Network science characteristics of brain-derived neuronal cultures deciphered from quantitative phase imaging data

From pixels to connections: exploring in vitro neuron reconstruction software for network graph generation

Digital reconstruction has been instrumental in deciphering how in vitro neuron architecture shapes information flow. Emerging approaches reconstruct neural systems as networks with the aim of understanding their organization through graph theory. Computational tools dedicated to this objective build models of nodes and edges based on key cellular features such as somata, axons, and dendrites. Fully automatic implementations of these tools are readily available, but they may also be purpose-built from specialized algorithms in the form of multi-step pipelines. Here we review software tools informing the construction of network models, spanning from noise reduction and segmentation to full network reconstruction. The scope and core specifications of each tool are explicitly defined to assist bench scientists in selecting the most suitable option for their microscopy dataset. Existing tools provide a foundation for complete network reconstruction, however more progress is needed in establishing morphological bases for directed/weighted connectivity and in software validation.

Beyond multilayer perceptrons: Investigating complex topologies in neural networks

This study delves into the crucial aspect of network topology in artificial neural networks (NNs) and its impact on model performance. Addressing the need to comprehend how network structures influence learning capabilities, the research contrasts traditional multilayer perceptrons (MLPs) with models built on various complex topologies using novel network generation techniques. Drawing insights from synthetic datasets, the study reveals the remarkable accuracy of complex NNs, particularly in high-difficulty scenarios, outperforming MLPs. Our exploration extends to real-world datasets, highlighting the task-specific nature of optimal network topologies and unveiling trade-offs, including increased computational demands and reduced robustness to graph damage in complex NNs compared to MLPs. This research underscores the pivotal role of complex topologies in addressing challenging learning tasks. However, it also signals the necessity for deeper insights into the complex interplay among topological attributes influencing NN performance. By shedding light on the advantages and limitations of complex topologies, this study provides valuable guidance for practitioners and paves the way for future endeavors to design more efficient and adaptable neural architectures across various applications.

A unified approach of detecting phase transition in time-varying complex networks

Deciphering the non-trivial interactions and mechanisms driving the evolution of time-varying complex networks (TVCNs) plays a crucial role in designing optimal control strategies for such networks or enhancing their causal predictive capabilities. In this paper, we advance the science of TVCNs by providing a mathematical framework through which we can gauge how local changes within a complex weighted network affect its global properties. More precisely, we focus on unraveling unknown geometric properties of a network and determine its implications on detecting phase transitions within the dynamics of a TVCN. In this vein, we aim at elaborating a novel and unified approach that can be used to depict the relationship between local interactions in a complex network and its global kinetics. We propose a geometric-inspired framework to characterize the network's state and detect a phase transition between different states, to infer the TVCN's dynamics. A phase of a TVCN is determined by its Forman-Ricci curvature property. Numerical experiments show the usefulness of the proposed curvature formalism to detect the transition between phases within artificially generated networks. Furthermore, we demonstrate the effectiveness of the proposed framework in identifying the phase transition phenomena governing the training and learning processes of artificial neural networks. Moreover, we exploit this approach to investigate the phase transition phenomena in cellular re-programming by interpreting the dynamics of Hi-C matrices as TVCNs and observing singularity trends in the curvature network entropy. Finally, we demonstrate that this curvature formalism can detect a political change. Specifically, our framework can be applied to the US Senate data to detect a political change in the United States of America after the 1994 election, as discussed by political scientists.

Hierarchical growth in neural networks structure: Organizing inputs by Order of Hierarchical Complexity

Several studies demonstrate that the structure of the brain increases in hierarchical complexity throughout development. We tested if the structure of artificial neural networks also increases in hierarchical complexity while learning a developing task, called the balance beam problem. Previous simulations of this developmental task do not reflect a necessary premise underlying development: a more complex structure can be built out of less complex ones, while ensuring that the more complex structure does not replace the less complex one. In order to address this necessity, we segregated the input set by subsets of increasing Orders of Hierarchical Complexity. This is a complexity measure that has been extensively shown to underlie the complexity behavior and hypothesized to underlie the complexity of the neural structure of the brain. After segregating the input set, minimal neural network models were trained separately for each input subset, and adjacent complexity models were analyzed sequentially to observe whether there was a structural progression. Results show that three different network structural progressions were found, performing with similar accuracy, pointing towards self-organization. Also, more complex structures could be built out of less complex ones without substituting them, successfully addressing catastrophic forgetting and leveraging performance of previous models in the literature. Furthermore, the model structures trained on the two highest complexity subsets performed better than simulations of the balance beam present in the literature. As a major contribution, this work was successful in addressing hierarchical complexity structural growth in neural networks, and is the first that segregates inputs by Order of Hierarchical Complexity. Since this measure can be applied to all domains of data, the present method can be applied to future simulations, systematizing the simulation of developmental and evolutionary structural growth in neural networks.

Network bypasses sustain complexity

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.

Topological energy of networks

Energy is an important network indicator defined by the eigenvalues of an adjacency matrix that includes the neighbor information for each node. This article expands the definition of network energy to include higher-order information between nodes. We use resistance distances to characterize the distances between nodes and order complexes to extract higher-order information. Topological energy ( T E), defined by the resistance distance and order complex, reveals the characteristics of the network structure from multiple scales. In particular, calculations show that the topological energy can be used to distinguish graphs with the same spectrum well. In addition, topological energy is robust, and small random perturbations of edges do not significantly affect the T E values. Finally, we find that the energy curve of the real network is significantly different from that of the random graph, thus showing that T E can be used to distinguish the network structure well. This study shows that T E is an indicator that distinguishes the structure of a network and has some potential applications for real-world problems.

Decoding the underlying mechanisms of Di-Tan-Decoction in treating intracerebral hemorrhage based on network pharmacology

BACKGROUND

Chinese medicine usually acts as "multi-ingredients, multi-targets and multi-pathways" on complex diseases, and these action modes reflect the coordination and integrity of the treatment process with traditional Chinese medicine (TCM). System pharmacology is developed based on the cross-disciplines of directional pharmacology, system biology, and mathematics, has the characteristics of integrity and synergy in the treatment process of TCM. Therefore, it is suitable for analyzing the key ingredients and mechanisms of TCM in treating complex diseases. Intracerebral Hemorrhage (ICH) is one of the leading causes of death in China, with the characteristics of high mortality and disability rate. Bring a significant burden on people and society. An increasing number of studies have shown that Chinese medicine prescriptions have good advantages in the treatment of ICH, and Ditan Decoction (DTT) is one of the commonly used prescriptions in the treatment of ICH. Modern pharmacological studies have shown that DTT may play a therapeutic role in treating ICH by inhibiting brain inflammation, abnormal oxidative stress reaction and reducing neurological damage, but the specific key ingredients and mechanism are still unclear.

METHODS

To solve this problem, we established PPI network based on the latest pathogenic gene data of ICH, and CT network based on ingredient and target data of DTT. Subsequently, we established optimization space based on PPI network and CT network, and constructed a new model for node importance calculation, and proposed a calculation method for PES score, thus calculating the functional core ingredients group (FCIG). These core functional groups may represent DTT therapy for ICH.

RESULTS

Based on the strategy, 44 ingredients were predicted as FCIG, results showed that 80.44% of the FCIG targets enriched pathways were coincided with the enriched pathways of pathogenic genes. Both the literature and molecular docking results confirm the therapeutic effect of FCIG on ICH via targeting MAPK signaling pathway and PI3K-Akt signaling pathway.

CONCLUSIONS

The FCIG obtained by our network pharmacology method can represent the effect of DTT in treating ICH. These results confirmed that our strategy of active ingredient group optimization and the mechanism inference could provide methodological reference for optimization and secondary development of TCM.

Adding links on minimum degree and longest distance strategies for improving network robustness and efficiency

Many real-world networks characterized by power-law degree distributions are extremely vulnerable against malicious attacks. Therefore, it is important to obtain effective methods for strengthening the robustness of the existing networks. Previous studies have been discussed some link addition methods for improving the robustness. In particular, two effective strategies for selecting nodes to add links have been proposed: the minimum degree and longest distance strategies. However, it is unclear whether the effects of these strategies on the robustness are independent or not. In this paper, we investigate the contributions of these strategies to improving the robustness by adding links in distinguishing the effects of degrees and distances as much as possible. Through numerical simulation, we find that the robustness is effectively improved by adding links on the minimum degree strategy for both synthetic trees and real networks. As an exception, only when the number of added links is small, the longest distance strategy is the best. Conversely, the robustness is only slightly improved by adding links on the shortest distance strategy in many cases, even combined with the minimum degree strategy. Therefore, enhancing global loops is essential for improving the robustness rather than local loops.

Objective Supervised Machine Learning-Based Classification and Inference of Biological Neuronal Networks

The classification of biological neuron types and networks poses challenges to the full understanding of the human brain’s organisation and functioning. In this paper, we develop a novel objective classification model of biological neuronal morphology and electrical types and their networks, based on the attributes of neuronal communication using supervised machine learning solutions. This presents advantages compared to the existing approaches in neuroinformatics since the data related to mutual information or delay between neurons obtained from spike trains are more abundant than conventional morphological data. We constructed two open-access computational platforms of various neuronal circuits from the Blue Brain Project realistic models, named Neurpy and Neurgen. Then, we investigated how we could perform network tomography with cortical neuronal circuits for the morphological, topological and electrical classification of neurons. We extracted the simulated data of 10,000 network topology combinations with five layers, 25 morphological type (m-type) cells, and 14 electrical type (e-type) cells. We applied the data to several different classifiers (including Support Vector Machine (SVM), Decision Trees, Random Forest, and Artificial Neural Networks). We achieved accuracies of up to 70%, and the inference of biological network structures using network tomography reached up to 65% of accuracy. Objective classification of biological networks can be achieved with cascaded machine learning methods using neuron communication data. SVM methods seem to perform better amongst used techniques. Our research not only contributes to existing classification efforts but sets the road-map for future usage of brain–machine interfaces towards an in vivo objective classification of neurons as a sensing mechanism of the brain’s structure.

The trend of disruption in the functional brain network topology of Alzheimer's disease

Alzheimer's disease (AD) is a progressive disorder associated with cognitive dysfunction that alters the brain's functional connectivity. Assessing these alterations has become a topic of increasing interest. However, a few studies have examined different stages of AD from a complex network perspective that cover different topological scales. This study used resting state fMRI data to analyze the trend of functional connectivity alterations from a cognitively normal (CN) state through early and late mild cognitive impairment (EMCI and LMCI) and to Alzheimer's disease. The analyses had been done at the local (hubs and activated links and areas), meso (clustering, assortativity, and rich-club), and global (small-world, small-worldness, and efficiency) topological scales. The results showed that the trends of changes in the topological architecture of the functional brain network were not entirely proportional to the AD progression. There were network characteristics that have changed non-linearly regarding the disease progression, especially at the earliest stage of the disease, i.e., EMCI. Further, it has been indicated that the diseased groups engaged somatomotor, frontoparietal, and default mode modules compared to the CN group. The diseased groups also shifted the functional network towards more random architecture. In the end, the methods introduced in this paper enable us to gain an extensive understanding of the pathological changes of the AD process.

Deciphering the generating rules and functionalities of complex networks

Network theory helps us understand, analyze, model, and design various complex systems. Complex networks encode the complex topology and structural interactions of various systems in nature. To mine the multiscale coupling, heterogeneity, and complexity of natural and technological systems, we need expressive and rigorous mathematical tools that can help us understand the growth, topology, dynamics, multiscale structures, and functionalities of complex networks and their interrelationships. Towards this end, we construct the node-based fractal dimension (NFD) and the node-based multifractal analysis (NMFA) framework to reveal the generating rules and quantify the scale-dependent topology and multifractal features of a dynamic complex network. We propose novel indicators for measuring the degree of complexity, heterogeneity, and asymmetry of network structures, as well as the structure distance between networks. This formalism provides new insights on learning the energy and phase transitions in the networked systems and can help us understand the multiple generating mechanisms governing the network evolution.

Fuzzy Recurrence Exponents of Subcellular-Nanostructure Dynamics in Time-lapse Confocal Imaging

Studying the dynamics of nanostructures in the intracellular space is important because it allows gaining insights into the mechanism of complex biological functions of organelles. Understanding such dynamical processes can contribute to the development of nanomedicine for the diagnosis and treatment of many diseases caused by the interaction of multiple genes and environmental factors. Here a quantitative measure of spatial-temporal dynamics of nanostructures within a cell line in the context of nonlinear dynamics is introduced, where early endosomes, late endosomes, and lysosomes recorded by time-lapse confocal imaging are examined. The mathematical derivation of the proposed technique is based on the concept of recurrence dynamics and sequential rate of change over time. The quantification introduced as fuzzy recurrence exponents can be generalized for characterizing the dynamics of experimental evolutions in other nanostructures of living cells captured under the optical microscope.

Principled network extraction from images

Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal definition of a network in terms of sets of nodes and edges. Instead, this information should be suitably extracted from the raw image data. Motivated by this, we present a principled model to extract network topologies from images that is scalable and efficient. We map this goal into solving a routing optimization problem where the solution is a network that minimizes an energy function which can be interpreted in terms of an operational and infrastructural cost. Our method relies on recent results from optimal transport theory and is a principled alternative to standard image-processing techniques that are based on heuristics. We test our model on real images of the retinal vascular system, slime mould and river networks and compare with routines combining image-processing techniques. Results are tested in terms of a similarity measure related to the amount of information preserved in the extraction. We find that our model finds networks from retina vascular network images that are more similar to hand-labelled ones, while also giving high performance in extracting networks from images of rivers and slime mould for which there is no ground truth available. While there is no unique method that fits all the images the best, our approach performs consistently across datasets, its algorithmic implementation is efficient and can be fully automatized to be run on several datasets with little supervision.

Spatial light interference microscopy: principle and applications to biomedicine

In this paper, we review spatial light interference microscopy (SLIM), a common-path, phase-shifting interferometer, built onto a phase-contrast microscope, with white-light illumination. As one of the most sensitive quantitative phase imaging (QPI) methods, SLIM allows for speckle-free phase reconstruction with sub-nanometer path-length stability. We first review image formation in QPI, scattering, and full-field methods. Then, we outline SLIM imaging from theory and instrumentation to diffraction tomography. Zernike's phase-contrast microscopy, phase retrieval in SLIM, and halo removal algorithms are discussed. Next, we discuss the requirements for operation, with a focus on software developed in-house for SLIM that enables high-throughput acquisition, whole slide scanning, mosaic tile registration, and imaging with a color camera. We introduce two methods for solving the inverse problem using SLIM, white-light tomography, and Wolf phase tomography. Lastly, we review the applications of SLIM in basic science and clinical studies. SLIM can study cell dynamics, cell growth and proliferation, cell migration, mass transport, etc. In clinical settings, SLIM can assist with cancer studies, reproductive technology, blood testing, etc. Finally, we review an emerging trend, where SLIM imaging in conjunction with artificial intelligence brings computational specificity and, in turn, offers new solutions to outstanding challenges in cell biology and pathology.

Deciphering the laws of social network-transcendent COVID-19 misinformation dynamics and implications for combating misinformation phenomena

The global rise of COVID-19 health risk has triggered the related misinformation infodemic. We present the first analysis of COVID-19 misinformation networks and determine few of its implications. Firstly, we analyze the spread trends of COVID-19 misinformation and discover that the COVID-19 misinformation statistics are well fitted by a log-normal distribution. Secondly, we form misinformation networks by taking individual misinformation as a node and similarity between misinformation nodes as links, and we decipher the laws of COVID-19 misinformation network evolution: (1) We discover that misinformation evolves to optimize the network information transfer over time with the sacrifice of robustness. (2) We demonstrate the co-existence of fit get richer and rich get richer phenomena in misinformation networks. (3) We show that a misinformation network evolution with node deletion mechanism captures well the public attention shift on social media. Lastly, we present a network science inspired deep learning framework to accurately predict which Twitter posts are likely to become central nodes (i.e., high centrality) in a misinformation network from only one sentence without the need to know the whole network topology. With the network analysis and the central node prediction, we propose that if we correctly suppress certain central nodes in the misinformation network, the information transfer of network would be severely impacted.

Moving towards accurate and early prediction of language delay with network science and machine learning approaches

Due to wide variability of typical language development, it has been historically difficult to distinguish typical and delayed trajectories of early language growth. Improving our understanding of factors that signal language disorder and delay has the potential to improve the lives of the millions with developmental language disorder (DLD). We develop predictive models of low language (LL) outcomes by analyzing parental report measures of early language skill using machine learning and network science approaches. We harmonized two longitudinal datasets including demographic and standardized measures of early language skills (the MacArthur-Bates Communicative Developmental Inventories; MBCDI) as well as a later measure of LL. MBCDI data was used to calculate several graph-theoretic measures of lexico-semantic structure in toddlers' expressive vocabularies. We use machine-learning techniques to construct predictive models with these datasets to identify toddlers who will have later LL outcomes at preschool and school-age. This approach yielded robust and reliable predictions of later LL outcome with classification accuracies in single datasets exceeding 90%. Generalization performance between different datasets was modest due to differences in outcome ages and diagnostic measures. Grammatical and lexico-semantic measures ranked highly in predictive classification, highlighting promising avenues for early screening and delineating the roots of language disorders.

Neuron type classification in rat brain based on integrative convolutional and tree-based recurrent neural networks

The study of cellular complexity in the nervous system based on anatomy has shown more practical and objective advantages in morphology than other perspectives on molecular, physiological, and evolutionary aspects. However, morphology-based neuron type classification in the whole rat brain is challenging, given the significant number of neuron types, limited reconstructed neuron samples, and diverse data formats. Here, we report that different types of deep neural network modules may well process different kinds of features and that the integration of these submodules will show power on the representation and classification of neuron types. For SWC-format data, which are compressed but unstructured, we construct a tree-based recurrent neural network (Tree-RNN) module. For 2D or 3D slice-format data, which are structured but with large volumes of pixels, we construct a convolutional neural network (CNN) module. We also generate a virtually simulated dataset with two classes, reconstruct a CASIA rat-neuron dataset with 2.6 million neurons without labels, and select the NeuroMorpho-rat dataset with 35,000 neurons containing hierarchical labels. In the twelve-class classification task, the proposed model achieves state-of-the-art performance compared with other models, e.g., the CNN, RNN, and support vector machine based on hand-designed features.

Simultaneous measurement of neurite and neural body mass accumulation via quantitative phase imaging

Measurement of neuron behavior is crucial for studying neural development and evaluating the impact of potential therapies on neural regeneration. Conventional approaches to imaging neuronal behavior require labeling and do not separately quantify the growth processes that underlie neural regeneration. In this paper we demonstrate the use of quantitative phase imaging (QPI) as a label-free, quantitative measurement of neuron behavior in vitro. By combining QPI with image processing, our method separately measures the mass accumulation rates of soma and neurites. Additionally, the data provided by QPI can be used to separately measure the processes of maturation and formation of neurites. Overall, our approach has the potential to greatly simplify conventional neurite outgrowth measurements, while providing key data on the resources used to produce neurites during neural development.

Network extraction by routing optimization

Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally intractable. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system of equations, which can instead be solved efficiently using numerical methods. This results in enabling the acquisition of optimal network topologies from a variety of routing problems. However, the actual extraction of the solution in terms of a final network topology relies on numerical details which can prevent an accurate investigation of their topological properties. In fact, in this context, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. In particular, in this framework, final graph acquisition is a challenging problem in-and-of-itself. Here we introduce a method to extract network topologies from dynamical equations related to routing optimization under various parameters’ settings. Our method is made of three steps: first, it extracts an optimal trajectory by solving a dynamical system, then it pre-extracts a network, and finally, it filters out potential redundancies. Remarkably, we propose a principled model to address the filtering in the last step, and give a quantitative interpretation in terms of a transport-related cost function. This principled filtering can be applied to more general problems such as network extraction from images, thus going beyond the scenarios envisioned in the first step. Overall, this novel algorithm allows practitioners to easily extract optimal network topologies by combining basic tools from numerical methods, optimization and network theory. Thus, we provide an alternative to manual graph extraction which allows a grounded extraction from a large variety of optimal topologies. The analysis of these may open up the possibility to gain new insights into the structure and function of optimal networks. We provide an open source implementation of the code online.