Real Biological Networks Research Articles

Output Stabilizing Control of Complex Biological Networks Based on Boolean Algebra Analysis.

Output stabilizing control of biological systems is of utmost importance in systems biology since key phenotypes of biological networks are often encoded by a small subset of their phenotypic marker nodes. This study addresses the challenge of output stabilizing control for complex biological systems modeled by Boolean networks (BNs). The objective is to identify a set of constant control inputs capable of driving the BN toward a desirable long-term behavior with respect to specified output nodes. Leveraging the algebraic properties of Boolean logic, we develop a novel control algorithm that reformulates the output stabilizing control problem into a simple graph theoretic problem involving auxiliary BNs, the scale of which significantly decreases compared to the original BN. The proposed method ensures superiority over previous results in terms of both the number of control inputs and computational loads, since it searches for the solution within the reduced BNs while retaining essential structures needed for output stabilization. The efficacy of the proposed control scheme is demonstrated through extensive numerical experiments with complex random BNs and real biological networks. To support the reproducible research initiative, detailed results of numerical experiments are provided in the supplementary material, and all the implementation codes are made accessible at https://github.com/choonlog/OutputStabilization.

A 3D ray traced biological neural network learning model

Training large neural networks on big datasets requires significant computational resources and time. Transfer learning reduces training time by pre-training a base model on one dataset and transferring the knowledge to a new model for another dataset. However, current choices of transfer learning algorithms are limited because the transferred models always have to adhere to the dimensions of the base model and can not easily modify the neural architecture to solve other datasets. On the other hand, biological neural networks (BNNs) are adept at rearranging themselves to tackle completely different problems using transfer learning. Taking advantage of BNNs, we design a dynamic neural network that is transferable to any other network architecture and can accommodate many datasets. Our approach uses raytracing to connect neurons in a three-dimensional space, allowing the network to grow into any shape or size. In the Alcala dataset, our transfer learning algorithm trains the fastest across changing environments and input sizes. In addition, we show that our algorithm also outperformance the state of the art in EEG dataset. In the future, this network may be considered for implementation on real biological neural networks to decrease power consumption.

Hypergraph-Based Numerical Spiking Neural Membrane Systems with Novel Repartition Protocols.

The classic spiking neural P (SN P) systems abstract the real biological neural network into a simple structure based on graphs, where neurons can only communicate on the plane. This study proposes the hypergraph-based numerical spiking neural membrane (HNSNM) systems with novel repartition protocols. Through the introduction of hypergraphs, the HNSNM systems can characterize the high-order relationships among neurons and extend the traditional neuron structure to high-dimensional nonlinear spaces. The HNSNM systems also abstract two biological mechanisms of synapse creation and pruning, and use plasticity rules with repartition protocols to achieve planar, hierarchical and spatial communications among neurons in hypergraph neuron structures. Through imitating register machines, the Turing universality of the HNSNM systems is proved by using them as number generating and accepting devices. A universal HNSNM system consisting of 41 neurons is constructed to compute arbitrary functions. By solving NP-complete problems using the subset sum problem as an example, the computational efficiency and effectiveness of HNSNM systems are verified.

Parallel Particle Swarm Optimization Algorithm for Identifying Complex Communities in Biological Networks

Identification of complex communities in biological networks is a critical and ongoing challenge since lots of network-related problems correspond to the subgraph isomorphism problem known in the literature as NP-hard. Several optimization algorithms have been dedicated and applied to solve this problem. The main challenge regarding the application of optimization algorithms, specifically to handle large-scale complex networks, is their relatively long execution time. Thus, this paper proposes a parallel extension of the PSO algorithm to detect communities in complex biological networks. The main contribution of this study is summarized in three- fold; Firstly, a modified PSO algorithm with a local search operator is proposed to detect complex biological communities with high quality. Secondly, the variability in the capability of PSO to extract community structure in biological networks is studied when different types of crossover operators are used. Finally, to reduce the computational time needed to solve this problem, especially when detecting complex communities in large-scale biological networks, we have implemented parallel computing to execute the algorithm. The performance of the proposed algorithm was tested and evaluated on two real biological networks. The experimental results showed the effective performance of the proposed algorithm when using single-point crossover operator, and its superiority over other counterpart algorithms. Moreover, the use of parallel computing in the proposed algorithm representation has greatly reduced the computational time required for its execution.

A Unified and Biologically Plausible Relational Graph Representation of Vision Transformers.

Vision transformer (ViT) and its variants have achieved remarkable success in various tasks. The key characteristic of these ViT models is to adopt different aggregation strategies of spatial patch information within the artificial neural networks (ANNs). However, there is still a key lack of unified representation of different ViT architectures for systematic understanding and assessment of model representation performance. Moreover, how those well-performing ViT ANNs are similar to real biological neural networks (BNNs) is largely unexplored. To answer these fundamental questions, we, for the first time, propose a unified and biologically plausible relational graph representation of ViT models. Specifically, the proposed relational graph representation consists of two key subgraphs: an aggregation graph and an affine graph. The former considers ViT tokens as nodes and describes their spatial interaction, while the latter regards network channels as nodes and reflects the information communication between channels. Using this unified relational graph representation, we found that: 1) model performance was closely related to graph measures; 2) the proposed relational graph representation of ViT has high similarity with real BNNs; and 3) there was a further improvement in model performance when training with a superior model to constrain the aggregation graph.

Directed Acyclic Graph Learning on Attributed Heterogeneous Network

Learning the directed acyclic graph (DAG) among causal variables is a fundamental pre-task in causal discovery. Available DAG learning solutions canonically focus on homogeneous nodes with multiple variables and assume i.i.d. samples, how to learn DAG on typical attributed heterogeneous network (AHN) composed with different types of inter-dependent nodes and diverse attributes is a practical but more difficult task. In this paper, we propose HetDAG to identify DAG among nodes from heterogeneous network. HetDAG first embeds different types of node attributes and aggregates these embeddings as the node's raw representation. Then it uses contrastive learning with prior network structure to explore latent relationships between nodes and update the representation. Next, HetDAG introduces an attention-based DAG learning module that takes node representations as input to search DAG and orient edges between nodes. To the best of our knowledge, HetDAG is the first study to learn DAG on heterogeneous networks. Extensive experiments on both semi-synthetic and real data show that HetDAG can learn DAG in an efficacy way and outperforms the state-of-the-art approaches. The results on real biological networks confirm that HetDAG can find out the causal relations between lncRNAs and miRNAs.

Neuronal morphology and network properties modulate signal propagation in multi-layer feedforward network

The propagation and detection of weak signals play a vital role in the central nervous system's information processing. In this paper, a biophysical two-compartment model is adopted to investigate how the neuronal morphology and network properties modulate signal propagation in a multi-layer feedforward network (FFN). The numerical simulation results show that neurons with larger dendrites have higher firing rates and better responses to weak signals. Similarly, the output layer of FFN constructed by larger-dendrite neurons also exhibits better responses. A suitable chaotic current is necessary for the propagation of weak signals. Excessively strong or weak chaotic current leads to propagation failure. Sparse connection and weak synaptic strength optimize the responses of the output layer, which is consistent with real biological networks observed in the brain. It is found that weak signal propagation in FFN is highly correlated with the regulation of firing rate. Our results may provide novel insights into the modeling of complex networks and network function implementation.

Structure learning for gene regulatory networks.

Inference of biological network structures is often performed on high-dimensional data, yet is hindered by the limited sample size of high throughput "omics" data typically available. To overcome this challenge, often referred to as the "small n, large p problem," we exploit known organizing principles of biological networks that are sparse, modular, and likely share a large portion of their underlying architecture. We present SHINE-Structure Learning for Hierarchical Networks-a framework for defining data-driven structural constraints and incorporating a shared learning paradigm for efficiently learning multiple Markov networks from high-dimensional data at large p/n ratios not previously feasible. We evaluated SHINE on Pan-Cancer data comprising 23 tumor types, and found that learned tumor-specific networks exhibit expected graph properties of real biological networks, recapture previously validated interactions, and recapitulate findings in literature. Application of SHINE to the analysis of subtype-specific breast cancer networks identified key genes and biological processes for tumor maintenance and survival as well as potential therapeutic targets for modulating known breast cancer disease genes.

Network motifs and hypermotifs in TGFβ-induced epithelial to mesenchymal transition and metastasis

Epithelial to mesenchymal transition (EMT) is a complex, non-linear, dynamic multistep process that plays an integral role in the development of metastatic cancers. A diverse range of signaling molecules, along with their associated pathways, were observed to be involved in promoting EMT and cancer metastasis. Transforming growth factor–β (TGFβ), through its SMAD-dependent and SMAD-independent signaling, orchestrates numerous regulators that converge on key EMT transcription factors (TFs). These TFs further govern the phenotypic transition of cancer cells from epithelial to mesenchymal states. This study explores the TGFβ signaling pathway and its unique network architecture to understand their information processing roles in EMT. Two coherent type 1 feed forward network motifs regulating the expression of SNAIL and N-cadherin were observed. SNAIL, which is one of the crucial regulators of EMT, links both the coherent type 1 feed forward loops (C1FFLs) leading to hypermotif-like structure (Adler and Medzhitov, 2022). Systems modeling and analysis of these motifs and hypermotifs illustrated several interesting emergent information processing roles of the regulators involved. The known roles of these regulators, as described in the literature, were highly correlated with the emergent properties observed. The motifs illustrated persistence detection and noise filtration in regulating the expression of SNAIL and N-cadherin. Along with these system-level properties, the hypermotif architecture also exhibited temporal expression of GLI, SNAIL, ZEB, and N-cadherin. Furthermore, a hypothetical three-layered C1FFL hypermotif was postulated and analyzed. The analysis revealed various interesting system-level properties. However, possible existence of such real biological networks needs further exploration both theoretically and experimentally. Deciphering these network motifs and hypermotifs has provided an additional understanding of the complex biological phenomenon, such as EMT in cancer metastasis.

Biocode: A Data-Driven Procedure to Learn the Growth of Biological Networks.

Probabilistic biological network growth models have been utilized for many tasks including but not limited to capturing mechanism and dynamics of biological growth activities, null model representation, capturing anomalies, etc. Well-known examples of these probabilistic models are Kronecker model, preferential attachment model, and duplication-based model. However, we should frequently keep developing new models to better fit and explain the observed network features while new networks are being observed. Additionally, it is difficult to develop a growth model each time we study a new network. In this paper, we propose Biocode, a framework to automatically discover novel biological growth models matching user-specified graph attributes in directed and undirected biological graphs. Biocode designs a basic set of instructions which are common enough to model a number of well-known biological graph growth models. We combine such instruction-wise representation with a genetic algorithm based optimization procedure to encode models for various biological networks. We mainly evaluate the performance of Biocode in discovering models for biological collaboration networks, gene regulatory networks, and protein interaction networks which features such as assortativity, clustering coefficient, degree distribution closely match with the true ones in the corresponding real biological networks.

On the Distribution of Successor States in Boolean Threshold Networks.

We study the distribution of successor states in Boolean networks (BNs). The state vector y is called a successor of x if y = F(x) holds, where x, y ∈ {0,1}n are state vectors and F is an ordered set of Boolean functions describing the state transitions. This problem is motivated by analyzing how information propagates via hidden layers in Boolean threshold networks (discrete model of neural networks) and is kept or lost during time evolution in BNs. In this article, we measure the distribution via entropy and study how entropy changes via the transition from x to y , assuming that x is given uniformly at random. We focus on BNs consisting of exclusive OR (XOR) functions, canalyzing functions, and threshold functions. As a main result, we show that there exists a BN consisting of d -ary XOR functions, which preserves the entropy if d is odd and , whereas there does not exist such a BN if d is even. We also show that there exists a specific BN consisting of d -ary threshold functions, which preserves the entropy if [Formula: see text]. Furthermore, we theoretically analyze the upper and lower bounds of the entropy for BNs consisting of canalyzing functions and perform computational experiments using BN models of real biological networks.

From chaos to clock in recurrent neural net. Case study

What is the reason for complex dynamical patterns registered from real biological neuronal networks? Noise and dynamical reconfiguring of a network (functional/dynamic connectome) were proposed as possible answers. In this case study, we report a complex dynamical pattern observed in a simple deterministic network of 25 excitatory neurons with fixed connectome. After a short initial stimulation, the network is engaged into a complex dynamics, which lasts for a long time. Eventually, with no external intervention, the dynamics comes to a periodic one with a short period. The long transient is positively checked for being chaotic. We conclude that the complex dynamics observed is the output of neural computation performed in the process of neuronal firings and spikes propagation.

Systematic inference of indirect transcriptional regulation by protein kinases and phosphatases.

Gene expression is controlled by pathways of regulatory factors often involving the activity of protein kinases on transcription factor proteins. Despite this well established mechanism, the number of well described pathways that include the regulatory role of protein kinases on transcription factors is surprisingly scarce in eukaryotes.To address this, PhosTF was developed to infer functional regulatory interactions and pathways in both simulated and real biological networks, based on linear cyclic causal models with latent variables. GeneNetWeaverPhos, an extension of GeneNetWeaver, was developed to allow the simulation of perturbations in known networks that included the activity of protein kinases and phosphatases on gene regulation. Over 2000 genome-wide gene expression profiles, where the loss or gain of regulatory genes could be observed to perturb gene regulation, were then used to infer the existence of regulatory interactions, and their mode of regulation in the budding yeast Saccharomyces cerevisiae.Despite the additional complexity, our inference performed comparably to the best methods that inferred transcription factor regulation assessed in the DREAM4 challenge on similar simulated networks. Inference on integrated genome-scale data sets for yeast identified ∼ 8800 protein kinase/phosphatase-transcription factor interactions and ∼ 6500 interactions among protein kinases and/or phosphatases. Both types of regulatory predictions captured statistically significant numbers of known interactions of their type. Surprisingly, kinases and phosphatases regulated transcription factors by a negative mode or regulation (deactivation) in over 70% of the predictions.

Looking beyond community structure leads to the discovery of dynamical communities in weighted networks

A fundamental question is whether groups of nodes of a complex network can possibly display long-term cluster-synchronized behavior. While this question has been addressed for the restricted classes of unweighted and labeled graphs, it remains an open problem for the more general class of weighted networks. The emergence of coordinated motion of nodes in natural and technological networks is directly related to the network structure through the concept of an equitable partition, which determines which nodes can show long-term synchronized behavior and which nodes cannot. We provide a method to detect the presence of nearly equitable partitions in weighted networks, based on minimal information about the network structure. With this approach we are able to discover the presence of dynamical communities in both synthetic and real technological, biological, and social networks, to a statistically significant level. We show that our approach based on dynamical communities is better at predicting the emergence of synchronized behavior than existing methods to detect community structure.

Existence of physical measures in some excitation–inhibition networks* *MT acknowledges funding from the H2020 Marie Słodowska-Curie Actions, project: ‘Ergodic Theory of Complex Systems’ (Project No. 843880). LSY was supported in part by NSF Grant DMS 1901009.

In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but can be arbitrarily large. They are inspired by real biological networks, and possess features that are idealizations of those in biological systems. Individual components of the network are represented by simple, much studied dynamical systems. Complex dynamical patterns on the network level emerge as a result of the coupling among its constituent subsystems. Appealing to existing techniques in (nonuniform) hyperbolic theory, we study their Lyapunov exponents and entropy, and prove that large time network dynamics are governed by physical measures with the SRB property.

A Novel Evaluation Strategy to Artificial Neural Network Model Based on Bionics.

With the continuous deepening of Artificial Neural Network (ANN) research, ANN model structure and function are improving towards diversification and intelligence. However, the model is more evaluated from the pros and cons of the problem-solving results and the lack of evaluation from the biomimetic aspect of imitating neural networks is not inclusive enough. Hence, a new ANN models evaluation strategy is proposed from the perspective of bionics in response to this problem in the paper. Firstly, four classical neural network models are illustrated: Back Propagation (BP) network, Deep Belief Network (DBN), LeNet5 network, and olfactory bionic model (KIII model), and the neuron transmission mode and equation, network structure, and weight updating principle of the models are analyzed qualitatively. The analysis results show that the KIII model comes closer to the actual biological nervous system compared with other models, and the LeNet5 network simulates the nervous system in depth. Secondly, evaluation indexes of ANN are constructed from the perspective of bionics in this paper: small-world, synchronous, and chaotic characteristics. Finally, the network model is quantitatively analyzed by evaluation indexes from the perspective of bionics. The experimental results show that the DBN network, LeNet5 network, and BP network have synchronous characteristics. And the DBN network and LeNet5 network have certain chaotic characteristics, but there is still a certain distance between the three classical neural networks and actual biological neural networks. The KIII model has certain small-world characteristics in structure, and its network also exhibits synchronization characteristics and chaotic characteristics. Compared with the DBN network, LeNet5 network, and the BP network, the KIII model is closer to the real biological neural network.

An equivalent electrical circuit for the Hindmarsh‐Rose model

SummaryHardware realizations of neural networks can pave the way towards a new generation of processors due to the biological role model being superior in terms of speed and energy‐efficiency compared to today's processors. This can be achieved by deriving novel design principles for circuits being obtainable when replicating and investigating real biological neural networks in depth. This has, for example, been done by utilizing the Hindmarsh‐Rose model, offering a rich repertoire of neuronal firing patterns. Our aim is to synthesize a theoretical, equivalent electrical circuit of the Hindmarsh‐Rose model being well interpretable in terms of biology, since this supports the derivation of design principles from biology and can serve as a basis for a systematic circuit simplification. We do this by starting from a linearized model because this allows for a systematic approach and then first derive a linear and afterwards a nonlinear equivalent electrical circuit. The resulting circuit has a structure similar to conductance‐based models, where a deployed negative impedance converter can be seen as a deeper modeling of ion pump activity. Simulation results of the proposed circuits show the functionality of the equivalent circuits.

Controllability of Hypergraphs

In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed to achieve controllability of even uniform hypergraphs. We present an efficient heuristic to obtain the MCN. MCN can be used as a measure of robustness, and we show that it is related to the hypergraph degree distribution in simulated examples. Finally, we use MCN to examine robustness in real biological networks.

Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article further develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a data-driven diffusion process. Unlike related diffusion methods, DSDs incorporate information across time scales, which allows for the intrinsic data structure to be inferred in a parameter-free manner. This article develops a theory for DSD based on the multitemporal emergence of mesoscopic equilibria in the underlying diffusion process. New algorithms for denoising and dimension reduction with DSD are also proposed and analyzed. These approaches are based on a weighted spectral decomposition of the underlying diffusion process, and experiments on synthetic datasets and real biological networks illustrate the efficacy of the proposed algorithms in terms of both speed and accuracy. Throughout, comparisons with related methods are made in order to illustrate the distinct advantages of DSD for datasets exhibiting multiscale structure.

Neural networks and microelectronics parameters distribution measurements depending on sintering temperature and applied voltage

This research is based on the idea to design the interface structure around the grains and thin layers between two grains, as a possible solution for deep microelectronic parameters integrations. The experiments have been based on nano-BaTiO3 powders with Y-based additive. The advanced idea is to create the new observed directions to network microelectronic characteristics in thin films coated around and between the grains on the way to get and compare with global results on the samples. Biomimetic similarities are artificial neural networks which could be original method and tools that we use to map input–output data and could be applied on ceramics microelectronic parameters. This mapping is developed in the manner like signals that are processed in real biological neural networks. These signals are processed by using artificial neurons, which have a simple function to process input signal, as well as adjustable parameter which represents sensitivity to inputs. The integrated network output presents practically the large number of inner neurons outputs sum. This original idea is to connect analysis results and neural networks. It is of the great importance to connect microcapacitances by neural network with the goal to compare the experimental results in the bulk samples measurements and microelectronics parameters. The result of these researches is the study of functional relation definition between consolidation parameters, voltage (U), consolidation sintering temperature and relative capacitance change, from the bulk sample surface down to the coating thin films around the grains.