Advancing functional connectivity research from association to causation

Cognition and behavior emerge from brain network interactions, such that investigating causal interactions should be central to the study of brain function. Approaches that characterize statistical associations among neural time series-functional connectivity (FC) methods-are likely a good starting point for estimating brain network interactions. Yet only a subset of FC methods ('effective connectivity') is explicitly designed to infer causal interactions from statistical associations. Here we incorporate best practices from diverse areas of FC research to illustrate how FC methods can be refined to improve inferences about neural mechanisms, with properties of causal neural interactions as a common ontology to facilitate cumulative progress across FC approaches. We further demonstrate how the most common FC measures (correlation and coherence) reduce the set of likely causal models, facilitating causal inferences despite major limitations. Alternative FC measures are suggested to immediately start improving causal inferences beyond these common FC measures

Causal connectivity of evolved neural networks during behavior

To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics

Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems

Impact of environmental inputs on reverse-engineering approach to network structures

Background: Uncovering complex network structures from a biological system is one of the main topic in system biology. The network structures can be inferred by the dynamical Bayesian network or Granger causality, but neither techniques have seriously taken into account the impact of environmental inputs. Results: With considerations of natural rhythmic dynamics of biological data, we propose a system biology approach to reveal the impact of environmental inputs on network structures. We first represent the environmental inputs by a harmonic oscillator and combine them with Granger causality to identify environmental inputs and then uncover the causal network structures. We also generalize it to multiple harmonic oscillators to represent various exogenous influences. This system approach is extensively tested with toy models and successfully applied to a real biological network of microarray data of the flowering genes of the model plant Arabidopsis Thaliana. The aim is to identify those genes that are directly affected by the presence of the sunlight and uncover the interactive network structures associating with flowering metabolism. Conclusion: We demonstrate that environmental inputs are crucial for correctly inferring network structures. Harmonic causal method is proved to be a powerful technique to detect environment inputs and uncover network structures, especially when the biological data exhibit periodic oscillations

Prediction and Topological Models in Neuroscience

In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that topological predictions can and do guide interventions in science, both inside and outside of neuroscience. Topological models allow researchers to predict many phenomena, including diseases, treatment outcomes, aging, and cognition, among others. Moreover, we argue that these predictions also offer strategies for useful interventions. Topology-based predictions play this role regardless of whether they do or can receive a mechanistic interpretation. We conclude by making a case for philosophers to focus on prediction in neuroscience in addition to explanation alone

Challenges in identifying and interpreting organizational modules in morphology

Form is a rich concept that agglutinates information about the proportions and topological arrangement of body parts. Modularity is readily measurable in both features, the variation of proportions (variational modules) and the organization of topology (organizational modules). The study of variational modularity and of organizational modularity faces similar challenges regarding the identification of meaningful modules and the validation of generative processes; however, most studies in morphology focus solely on variational modularity, while organizational modularity is much less understood. A possible cause for this bias is the successful development in the last twenty years of morphometrics, and specially geometric morphometrics, to study patters of variation. This contrasts with the lack of a similar mathematical framework to deal with patterns of organization. Recently, a new mathematical framework has been proposed to study the organization of gross anatomy using tools from Network Theory, so‐called Anatomical Network Analysis (AnNA). In this essay, I explore the potential use of this new framework—and the challenges it faces in identifying and validating biologically meaningful modules in morphological systems—by providing working examples of a complete analysis of modularity of the human skull and upper limb. Finally, I suggest further directions of research that may bridge the gap between variational and organizational modularity studies, and discuss how alternative modeling strategies of morphological systems using networks can benefit from each other

Beyond element-wise interactions: identifying complex interactions in biological processes

Background: Biological processes typically involve the interactions of a number of elements (genes, cells) acting on each others. Such processes are often modelled as networks whose nodes are the elements in question and edges pairwise relations between them (transcription, inhibition). But more often than not, elements actually work cooperatively or competitively to achieve a task. Or an element can act on the interaction between two others, as in the case of an enzyme controlling a reaction rate. We call “complex” these types of interaction and propose ways to identify them from time-series observations. Methodology: We use Granger Causality, a measure of the interaction between two signals, to characterize the influence of an enzyme on a reaction rate. We extend its traditional formulation to the case of multi-dimensional signals in order to capture group interactions, and not only element interactions. Our method is extensively tested on simulated data and applied to three biological datasets: microarray data of the Saccharomyces cerevisiae yeast, local field potential recordings of two brain areas and a metabolic reaction. Conclusions: Our results demonstrate that complex Granger causality can reveal new types of relation between signals and is particularly suited to biological data. Our approach raises some fundamental issues of the systems biology approach since finding all complex causalities (interactions) is an NP hard problem