Delayed mutual information infers patterns of synaptic connectivity in a proprioceptive neural network

Probing Asymmetric Interactions with Time-Separated Mutual Information: A Case Study Using Golden Shiners

Leader-follower modalities and other asymmetric interactions that drive the collective motion of organisms are often quantified using information theory metrics like transfer or causation entropy. These metrics are difficult to accurately evaluate without a much larger number of data than is typically available from a time series of animal trajectories collected in the field or from experiments. In this paper, we use a generalized leader-follower model to argue that the time-separated mutual information between two organism positions can serve as an alternative metric for capturing asymmetric correlations that is much less data intensive and more accurately estimated by popular k-nearest neighbor algorithms than transfer entropy. Our model predicts a local maximum of this mutual information at a time separation value corresponding to the fundamental reaction timescale of the follower organism. We confirm this prediction by analyzing time series trajectories recorded for a pair of golden shiner fish circling an annular tank.

The processing of proprioceptive signals in distributed networks: insights from insect motor control

The integration of sensory information is required to maintain body posture and to generate robust yet flexible locomotion through unpredictable environments. To anticipate required adaptations in limb posture and enable compensation of sudden perturbations, an animal's nervous system assembles external (exteroception) and internal (proprioception) cues. Coherent neuronal representations of the proprioceptive context of the body and the appendages arise from the concerted action of multiple sense organs monitoring body kinetics and kinematics. This multimodal proprioceptive information, together with exteroceptive signals and brain-derived descending motor commands, converges onto premotor networks - i.e. the local neuronal circuitry controlling motor output and movements - within the ventral nerve cord (VNC), the insect equivalent of the vertebrate spinal cord. This Review summarizes existing knowledge and recent advances in understanding how local premotor networks in the VNC use convergent information to generate contextually appropriate activity, focusing on the example of posture control. We compare the role and advantages of distributed sensory processing over dedicated neuronal pathways, and the challenges of multimodal integration in distributed networks. We discuss how the gain of distributed networks may be tuned to enable the behavioral repertoire of these systems, and argue that insect premotor networks might compensate for their limited neuronal population size by, in comparison to vertebrate networks, relying more heavily on the specificity of their connections. At a time in which connectomics and physiological recording techniques enable anatomical and functional circuit dissection at an unprecedented resolution, insect motor systems offer unique opportunities to identify the mechanisms underlying multimodal integration for flexible motor control.

Data-Driven Network Dynamical Model of Rat Brains During Acute Ictogenesis

Epilepsy is one of the most common neurological disorders worldwide. Recent findings suggest that the brain is a complex system composed of a network of neurons, and seizure is considered an emergent property resulting from its interactions. Based on this perspective, network physiology has emerged as a promising approach to explore how brain areas coordinate, synchronize and integrate their dynamics, both under perfect health and critical illness conditions. Therefore, the objective of this paper is to present an application of (Dynamic) Bayesian Networks (DBN) to model Local Field Potentials (LFP) data on rats induced to epileptic seizures based on the number of arcs found using threshold analytics. Results showed that DBN analysis captured the dynamic nature of brain connectivity across ictogenesis and a significant correlation with neurobiology derived from pioneering studies employing techniques of pharmacological manipulation, lesion, and modern optogenetics. The arcs evaluated under the proposed approach achieved consistent results based on previous literature, in addition to demonstrating robustness regarding functional connectivity analysis. Moreover, it provided fascinating and novel insights, such as discontinuity between forelimb clonus and generalized tonic-clonic seizure (GTCS) dynamics. Thus, DBN coupled with threshold analytics may be an excellent tool for investigating brain circuitry and their dynamical interplay, both in homeostasis and dysfunction conditions.

Non-linear multimodal integration in a distributed premotor network controls proprioceptive reflex gain in the insect leg

Producing context-appropriate motor acts requires integrating multiple sensory modalities. Presynaptic inhibition of proprioceptive afferent neurons^1-4 and afferents of different modalities targeting the same motor neurons (MNs)^5-7 underlies some of this integration. However, in most systems, an interneuronal network is interposed between sensory afferents and MNs. How these networks contribute to this integration, particularly at single-neuron resolution, is little understood. Context-specific integration of load and movement sensory inputs occurs in the stick insect locomotory system,^6,8-12 and both inputs feed into a network of premotor nonspiking interneurons (NSIs).⁸ We analyzed how load altered movement signal processing in the stick insect femur-tibia (FTi) joint control system by tracing the interaction of FTi movement^13-15 (femoral chordotonal organ [fCO]) and load^13,15,16 (tibial campaniform sensilla [CS]) signals through the NSI network to the slow extensor tibiae (SETi) MN, the extensor MN primarily active in non-walking animals.^17-19 On the afferent level, load reduced movement signal gain by presynaptic inhibition. In the NSI network, graded responses to movement and load inputs summed nonlinearly, increasing the gain of NSIs opposing movement-induced reflexes and thus decreasing the SETi and extensor tibiae muscle movement reflex responses. Gain modulation was movement-parameter specific and required presynaptic inhibition. These data suggest that gain changes in distributed premotor networks, specifically the relative weighting of antagonistic pathways, could be a general mechanism by which multiple sensory modalities are integrated to generate context-appropriate motor activity.

Identifying bidirectional total and non-linear information flow in functional corticomuscular coupling during a dorsiflexion task: a pilot study

Background

The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients.

Methods

We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients.

Results

The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14–30 Hz) had higher information flow in FCMC than the gamma band (31–45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group.

Conclusions

The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.

Parallelism Strategies for Big Data Delayed Transfer Entropy Evaluation

Generated and collected data have been rising with the popularization of technologies such as Internet of Things, social media, and smartphone, leading big data term creation. One class of big data hidden information is causality. Among the tools to infer causal relationships, there is Delay Transfer Entropy (DTE); however, it has a high demanding processing power. Many approaches were proposed to overcome DTE performance issues such as GPU and FPGA implementations. Our study compared different parallel strategies to calculate DTE from big data series using a heterogeneous Beowulf cluster. Task Parallelism was significantly faster in comparison to Data Parallelism. With big data trend in sight, these results may enable bigger datasets analysis or better statistical evidence.

Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems-it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

Ensemble stacking mitigates biases in inference of synaptic connectivity

A promising alternative to directly measuring the anatomical connections in a neuronal population is inferring the connections from the activity. We employ simulated spiking neuronal networks to compare and contrast commonly used inference methods that identify likely excitatory synaptic connections using statistical regularities in spike timing. We find that simple adjustments to standard algorithms improve inference accuracy: A signing procedure improves the power of unsigned mutual-information-based approaches and a correction that accounts for differences in mean and variance of background timing relationships, such as those expected to be induced by heterogeneous firing rates, increases the sensitivity of frequency-based methods. We also find that different inference methods reveal distinct subsets of the synaptic network and each method exhibits different biases in the accurate detection of reciprocity and local clustering. To correct for errors and biases specific to single inference algorithms, we combine methods into an ensemble. Ensemble predictions, generated as a linear combination of multiple inference algorithms, are more sensitive than the best individual measures alone, and are more faithful to ground-truth statistics of connectivity, mitigating biases specific to single inference methods. These weightings generalize across simulated datasets, emphasizing the potential for the broad utility of ensemble-based approaches.

Pre-processing and transfer entropy measures in motor neurons controlling limb movements

Directed information transfer measures are increasingly being employed in modeling neural system behavior due to their model-free approach, applicability to nonlinear and stochastic signals, and the potential to integrate repetitions of an experiment. Intracellular physiological recordings of graded synaptic potentials provide a number of additional challenges compared to spike signals due to non-stationary behaviour generated through extrinsic processes. We therefore propose a method to overcome this difficulty by using a preprocessing step based on Singular Spectrum Analysis (SSA) to remove nonlinear trends and discontinuities. We apply the method to intracellular recordings of synaptic responses of identified motor neurons evoked by stimulation of a proprioceptor that monitors limb position in leg of the desert locust. We then apply normalized delayed transfer entropy measures to neural responses evoked by displacements of the proprioceptor, the femoral chordotonal organ, that contains sensory neurones that monitor movements about the femoral-tibial joint. We then determine the consistency of responses within an individual recording of an identified motor neuron in a single animal, between repetitions of the same experiment in an identified motor neurons in the same animal and in repetitions of the same experiment from the same identified motor neuron in different animals. We found that delayed transfer entropy measures were consistent for a given identified neuron within and between animals and that they predict neural connectivity for the fast extensor tibiae motor neuron.

The characterization of hippocampal theta-driving neurons - a time-delayed mutual information approach

Interneurons are important for computation in the brain, in particular, in the information processing involving the generation of theta oscillations in the hippocampus. Yet the functional role of interneurons in the theta generation remains to be elucidated. Here we use time-delayed mutual information to investigate information flow related to a special class of interneurons—theta-driving neurons in the hippocampal CA1 region of the mouse—to characterize the interactions between theta-driving neurons and theta oscillations. For freely behaving mice, our results show that information flows from the activity of theta-driving neurons to the theta wave, and the firing activity of theta-driving neurons shares a substantial amount of information with the theta wave regardless of behavioral states. Via realistic simulations of a CA1 pyramidal neuron, we further demonstrate that theta-driving neurons possess the characteristics of the cholecystokinin-expressing basket cells (CCK-BC). Our results suggest that it is important to take into account the role of CCK-BC in the generation and information processing of theta oscillations.

Predictive control of intersegmental tarsal movements in an insect

In many animals intersegmental reflexes are important for postural and movement control but are still poorly undesrtood. Mathematical methods can be used to model the responses to stimulation, and thus go beyond a simple description of responses to specific inputs. Here we analyse an intersegmental reflex of the foot (tarsus) of the locust hind leg, which raises the tarsus when the tibia is flexed and depresses it when the tibia is extended. A novel method is described to measure and quantify the intersegmental responses of the tarsus to a stimulus to the femoro-tibial chordotonal organ. An Artificial Neural Network, the Time Delay Neural Network, was applied to understand the properties and dynamics of the reflex responses. The aim of this study was twofold: first to develop an accurate method to record and analyse the movement of an appendage and second, to apply methods to model the responses using Artificial Neural Networks. The results show that Artificial Neural Networks provide accurate predictions of tarsal movement when trained with an average reflex response to Gaussian White Noise stimulation compared to linear models. Furthermore, the Artificial Neural Network model can predict the individual responses of each animal and responses to others inputs such as a sinusoid. A detailed understanding of such a reflex response could be included in the design of orthoses or functional electrical stimulation treatments to improve walking in patients with neurological disorders as well as the bio/inspired design of robots.

Current Challenges Facing the Translation of Brain Computer Interfaces from Preclinical Trials to Use in Human Patients

Current research in brain computer interface (BCI) technology is advancing beyond preclinical studies, with trials beginning in human patients. To date, these trials have been carried out with several different types of recording interfaces. The success of these devices has varied widely, but different factors such as the level of invasiveness, timescale of recorded information, and ability to maintain stable functionality of the device over a long period of time all must be considered in addition to accuracy in decoding intent when assessing the most practical type of device moving forward. Here, we discuss various approaches to BCIs, distinguishing between devices focusing on control of operations extrinsic to the subject (e.g., prosthetic limbs, computer cursors) and those focusing on control of operations intrinsic to the brain (e.g., using stimulation or external feedback), including closed-loop or adaptive devices. In this discussion, we consider the current challenges facing the translation of various types of BCI technology to eventual human application.