Irrelevance of linear controllability to nonlinear dynamical networks

Controllability and accessibility analysis of nonlinear biosystems

BACKGROUND

We address the problem of determining the controllability and accessibility of nonlinear biosystems. We consider models described by affine-in-inputs ordinary differential equations, which are adequate for a wide array of biological processes. Roughly speaking, the controllability of a dynamical system determines the possibility of steering it from an initial state to any point in its neighbourhood; accessibility is a weaker form of controllability.

METHODS

While the methodology for analysing the controllability of linear systems is well established, its generalization to the nonlinear case has proven elusive. Thus, a number of related but different properties - including different versions of accessibility, reachability or weak local controllability - have been defined to approach its study, and several partial results exist in lieu of a general test. Here, leveraging the applicable results from differential geometric control theory, we source sufficient conditions to assess nonlinear controllability, as well as a necessary and sufficient condition for accessibility.

RESULTS

We develop an algorithmic procedure to evaluate these conditions efficiently, and we provide its open source implementation. Using this software tool, we analyse the accessibility and controllability of a number of models of biomedical interest. While some of them are fully controllable, we find others that are not, as is the case of some models of EGF and NFκB signalling networks.

CONCLUSIONS

The contributions in this paper facilitate the accessibility and controllability analysis of nonlinear models, not only in biomedicine but also in other areas in which they have been rarely performed to date.

Physical approach of a neuron model with memristive membranes

The membrane potential of a neuron is mainly controlled by the gradient distribution of electromagnetic field and concentration diversity between intracellular and extracellular ions. Without considering the thickness and material property, the electric characteristic of cell membrane is described by a capacitive variable and output voltage in an equivalent neural circuit. The flexible property of cell membrane enables controllability of endomembrane and outer membrane, and the capacitive properties and gradient field can be approached by double membranes connected by a memristor in an equivalent neural circuit. In this work, two capacitors connected by a memristor are used to mimic the physical property of two-layer membranes, and an inductive channel is added to the neural circuit. A biophysical neuron is obtained and the energy characteristic, dynamics, self-adaption is discussed, respectively. Coherence resonance and mode selection in adaptive way are detected under noisy excitation. The distribution of average energy function is effective to predict the appearance of coherence resonance. An adaptive law is proposed to control the capacitive parameters, and the controllability of cell membrane under external stimulus can be explained in theoretical way. The neuron with memristive membranes explains the self-adaptive mechanism of parameter changes and mode transition from energy viewpoint.

Identifying cancer driver genes in individual tumours

Cancer is a heterogeneous disease with a strong genetic component making it suitable for precision medicine approaches aimed at identifying the underlying molecular drivers within a tumour. Large scale population-level cancer sequencing consortia have identified many actionable mutations common across both cancer types and sub-types, resulting in an increasing number of successful precision medicine programs. Nonetheless, such approaches fail to consider the effects of mutations unique to an individual patient and may miss rare driver mutations, necessitating personalised approaches to driver-gene prioritisation. One approach is to quantify the functional importance of individual mutations in a single tumour based on how they affect the expression of genes in a gene interaction network (GIN). These GIN-based approaches can be broadly divided into those that utilise an existing reference GIN and those that construct de novo patient-specific GINs. These single-tumour approaches have several limitations that likely influence their results, such as use of reference cohort data, network choice, and approaches to mathematical approximation, and more research is required to evaluate the in vitro and in vivo applicability of their predictions. This review examines the current state of the art methods that identify driver genes in single tumours with a focus on GIN-based driver prioritisation.

Model-free tracking control of complex dynamical trajectories with machine learning

Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.

Impact of White Adipose Tissue on Brain Structure, Perfusion, and Cognitive Function in Patients With Severe Obesity: The BARICO Study

BACKGROUND AND OBJECTIVE

While underlying pathophysiology linking obesity to brain health is not completely understood, white adipose tissue (WAT) is considered a key player. In obesity, WAT becomes dysregulated, showing hyperplasia, hypertrophy, and eventually inflammation. This disbalance leads to dysregulated secretion of adipokines influencing both (cardio)vascular and brain health. Within this study, we investigated the association between omental WAT (oWAT) and subcutaneous WAT (scWAT) with brain structure and perfusion and cognition in adults with severe obesity.

METHODS

Within the cross-sectional BARICO study, brain structure and perfusion and cognitive function were measured before bariatric surgery (BS) using MRI and cognitive assessments. During BS, oWAT and scWAT depots were collected and analyzed by histopathology. The number and diameter of adipocytes were quantified together with the amount of crown-like structures (CLS) as an indication of inflammation. Blood samples were collected to analyze adipokines and inflammatory markers. Neuroimaging outcomes included brain volumes, cortical thickness, white matter (WM) integrity, WM hyperintensities, cerebral blood flow using arterial spin labeling (ASL), and the ASL spatial coefficient of variation (sCoV), reflecting cerebrovascular health.

RESULTS

Seventy-one patients were included (mean age 45.1 ± 5.8 years; 83.1% women; mean body mass index 40.8 ± 3.8 kg/m²). scWAT showed more CLS (z = -2.72, p < 0.01, r = -0.24) and hypertrophy compared with oWAT (F(1,64) = 3.99, p < 0.05, η² = 0.06). Adiponectin levels were inversely associated with the average diameter of scWAT (β = -0.31, 95% CI -0.54 to -0.08) and oWAT (β = -0.33, 95% CI -0.55 to -0.09). Furthermore, the adipocyte diameter in oWAT was positively associated with the sCoV in the parietal cortex (β = 0.33, 95% CI 0.10-0.60), and the number of adipocytes (per mm²) was positively associated with sCoV in the nucleus accumbens (NAcc) (β = 0.34, 95% CI 0.09-0.61). Cognitive function did not correlate with any WAT parameter or plasma marker. These associations were highly influenced by age and sex. sCoV in the NAcc was positively associated with fasting plasma glucose (β = 0.35, 95% CI 0.10-0.56).

DISCUSSION

scWAT and oWAT are different in morphology and in their relationship with plasma markers and cerebrovascular health. Although scWAT showed more CLS and hypertrophy, scWAT was not associated with brain readouts. This study showed, however, important relationships between oWAT morphology and cerebrovascular health in obesity.

TRIAL REGISTRATION INFORMATION

Trial Registration Number NTR7288 (trialregister.nl/trial/7090).

Global stabilizing control of large-scale biomolecular regulatory networks

MOTIVATION

Cellular behavior is determined by complex non-linear interactions between numerous intracellular molecules that are often represented by Boolean network models. To achieve a desired cellular behavior with minimal intervention, we need to identify optimal control targets that can drive heterogeneous cellular states to the desired phenotypic cellular state with minimal node intervention. Previous attempts to realize such global stabilization were based solely on either network structure information or simple linear dynamics. Other attempts based on non-linear dynamics are not scalable.

RESULTS

Here, we investigate the underlying relationship between structurally identified control targets and optimal global stabilizing control targets based on non-linear dynamics. We discovered that optimal global stabilizing control targets can be identified by analyzing the dynamics between structurally identified control targets. Utilizing these findings, we developed a scalable global stabilizing control framework using both structural and dynamic information. Our framework narrows down the search space based on strongly connected components and feedback vertex sets then identifies global stabilizing control targets based on the canalization of Boolean network dynamics. We find that the proposed global stabilizing control is superior with respect to the number of control target nodes, scalability, and computational complexity.

AVAILABILITY AND IMPLEMENTATION

We provide a GitHub repository that contains the DCGS framework written in Python as well as biological random Boolean network datasets (https://github.com/sugyun/DCGS).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Observability analysis and state reconstruction for networks of nonlinear systems

We address the problem of retrieving the full state of a network of Rössler systems from the knowledge of the actual state of a limited set of nodes. The selection of nodes where sensors are placed is carried out in a hierarchical way through a procedure based on graphical and symbolic observability approaches applied to pairs of coupled dynamical systems. By using a map directly obtained from governing equations, we design a nonlinear network reconstructor that is able to unfold the state of non-measured nodes with working accuracy. For sparse networks, the number of sensor scales with half the network size and node reconstruction errors are lower in networks with heterogeneous degree distributions. The method performs well even in the presence of parameter mismatch and non-coherent dynamics and for dynamical systems with completely different algebraic structures like the Hindmarsch-Rose; therefore, we expect it to be useful for designing robust network control laws.

NETISCE: a network-based tool for cell fate reprogramming

The search for effective therapeutic targets in fields like regenerative medicine and cancer research has generated interest in cell fate reprogramming. This cellular reprogramming paradigm can drive cells to a desired target state from any initial state. However, methods for identifying reprogramming targets remain limited for biological systems that lack large sets of experimental data or a dynamical characterization. We present NETISCE, a novel computational tool for identifying cell fate reprogramming targets in static networks. In combination with machine learning algorithms, NETISCE estimates the attractor landscape and predicts reprogramming targets using signal flow analysis and feedback vertex set control, respectively. Through validations in studies of cell fate reprogramming from developmental, stem cell, and cancer biology, we show that NETISCE can predict previously identified cell fate reprogramming targets and identify potentially novel combinations of targets. NETISCE extends cell fate reprogramming studies to larger-scale biological networks without the need for full model parameterization and can be implemented by experimental and computational biologists to identify parts of a biological system relevant to the desired reprogramming task.

Fixed Point Attractor Theory Bridges Structure and Function in C. elegans Neuronal Network

Understanding the structure–function relationship in a neuronal network is one of the major challenges in neuroscience research. Despite increasing researches at circuit connectivity and neural network structure, their structure-based biological interpretability remains unclear. Based on the attractor theory, here we develop an analytical framework that links neural circuit structures and their functions together through fixed point attractor in Caenorhabditis elegans. In this framework, we successfully established the structural condition for the emergence of multiple fixed points in C. elegans connectome. Then we construct a finite state machine to explain how functions related to bistable phenomena at the neural activity and behavioral levels are encoded. By applying the proposed framework to the command circuit in C. elegans, we provide a circuit level interpretation for the forward-reverse switching behaviors. Interestingly, network properties of the command circuit and first layer amphid interneuron circuit can also be inferred from their functions in this framework. Our research indicates the reliability of the fixed point attractor bridging circuit structure and functions, suggesting its potential applicability to more complex neuronal circuits in other species.

Energy cost study for controlling complex social networks with conformity behavior

To understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time linear dynamics. However, continuous-time linear dynamics is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modeling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, the energy costs needed for controlling systems with and without conformity are compared, and it was found that controlling networked systems with conformity features always requires less control energy. Finally, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since the conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward toward developing realistic control of complex social systems.

The missing role of gray matter in studying brain controllability

Brain controllability properties are normally derived from the white matter fiber tracts in which the neural substrate of the actual energy consumption, namely the gray matter, has been widely ignored. Here, we study the relationship between gray matter volume of regions across the whole cortex and their respective control properties derived from the structural architecture of the white matter fiber tracts. The data suggests that the ability of white fiber tracts to exhibit control at specific nodes not only depends on the connection strength of the structural connectome but additionally depends on gray matter volume at the host nodes. Our data indicate that connectivity strength and gray matter volume interact with respect to the brain’s control properties. Disentangling effects of the regional gray matter volume and connectivity strength, we found that frontal and sensory areas play crucial roles in controllability. Together these results suggest that structural and regional properties of the white matter and gray matter provide complementary information in studying the control properties of the intrinsic structural and functional architecture of the brain.

Network control theory suggests that the functions of large-scale brain circuits can be partially described with respect to the ability of brain regions to steer brain activity to different states. This ability, often quantified in terms of controllability metrics, has normally been derived from the structural architecture of the white matter fiber tracts. However, gray matter as the substrate that engenders much of the neural processes is widely ignored in this context. In the present work, we study the relationship between regional gray matter volume and control properties across the whole cortex and provide evidence that control properties not only depend on the connection strength of the structural connectome but also depend on sufficient gray matter volume at the host nodes.

Integrated Value of Influence: An Integrative Method for the Identification of the Most Influential Nodes within Networks

Biological systems are composed of highly complex networks, and decoding the functional significance of individual network components is critical for understanding healthy and diseased states. Several algorithms have been designed to identify the most influential regulatory points within a network. However, current methods do not address all the topological dimensions of a network or correct for inherent positional biases, which limits their applicability. To overcome this computational deficit, we undertook a statistical assessment of 200 real-world and simulated networks to decipher associations between centrality measures and developed an algorithm termed Integrated Value of Influence (IVI), which integrates the most important and commonly used network centrality measures in an unbiased way. When compared against 12 other contemporary influential node identification methods on ten different networks, the IVI algorithm outperformed all other assessed methods. Using this versatile method, network researchers can now identify the most influential network nodes.

Control of brain network dynamics across diverse scales of space and time

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow timescales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast timescales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.