Causal connectivity measures for pulse-output network reconstruction: Analysis and applications.

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

Single-Atom Alloys Materials for CO2 and CH4 Catalytic Conversion.

The catalytic conversion of greenhouse gases CH4 and CO2 constitutes an effective approach for alleviating the greenhouse effect and generating valuable chemical products. However, the intricate molecular characteristics characterized by high symmetry and bond energies, coupled with the complexity of associated reactions, pose challenges for conventional catalysts to attain high activity, product selectivity, and enduring stability. Single-atom alloys (SAAs) materials, distinguished by their tunable composition and unique electronic structures, confer versatile physicochemical properties and modulable functionalities. In recent years, SAAs materials demonstrate pronounced advantages and expansive prospects in catalytic conversion of CH4 and CO2. This review begins by introducing the challenges entailed in catalytic conversion of CH4 and CO2 and the advantages offered by SAAs. Subsequently, the intricacies of synthesis strategies employed for SAAs are presented and characterization techniques and methodologies are introduced. The subsequent section furnishes a meticulous and inclusive overview of research endeavors concerning SAAs in CO2 catalytic conversion, CH4 conversion, and synergy CH4 and CO2 conversion. The particular emphasis is directed toward scrutinizing the intricate mechanisms underlying the influence of SAAs on reaction activity and product selectivity. Finally, insights are presented on the development and future challenges of SAAs in CH4 and CO2 conversion reactions.

Nasal Tip Cutaneous Metastasis of Hepatocellular Carcinoma: A Case Report.

Background: Cutaneous metastasis is rare in clinical practice, especially that from primary hepatocellular carcinoma (HCC), which is even rarer. Case Presentation: This report describes a male patient with HCC with cutaneous metastases to the nasal tip. The patient developed a raised nodule at the nasal tip 5 years after surgery for HCC, with surface ulceration and crusting and no obvious symptoms. Abdominal computed tomography (CT) showed an obvious mass in the liver. The skin lesions on the nasal tip were confirmed to be cutaneous metastasis of HCC by histopathological and immunohistochemical examinations. Conclusion: The incidence of cutaneous metastasis of HCC is extremely low, and nasal tip cutaneous metastasis of HCC has no specific clinical manifestations; therefore, it needs to be distinguished from rosacea rhinophyma, fungal and atypical mycobacterial infections, tumours of vascular origin, and tumours of skin appendages that occur in the nasal tip and is prone to misdiagnosis and missed diagnosis, thus requiring clinical dermatologists and otolaryngologists to be aware of such metastasis.

A striatal SOM-driven ChAT-iMSN loop generates beta oscillations and produces motor deficits.

Enhanced beta oscillations within the cortico-basal ganglia-thalamic (CBT) network are correlated with motor deficits in Parkinson's disease (PD), whose generation has been associated recently with amplified network dynamics in the striatum. However, how distinct striatal cell subtypes interact to orchestrate beta oscillations remains largely unknown. Here, we show that optogenetic suppression of dopaminergic control over the dorsal striatum (DS) elevates the power of local field potentials (LFPs) selectively at beta band (12-25 Hz), accompanied by impairments in locomotion. The amplified beta power originates from a striatal loop driven by somatostatin-expressing (SOM) interneurons and constituted by choline acetyltransferase (ChAT)-expressing interneurons and dopamine D2 receptor (D2R)-expressing medium spiny neurons (iMSNs). Moreover, closed-loop intervention selectively targeting striatal iMSNs or ChATs diminishes beta oscillations and restores motor function. Thus, we reveal a striatal microcircuit motif that underlies beta oscillation generation and accompanied motor deficits upon perturbation of dopaminergic control over the striatum.

Hierarchical timescales in the neocortex: Mathematical mechanism and biological insights.

A cardinal feature of the neocortex is the progressive increase of the spatial receptive fields along the cortical hierarchy. Recently, theoretical and experimental findings have shown that the temporal response windows also gradually enlarge, so that early sensory neural circuits operate on short timescales whereas higher-association areas are capable of integrating information over a long period of time. While an increased receptive field is accounted for by spatial summation of inputs from neurons in an upstream area, the emergence of timescale hierarchy cannot be readily explained, especially given the dense interareal cortical connectivity known in the modern connectome. To uncover the required neurobiological properties, we carried out a rigorous analysis of an anatomically based large-scale cortex model of macaque monkeys. Using a perturbation method, we show that the segregation of disparate timescales is defined in terms of the localization of eigenvectors of the connectivity matrix, which depends on three circuit properties: 1) a macroscopic gradient of synaptic excitation, 2) distinct electrophysiological properties between excitatory and inhibitory neuronal populations, and 3) a detailed balance between long-range excitatory inputs and local inhibitory inputs for each area-to-area pathway. Our work thus provides a quantitative understanding of the mechanism underlying the emergence of timescale hierarchy in large-scale primate cortical networks.

Clinical efficacy and safety of electro-acupuncture combined with beraprost sodium and α-lipoic acid for diabetic peripheral neuropathy.

BACKGROUND: The pathogenic triggers of diabetic peripheral neuropathy (DPN) mainly include ischemia and hypoxic factors. The combined use of Chinese and Western medicine may be a new perspective for the treatment of DPN. Accordingly, this study explores the clinical efficacy and safety of electro-acupuncture (EA) combined with beraprost sodium (BPS) and α-lipoic acid (α-LA) in the treatment of patients with DPN. METHODS: A total of 184 patients with DPN meeting the inclusion criteria were enrolled and divided into electric-acupuncture group (n=54), medication group (n=62) and combination group (n=68), which were treated by EA, BPS+α-LA, and EA+BPS+α-LA, respectively. The three groups were compared with respect to the following factors: clinical efficacy; motor conduction velocities (MCVs) of nervus medianus, nervus peroneus communis and tibial nerve and sensory conduction velocities (SCVs) of nervus medianus, sural nerve and ulnar nerve before and after treatment; the Toronto Clinical Scoring System (TCSS), total symptom score (TSS) and Michigan Diabetes Neuropathy Score (MDNS) before and after treatment; changes of serum homocysteine and cysteine (Cys) levels, oxidative stress indicators and inflammatory factors; incidence of adverse reactions. RESULTS: The overall response rate of the combination group was higher than that of the electric acupuncture group or the medication group. After treatment, the SCV of nervus medianus, sural nerve and ulnar nerve and the MCV of nervus medianus, nervus peroneus communis and tibial nerve were the highest in the combination group among the three groups (P<0.05). After treatment, the scores of TCSS, TSS and MDNS in the combination group was notably lower than those in the medication group and the electric acupuncture group (P<0.05). The amelioration of inflammatory factors in the combination group were the best among the three groups (P<0.05). The incidence of adverse reactions was lower in the combination group compared with the electric acupuncture group and the medication group (P<0.05). CONCLUSION: EA combined with BPS and α-LA is effective in the treatment of DPN, which can effectively reduce the levels of serum inflammatory factors in patients, with a lower complication rate and higher safety.

Maximum Entropy Principle Underlies Wiring Length Distribution in Brain Networks.

A brain network comprises a substantial amount of short-range connections with an admixture of long-range connections. The portion of long-range connections in brain networks is observed to be quantitatively dissimilar across species. It is hypothesized that the length of connections is constrained by the spatial embedding of brain networks, yet fundamental principles that underlie the wiring length distribution remain unclear. By quantifying the structural diversity of a brain network using Shannon's entropy, here we show that the wiring length distribution across multiple species-including Drosophila, mouse, macaque, human, and C. elegans-follows the maximum entropy principle (MAP) under the constraints of limited wiring material and the spatial locations of brain areas or neurons. In addition, by considering stochastic axonal growth, we propose a network formation process capable of reproducing wiring length distributions of the 5 species, thereby implementing MAP in a biologically plausible manner. We further develop a generative model incorporating MAP, and show that, for the 5 species, the generated network exhibits high similarity to the real network. Our work indicates that the brain connectivity evolves to be structurally diversified by maximizing entropy to support efficient interareal communication, providing a potential organizational principle of brain networks.

Further phenotypic features and two novel POC1A variants in a patient with SOFT syndrome: A case report.

Short stature, onychodysplasia, facial dysmorphism and hypotrichosis (SOFT) syndrome is a rare autosomal recessive disease caused by POC1 centriolar protein A (POC1A) pathogenic variants. However, knowledge of genotypic and phenotypic features of SOFT syndrome remain limited as few families have been examined; therefore, the clinical identification of SOFT syndrome remains a challenge. The aim of the present case report was to investigate the genetic cause of this syndrome in a patient with a short stature, unusual facial appearance, skeletal dysplasia and sparse body hair. Giemsa banding and exome sequencing were performed to investigate the genetic background of the family. Spiral computed tomography and magnetic resonance imaging were used for investigating further phenotypic features of the patient. Exome sequencing identified that POC1A had two compound heterozygous variants, namely c.850_851insG and c.593_605delGTGGGACGTGCAT, which, to the best of our knowledge, have not been reported elsewhere. Novel phenotypes were also identified as follows: i) Metaphyseal dysplasia was alleviated (and/or even disappeared) with age; ii) the density of the femoral neck was uneven and the hyperintensity signal of the metaphysis was stripe­like. Thus, the present case report expands the knowledge regarding phenotypic and genotypic features of SOFT syndrome.

Emergence of spatially periodic diffusive waves in small-world neuronal networks.

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

Dendritic computations captured by an effective point neuron model.

Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.

Determination of effective synaptic conductances using somatic voltage clamp.

The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance measurement and provides a reliable approach to assess synaptic influence on neuronal computation.

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.

Balanced Active Core in Heterogeneous Neuronal Networks.

It is hypothesized that cortical neuronal circuits operate in a global balanced state, i.e., the majority of neurons fire irregularly by receiving balanced inputs of excitation and inhibition. Meanwhile, it has been observed in experiments that sensory information is often sparsely encoded by only a small set of firing neurons, while neurons in the rest of the network are silent. The phenomenon of sparse coding challenges the hypothesis of a global balanced state in the brain. To reconcile this, here we address the issue of whether a balanced state can exist in a small number of firing neurons by taking account of the heterogeneity of network structure such as scale-free and small-world networks. We propose necessary conditions and show that, under these conditions, for sparsely but strongly connected heterogeneous networks with various types of single-neuron dynamics, despite the fact that the whole network receives external inputs, there is a small active subnetwork (active core) inherently embedded within it. The neurons in this active core have relatively high firing rates while the neurons in the rest of the network are quiescent. Surprisingly, although the whole network is heterogeneous and unbalanced, the active core possesses a balanced state and its connectivity structure is close to a homogeneous Erdös-Rényi network. The dynamics of the active core can be well-predicted using the Fokker-Planck equation. Our results suggest that the balanced state may be maintained by a small group of spiking neurons embedded in a large heterogeneous network in the brain. The existence of the small active core reconciles the balanced state and the sparse coding, and also provides a potential dynamical scenario underlying sparse coding in neuronal networks.

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.

Bilinearity in spatiotemporal integration of synaptic inputs.

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient [Formula: see text]. The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient [Formula: see text] is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.

Phenomenological incorporation of nonlinear dendritic integration using integrate-and-fire neuronal frameworks.

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as V(S)(Exp) ≈ V(E)(Exp) + V(I)(Exp) + kV(E)(Exp) V(I)(Exp), where V(S)(Exp), V(E)(Exp) and V(I)(Exp) are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient k in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient k by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.