Les Houches lectures on flow networks in biology

Optimizing information flow in a dense wireless network using discrete methods can be computationally prohibitive. Instead of treating the nodes as discrete entities, these networks can be modeled as continuum of nodes providing a medium for information transport. To model information routes in continuous space, information flow vector field is defined over the geographical domain of the network. At each point of the network, the orientation of the vector field shows the direction of the flow of information, and its magnitude shows the density of information flow. Using multivariate calculus techniques in continuous domain, an information flow vector field can be found such that it minimizes a suitable cost function. Then the solution is discretized. Conventionally, a centralized method of calculating the optimal information flow in the network is suggested; however, using a centralized method to optimize information flow in a dynamic network is prohibitive. Additionally, the value of information flow vector field is needed only at the locations of nodes in the network. This poses a gap between the continuous space and discrete space models of information flow in dense wireless networks. This gap is how to calculate and apply the optimum information flow derived in continuous domain in a network with finite number of nodes. As a first step to fill this gap, a specific quadratic cost function is considered. It is proved that the the vector field that minimizes this cost function is irrotational, thus it is written as the gradient of a potential function. This potential function satisfies a Poisson Partial Differential Equation (PDE) which in conjunction with Neumann boundary condition has a unique solution up to a constant. The PDE resulted by optimization in continuous domain is first discretized and then solved in a distributed fashion. The solution requires only neighboring nodes to communicate with each other. The gradient of the resulting potential defines the routes that the traffic should be forwarded.

Structural controllability of dynamic transcriptional regulatory networks for Saccharomyces cerevisiae

Modules are common functional and structural properties of many social, technical and biological networks. Especially for biological systems it is important to understand how modularity is related to function and how modularity evolves. It is known that time-varying or spatially organized goals can lead to modularity in a simulated evolution of signaling networks. Here, we study a minimal model of material flow in networks. We discuss the relation between the shared use of nodes, i.e., the cooperativity of modules, and the orthogonality of a prescribed output pattern. We study the persistence of cooperativity through an evolution of robustness against local damages. We expect the results to be valid for a large class of flow-based biological and technical networks.

We study the minimum-cost flow problem on dynamic networks with nonlinear cost functions that depend on time and edge flow. A general procedure for solving the problem using the time-expanded network is described. The main properties of dynamic flows on networks with concave cost functions are studied. We propose an algorithm for finding the optimal flow in networks with exactly one source; its running time is polynomial for a fixed number of sinks. Some details concerning the correctness of the algorithm and its computational complexity are discussed.

PurposeSimple methods for the steady‐state analysis of a flow network are readily available, but the dynamic behavior of a large‐scale flow network is difficult to study due to the complex differential‐algebraic equation system resulting from its modeling. It is the aim of this paper to present two simple methods for the dynamic analysis of large‐scale flow networks and to demonstrate their use by examining the dynamics of a self‐similar branching tree network.Design/methodology/approachTwo numerical projection methods are proposed for one‐dimensional dynamic analysis of large piping networks. Both are extensions of that suggested by Chorin for the nonlinear differential‐algebraic system resulting from the Navier‐Stokes equations. Each numerical algorithm is discussed and verified for turbulent flow in a nonlinear, self‐similar, branching tree network with constant friction factor for which an exact solution is available.FindingsThe dynamics of this network are calculated for more realistic friction factors and described as system parameters are varied. Self‐excited oscillations due to laminar‐turbulent transition are found for some parameter values and dynamic component behavior is observed in the network which is not observable in components apart from it.Practical implicationsIt is shown that the dynamics of a flow network can exhibit unexpected behavior, reinforcing the need for simple methods to perform dynamic analysis.Originality/valueThis paper presents two numerical projection schemes for dynamic analysis of large‐scale flow networks to aid in their study and design.

Existing theories of structural adaptation in biological flow networks are largely concerned with steady flows. However, biological networks are composed of elastic vessels, and many are driven by a pulsatile or periodic source, leading to spatiotemporal variations in the pressure and flow fields on short time-scales within each vessel. Here, we investigate the mathematical problem of how long-term adaptation in elastic networks is impacted by short-term pulsatile dynamics at the level of individual vessels. Using a a minimal one-loop network, we show that pulsatility gives rise to resonances that stabilize the loop for a much broader range of metabolic cost functions than predicted by existing theories. Our paper emphasizes the importance of correctly capturing the interplay of the short and long time-scales for a more realistic treatment of adaptation in periodically driven elastic flow networks. Published by the American Physical Society 2024

Together with computational analysis and modeling, the development of whole-genome measurement technologies holds the potential to fundamentally change research on complex disorders such as coronary artery disease. With these tools, the stage has been set to reveal the full repertoire of biological components (genes, proteins, and metabolites) in complex diseases and their interplay in modules and networks. Here we review how network identification based on reverse engineering, as applied to whole-genome datasets from simpler organisms, is now being adapted to more complex settings such as datasets from human cell lines and organs in relation to physiological and pathological states. Our focus is on the use of a systems biological approach to identify gene networks in coronary atherosclerosis. We also address how gene networks will probably play a key role in the development of early diagnostics and treatments for complex disorders in the coming era of individualized medicine.

Plasma skimming and the Fahraeus-Lindqvist effect are well-known phenomena in blood rheology. By combining these peculiarities of blood flow in the microcirculation with simple topological models of microvascular networks, we have uncovered interesting nonlinear behavior regarding blood flow in networks. Nonlinearity manifests itself in the existence of multiple steady states. This is due to the nonlinear dependence of viscosity on blood cell concentration. Nonlinearity also appears in the form of spontaneous oscillations in limit cycles. These limit cycles arise from the fact that the physics of blood flow can be modeled in terms of state dependent delay equations with multiple interacting delay times. In this paper we extend our previous work on blood flow in a simple two node network and begin to explore how topological complexity influences the dynamics of network blood flow. In addition we present initial evidence that the nonlinear phenomena predicted by our model are observed experimentally.

Reconstruction of biological and biochemical networks is a crucial step in extracting knowledge and causal information from large biological data sets. This task is particularly challenging when dealing with time-series data from dynamic networks. We have developed a new method, called doubly penalized least absolute shrinkage and selection operator (DPLASSO), for the reconstruction of dynamic biological networks. Our method consists of two components: statistical significance testing of model coefficients and penalized/constrained optimization. A partial least squares (PLS) with statistical significance testing acts as a supervisory-level filter to extract the most informative components of the network from a data set. Then, LASSO with extra weights on the smaller parameters identified in the first layer is employed to retain the main predictors and to set the smallest coefficients to zero. We present two case studies to compare the relative performance of DPLASSO and LASSO in terms of several metrics, such as sensitivity, specificity, and accuracy. The first case study employs a synthetic data set; it demonstrates that DPLASSO substantially improves network reconstruction in terms of accuracy and specificity. The second case study relies on simulated data sets for cell division cycle of fission yeast and shows that DPLASSO overall outperforms LASSO and PLS in terms of sensitivity, specificity, and accuracy. Combining PLS with statistical significance testing and LASSO provides good performance with respect to several metrics. DPLASSO is well suited for reconstruction of networks with low and moderate density. For high-density networks, high specificity is desired, making PLS a more suitable approach.

Dynamic biological networks model changes in the network topology over time. However, often the topologies of these networks are not available at specific time points. Existing algorithms for studying dynamic networks often ignore this problem and focus only on the time points at which experimental data is available. In this paper, we develop a novel alignment based network construction algorithm, ANCA, that constructs the dynamic networks at the missing time points by exploiting the information from a reference dynamic network. Our experiments on synthetic and real networks demonstrate that ANCA predicts the missing target networks accurately, and scales to large-scale biological networks in practical time. Our analysis of an E. coli protein-protein interaction network shows that ANCA successfully identifies key temporal changes in the biological networks. Our analysis also suggests that by focusing on the topological differences in the network, our method can be used to find important genes and temporal functional changes in the biological networks.

Dynamic biological networks model changes in the network topology over time. However, often the topologies of these networks are not available at specific time points. Existing algorithms for studying dynamic networks often ignore this problem and focus only on the time points at which experimental data is available. In this paper, we develop a novel alignment based network construction algorithm, ANCA, that constructs the dynamic networks at the missing time points by exploiting the information from a reference dynamic network. Our experiments on synthetic and real networks demonstrate that ANCA predicts the missing target networks accurately, and scales to large biological networks in practical time. Our analysis of an E. coli protein-protein interaction network shows that ANCA successfully identifies key temporal changes in the biological networks. Our analysis also suggests that by focusing on the topological differences in the network, our method can be used to find important genes and temporal functional changes in the biological networks.

Synchronization is an omnipresent phenomenon in the dynamics of complex neuronal networks, emerging between single neurons as the simultaneous generation of action potentials and on larger spatial scales in the collective oscillations of neuronal ensembles. Synchronized neuronal activity is connected to various brain functions, neuronal processing and coding but is also associated with brain diseases. Several regulatory mechanism in the brain act locally by changing the dynamical properties of individual neurons or their synaptic connections. Understanding how local properties affect or even control the collective synchronization dynamics thus may provide helpful insights for the study of e.g. pathological synchronization or information transmission in the brain. In this dissertation, we theoretically and experimentally study how local properties of neurons or groups of neurons affect network wide synchronization, dynamic grouping and information routing. First, we propose and derive a general model of pulse-coupled neuronal threshold units with a partial reset that captures the response of neurons to supra-threshold stimulation. We analytically show that this partial reset controls a sequence of desynchronizing bifurcations that destabilize synchronized groups of neurons in the collective network dynamics. Moreover, we develop a general mathematical formalism to study the phase space structure of pulse-coupled units with delayed interactions and reveal that the partial reset controls a novel type of bifurcation scenario from unstable attractor networks prevalent in units with delayed pulse-coupling to heteroclinic switching dynamics. Second, we show that the excitability type of neurons, i.e. their intrinsic characteristic dynamics of generating action potentials, can be changed dynamically. For the general class of conductance based neuron models we analytically derive the bifurcation structure of the neuronal excitability transition and show that it can be induced by a change in neuronal morphology or in leak conductance. Using dynamic patch clamp experiments we confirm the main theoretical predictions, including a qualitative change in the relation between input current to output spike rate, a transition from integration to resonance properties and a region of bistable dynamics. The results indicate that synaptic activity is sufficient to dynamically induce this neuronal excitability switch, thereby providing a flexible mechanism for the dynamic control of synchronization and grouping of neurons in the collective network dynamics. Third, we study the impact of local changes on the information flow in neuronal networks undergoing collective neuronal oscillations. For the general class of stochastic phase-reduced oscillator networks we derive expressions for the delayed mutual information between clusters as a function of the underlying network structure. We use this theory to reveal how information can be rerouted dynamically by switching between different dynamical states. In hierarchical clustered networks we further show how local changes within a group of neurons control the global inter-cluster information flow. Finally, we confirm these findings in a more biophysical realistic network model of spiking neurons undergoing collective gamma oscillations and extend the results to information transfer in the precisely timed spike patterns.

Understanding the macro‐scale flow characteristics in the fractured vadose zone is of great importance for subsurface hydrological and environmental applications. Here we develop an idealized fracture network model composed of a series of linked intersections, aiming to reveal the roles of local fluid flow, storage and splitting behaviors at intersections in controlling macroscopic unsaturated flow in a fracture network. By setting different local flow rules, unsaturated flow dynamics and structure in networks are systematically investigated. Numerical simulations suggest that avalanche infiltration mode, that is, sudden release of a large amount of water from the network, emerges spontaneously, and is modulated by the local splitting behavior. In terms of water infiltration structure, we find that uneven liquid splitting at intersections inevitably leads to preferential flow in networks. The preferential paths strongly rely on the competition between gravitational and capillary forces, relating to network structure and water saturation. When flow is dominated by gravity, preferential paths extend along large‐aperture routes; conversely, when flow is dominated by capillarity, the small‐aperture paths are preferred. In terms of infiltration dynamics, we show that the power spectral density of the water saturation time series in the network follows a power law with an exponent of −2 for all simulations with different structural parameters and local flow rules, suggesting a universal self‐organized criticality behavior for unsaturated flow in fractured rocks. The improved understanding from this study may shed new light on the complex flow dynamics for unsaturated flow in fractured media.

A travelling wave approach to power flow in structural networks

SummaryCOVID-19 (coronavirus disease 2019) is a respiratory illness caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Although the pathophysiology of this virus is complex and largely unknown, we employed a network-biology-fueled approach and integrated transcriptome data pertaining to lung epithelial cells with human interactome to generate Calu-3-specific human-SARS-CoV-2 interactome (CSI). Topological clustering and pathway enrichment analysis show that SARS-CoV-2 targets central nodes of the host-viral network, which participate in core functional pathways. Network centrality analyses discover 33 high-value SARS-CoV-2 targets, which are possibly involved in viral entry, proliferation, and survival to establish infection and facilitate disease progression. Our probabilistic modeling framework elucidates critical regulatory circuitry and molecular events pertinent to COVID-19, particularly the host-modifying responses and cytokine storm. Overall, our network-centric analyses reveal novel molecular components, uncover structural and functional modules, and provide molecular insights into the pathogenicity of SARS-CoV-2 that may help foster effective therapeutic design.