Milinkovic Borjan, Barnett Lionel, Carter Olivia, Seth Anil K, Andrillon Thomas
Melbourne School of Psychological Sciences, University of Melbourne, Melbourne, Australia.
Sussex Centre for Consciousness Science, University of Sussex, Brighton, United Kingdom.
PLoS Comput Biol. 2025 May 12;21(5):e1012572. doi: 10.1371/journal.pcbi.1012572. eCollection 2025 May.
Complex neural systems can display structured emergent dynamics. Capturing this structure remains a significant scientific challenge. Using information theory, we apply Dynamical Independence (DI) to uncover the emergent dynamical structure in a minimal 5-node biophysical neural model, shaped by the interplay of two key aspects of brain organisation: integration and segregation. In our study, functional integration within the biophysical neural model is modulated by a global coupling parameter, while functional segregation is influenced by adding dynamical noise, which counteracts global coupling. Leveraging transfer entropy, DI defines a dimensionally-reduced macroscopic variable (e.g., a coarse-graining) as emergent to the extent that it behaves as an independent dynamical process, distinct from the micro-level dynamics. Dynamical dependence (a departure from dynamical independence) is measured by minimising the transfer entropy from microlevel variables to macroscopic variables across spatial scales. Our results indicate that the degree of emergence of macroscopic variables is relatively minimised at balanced points of integration and segregation and maximised at the extremes. Additionally, our method identifies to which degree the macroscopic dynamics are localised across microlevel nodes, thereby elucidating the emergent dynamical structure through the relationship between microscopic and macroscopic processes. We find that deviation from a balanced point between integration and segregation results in a less localised, more distributed emergent dynamical structure as identified by DI. This finding suggests that a balance of functional integration and segregation is associated with lower levels of emergence (higher dynamical dependence), which may be crucial for sustaining coherent, localised emergent macroscopic dynamical structures. This work also provides a complete computational implementation for the identification of emergent neural dynamics that could be applied both in silico and in vivo.
复杂的神经系统能够展现出结构化的涌现动力学。捕捉这种结构仍然是一项重大的科学挑战。我们运用信息论，通过动态独立性（DI）来揭示一个最小的5节点生物物理神经模型中的涌现动力学结构，该模型由大脑组织的两个关键方面的相互作用塑造而成：整合与分离。在我们的研究中，生物物理神经模型中的功能整合由一个全局耦合参数调节，而功能分离则受到添加动态噪声的影响，动态噪声会抵消全局耦合。利用转移熵，DI定义了一个维度降低的宏观变量（例如，一种粗粒化），只要它表现为一个独立的动态过程，与微观层面的动力学不同，就认为它是涌现的。动态依赖性（偏离动态独立性）通过最小化跨空间尺度从微观层面变量到宏观变量的转移熵来衡量。我们的结果表明，宏观变量的涌现程度在整合与分离的平衡点相对最小，而在极端情况下最大。此外，我们的方法确定了宏观动力学在微观层面节点上的局部化程度，从而通过微观和宏观过程之间的关系阐明涌现动力学结构。我们发现，与DI所确定的情况一样，偏离整合与分离之间的平衡点会导致涌现动力学结构的局部化程度降低，分布更广。这一发现表明，功能整合与分离的平衡与较低的涌现水平（较高的动态依赖性）相关，这对于维持连贯的、局部化的涌现宏观动力学结构可能至关重要。这项工作还为识别涌现神经动力学提供了一个完整的计算实现方法，该方法可应用于计算机模拟和体内研究。
