexity. But physiology is very complex, and physiological details should be work out, then at this point we prefer to suggest the model in more qualitative terms, and acknowledging the complexity of biological systems:

 

“In present report, the notion of alternation across-levels of Gaussian distributions (microscopic voltage distributions ion-mediated, intracellular voltages mediated by ionic channels, global activity in macroscopic structures as the abducens nerve), geometric (and exponential distributions) mediated by a threshold to be overcome (ionic channels opening, spike firing, perception and responses), would be a functional characteristic in the transition from the microscopic to the macroscopic in the nervous system.”

 

 

 

There is one extra concern, and that is about the true nature of the random behavior, does it really comes from a physiological behavior or it is just simply caused by noise or perturbations? I think is the first case, but it should be mentioned and somehow justified in the paper. Also, one can have (as mentioned in page 6, line 196) that the time series present no autocorrelation (or low autocorrelation) but still be produced by some dynamical system or process that is chaotic, and thus, it may have some random-like behavior, this issue really needs to be addressed by the authors in all four cases of study.

 

With respect to the possible influence of neural noise:

 

Our guess is that the main source is in the thermal noise around ionic channels although other sources cannot be discarded. From the very beginning in the introduction section:

 

“. Opening and closing of these channels are considered as probabilistic random processes and are modelled by an exponential probability distribution [1]. Open dwelling times follow a simple exponential model, but to model closed channel interval a sum of many exponential functions is needed. The quantal nature of synaptic vesicles liberation is another source of neural activity variability [2,3]. The stochastic activity of ionic channels would be an intrinsic source of randomness in the nervous system, but also the random structure of stimulation would be another source of variability, i.e. in the case of light perception, the quantal nature of photon emission.”

Now in the discussion section and in order to acknowledge other possible sources of random influences::

 

“The phenotypical variability in life is huge for the organization levels presented in this review, but also in any other order of complexity level of life. We have tried only to highlight the influence of neural noise based in biophysical concepts on behavioral variability. Future studies should delimitate the relative importance of each of the factors influencing behavioral freedom of degrees in similar sensory contexts.”

With respect to the possible presence of chaotic dynamical systems:

For perception of ambiguous figures:

 

“Lehky [26] also showed that the time series presented no autocorrelations and that this time series were not explained by a chaotic system. The demonstration of not being a chaotic system was based in correlation dimensions and in nonlinear forecasting of the time series,  giving ground for a random process to govern the transitions of perceptual states.”

 

And in the discussion section:

 

The possible random behavior for ambiguous figures perceptual changes over chaotic deterministic dynamics has been previously explored [26], and for the ocular tremor and the psychometric function the compelling argument that the constituents of the model are random processes (inter-spike modelling and open and closing of ionic channels, respectively) suggest a random basis for these organismic phenomena. But of course, it does not discard other alternative models based in deterministic chaotic dynamics. For the case of IRT probability density functions have been fitted to the data and, no time dependence in the data time series has been found. Although these results suggest random behavior more compelling evidence, as this suggested by Lehky [26], would be needed.

 

In conclusion, I find the paper interesting and it contributes to the area of study by providing further directions of research. However, regarding my previous concerns, I cannot recommend the paper in its present version, to be considered for publication. Nevertheless, I strongly suggest a major

revision, emphasizing in the new contributions or insights, clarifying the confusing parts of the paper and justifying the theoretical claims as well as to make the paper more self-contained.

Finally, one minor detail, reference [14] is repeated (see ref. [46]).

Reference [46] has been eliminated.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have thoroughly satisfied all my concerns. I endorse the article for acceptance in its present form.

Best of luck to the authors.

Reviewer 2 Report

Comments and Suggestions for Authors

I think the comments and corrections made by the authors complied with my suggestions, although they can still improved the paper, I find this version suitable for publication. They also have answered to all comments in a satisfactory way.