Connectome-Based Attractor Dynamics Underlie Brain Activity in Rest, Task, and Disease

Reviewer #1 (Public Review):

Summary:

Englert et al. proposed a functional connectome-based Hopfield artificial neural network (fcHNN) architecture to reveal attractor states and activity flows across various conditions, including resting state, task-evoked, and pathological conditions. The fcHNN can reconstruct characteristics of resting-state and task-evoked brain activities. Additionally, the fcHNN demonstrates differences in attractor states between individuals with autism and typically developing individuals.

Strengths:

(1) The study used seven datasets, which somewhat ensures robust replication and validation of generalization across various conditions.

(2) The proposed fcHNN improves upon existing activity flow models by mimicking artificial neural networks, thereby enhancing the representational ability of the model. This advancement enables the model to more accurately reconstruct the dynamic characteristics of brain activity.

(3) The fcHNN projection offers an interesting visualization, allowing researchers to observe attractor states and activity flow patterns directly.

Weaknesses:

(1) The fcHNN projection can offer low-dimensional dynamic visualizations, but its interpretability is limited, making it difficult to make strong claims based on these projections. The interpretability should be enhanced in the results and discussion.

(2) The presentation of results is not clear enough, including figures, wording, and statistical analysis, which contributes to the overall difficulty in understanding the manuscript. This lack of clarity in presenting key findings can obscure the insights that the study aims to convey, making it challenging for readers to fully grasp the implications and significance of the research.

Reviewer #2 (Public Review):

Summary:

Englert et al. use a novel modelling approach called functional connectome-based Hopfield Neural Networks (fcHNN) to describe spontaneous and task-evoked brain activity and the alterations in brain disorders. Given its novelty, the authors first validate the model parameters (the temperature and noise) with empirical resting-state function data and against null models. Through the optimisation of the temperature parameter, they first show that the optimal number of attractor states is four before fixing the optimal noise that best reflects the empirical data, through stochastic relaxation. Then, they demonstrate how these fcHNN-generated dynamics predict task-based functional activity relating to pain and self-regulation. To do so, they characterise the different brain states (here as different conditions of the experimental pain paradigm) in terms of the distribution of the data on the fcHNN projections and flow analysis. Lastly, a similar analysis was performed on a population with autism condition. Through Hopfield modeling, this work proposes a comprehensive framework that links various types of functional activity under a unified interpretation with high predictive validity.

Strengths:

The phenomenological nature of the Hopfield model and its validation across multiple datasets presents a comprehensive and intuitive framework for the analysis of functional activity. The results presented in this work further motivate the study of phenomenological models as an adequate mechanistic characterisation of large-scale brain activity.

Following up on Cole et al. 2016, the authors put forward a hypothesis that many of the changes to the brain activity, here, in terms of task-evoked and clinical data, can be inferred from the resting-state brain data alone. This brings together neatly the idea of different facets of brain activity emerging from a common space of functional (ghost) attractors.

The use of the null models motivates the benefit of non-linear dynamics in the context of phenomenological models when assessing the similarity to the real empirical data.

Weaknesses:

While the use of the Hopfield model is neat and very well presented, it still begs the question of why to use the functional connectome (as derived by activity flow analysis from Cole et al. 2016). Deriving the functional connectome on the resting-state data that are then used for the analysis reads as circular. If the fcHNN derives the basins of four attractors that reflect the first two principal components of functional connectivity, it perhaps suffices to use the empirically derived components alone and project the task and clinical data on it without the need for the fcHNN framework.

As presented here, the Hopfield model is excellent in its simplicity and power, and it seems suited to tackle the structure-function relationship with the power of going further to explain task-evoked and clinical data. The work could be strengthened if that was taken into consideration. As such the model would not suffer from circularity problems and it would be possible to claim its mechanistic properties. Furthermore, as mentioned above, in the current setup, the connectivity matrix is based on statistical properties of functional activity amongst regions, and as such it is difficult to talk about a certain mechanism. This contention has for example been addressed in the Cole et al. 2016 paper with the use of a biophysical model linking structure and function, thus strengthening the mechanistic claim of the work.

Author Response:

We would like to thank the reviewers for their constructive feedback and for acknowledging that our approach offers a simple yet powerful framework with the potential to serve as a comprehensive and intuitive tool for analyzing functional activity and connectivity.

In response to the reviewers’ recommendations, we will aim to improve and clarify the following aspects of our work in an upcoming revision:

Scope and limitations of the “fcHNN projection” (R#1 and R#2):

Both reviewers have correctly noted that the interpretability and explanatory power of the simplistic, two-dimensional fcHNN-based projection is limited. In the revised manuscript, we will clarify that, indeed, attractors are in a close mathematical relationship with the principal components of the raw data (i.e., the eigenvectors of the connectome) within our framework. The fcHNN-projection was introduced solely to establish a link between the proposed framework and concepts with which the reader may be more familiar.

We will enhance the presentation and discussion of our results to emphasize that – as the reviewers also kindly pointed out - the value of our approach lies in modelling how different facets of brain activity dynamically emerge from a common space of functional (ghost) attractors, rather than studying in the static attractor patterns themselves.

Motivations and Rationale for Using the Functional Connectome (R#2):

We agree with Reviewer #2 that a deeper mechanistic explanatory power could be achieved by modeling structure-function coupling, and that our framework is well-suited for this challenge. In our revision, we will highlight this as one of the promising future applications of our framework. We will, furthermore, clarify that the scope of the present work was deliberately restricted to functional connectivity to demonstrate that our framework also allows us to “bypass” the significant challenge of structure-function coupling. This enables us to focus on understanding the origins of canonical resting-state networks, the dynamic responses of the system to perturbations and the complex relationship between task-induced activity and resting-state connectivity, without first solving the structure-function coupling problem.

Additionally, we will mathematically justify the use of linear measures of the functional connectome to reconstruct the underlying non-linear dynamic system, thereby clearly delineating which results can and cannot be considered circular when starting from the functional connectome.

Improvements in Overall Clarity of Presentation (R#1):

In line with the above points and in general, we will strive to enhance the overall clarity of the presentation of our results, including figures, wording, and statistical analysis.