Nonlinear Feedback Loops Research Articles

Capacity investment portfolio optimization considering EV charging flexibility: A heuristic algorithm-informed system dynamics approach

Orderly charging of electric vehicles (EVs) functions as a flexible tool for peak shaving to help integrate renewable energy sources effectively. Coordinating investments in charging resources and generation resources can enhance social benefits while ensuring the charging needs of EVs are met. This study aims to optimize the long-term investment strategies for these resources using a heuristic algorithm-informed system dynamic (SD) approach. Firstly, a SD model is developed to simulate the long-term interactions among generation resources, EVs, and power demand, capturing their dynamic relationships. Then, the fixed feedback functions of investment parameters in the SD model are replaced with an optimization model, enabling parameter optimization for environmental and economic objectives. Given that the process must quantify the aforementioned long-term interrelationships with potential high-order, nonlinear feedback loops, the solution is implemented using Particle Swarm Optimization (PSO). Data from a specific province in China was used for the case study. The results show that the optimized investment portfolio reduced carbon costs and total investment by 2.4% and 22%, respectively, while total social costs decreased by 17% compared to the pre-set investment strategy. Lastly, we also conducted sensitivity analysis and algorithm comparison.

Broadband electro-optic chaotic system using coupling mutual feedback for intensity and phase chaos generation

An innovative dual-coupled dispersive electro-optic chaotic system utilizing two interlinked nonlinear feedback loops is introduced and demonstrated experimentally. This system efficiently converts phase chaos into intensity chaos while incorporating dispersion, achieved by integrating a broadband chirped fiber Bragg grating (CFBG) into a dual-loop opto-electronic oscillator (OEO) system. Consequently, this leads to the generation of broadband intensity and phase chaos with heightened complexity. Experimental findings indicate that the system achieved up to 24 GHz of 80% bandwidth and 35.5 GHz of 10 dB bandwidth for intensity chaos carriers, and up to 26 GHz of bandwidth with 40.52 GHz of 10 dB bandwidth for phase chaos carriers. The approach features a straightforward structure and mitigates delay characteristics inherently within the system itself. This two-dimensional chaotic source presents potential for secure communications in high-speed Quadrature Amplitude Modulation (QAM) systems.

Automatic design of gene regulatory mechanisms for spatial pattern formation

Gene regulatory mechanisms (GRMs) control the formation of spatial and temporal expression patterns that can serve as regulatory signals for the development of complex shapes. Synthetic developmental biology aims to engineer such genetic circuits for understanding and producing desired multicellular spatial patterns. However, designing synthetic GRMs for complex, multi-dimensional spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given two-dimensional spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms—including the number of genes necessary for the formation of the target spatial pattern—we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover complex genetic circuits producing spatial patterns.

A system dynamics model for vehicle fleet transformation towards energy efficiency and low-carbon development: A case study of Sri Lanka and its strategies

Improving the energy efficiency of a vehicle fleet is a complex task that can be identified as having multiple variables and nonlinear feedback loops influenced by different mobility, socio-economical, and environmental factors. Due to the prevailing concerns on the fuel economy and vehicular emissions, formulating a clear policy for electric and other alternative mobility forms requires a clear decision support tool to adequately consider the complexities involved. This paper presents a novel System Dynamics (SD) approach based on the cause-and-effect analysis and feedback loop structures as a suitable tool. The proposed SD model comprises four sub-models: socio-economic, new vehicle registrations, environmental influence, and fuel economy and e-mobility policy measures. The study presents the analysis of historical data and results from the impact analysis of fuel economy policies in Sri Lanka, including the introduction of electric mobility. The authors leveraged the Vensim SD software package for modelling, expert-in-the-loop sensitivity analysis and optimization. Three strategic fuel economy and e-mobility policy intervention scenarios have been developed to estimate the forecasted fuel economy for Four-Wheeled Passenger Vehicles (FWPVs) as per strategic interventions to change the fuel type of new vehicles registered. It is shown that hybrid and electric FWPVs can improve fuel economy by between 13 and 39% by 2030.

An adjustable machine learning gradient boosting-based controller for PV applications

Traditional Proportional, Integral, and Derivative (PID) controllers are employed in most industrial control applications because they are simple and easy to implement. However, they are fallible and exhibit poor performance in complicated, non-linear, time-delayed systems, and noisy feedback loops. In photovoltaic systems applications such as maximum power point (MPP) tracking, PI controller performance in low irradiance levels, varying load conditions, and partial shading scenarios is considerably inefficient in tracking the corresponding reference current, which generates MPP and causes considerable steady-state error. Machine learning can be used with selective input/output data from the PI controller to build a model that has the ability to adjust in case of steady-state error. Thus, an adjustable Machine Learning Gradient Boosting-based (MLGB) controller with a PV module and a DC-DC boost converter is proposed in this work. To create the raw dataset, a PI controller was simulated, and the input/output signals were recorded. Data preprocessing, utilizing feature engineering and Shapley Additive Explanations (SHAP) values, was used to explain the dynamic behavior of each feature, the inter-feature dependability, and their significance with reference to the model output. Hyperparameters were tuned with cross-validation while the model was being created using the CatBoost method. To assess the adjustment of each feature to minimize the error, particularly for lower irradiance values, varying load conditions, and partial shading, a regression model was built. Using the MATLAB Simulink Environment, a complete system controlled by both the PI and the MLGB controller was developed and tested. A random irradiance level fluctuation profile, along with varying load and partial shading scenarios, was used to compare three controllers, namely the PI, conventional MLGB, and adjusted MLGB controllers, to see how they respond to rapidly changing environmental conditions. It has been proven through a thorough simulation analysis that the novel adjustable MLGB controller exhibits good tracking performance to follow the DC-DC boost converter's inductor current. When compared to the traditional PI controller, the new controller exhibits better results in terms of steady-state behavior and transient responsiveness in general, with a much lower mean (3.059E-03), median (1.908E-03), and RMS value (2.168E-02) of the signal error under various conditions.

A modified frequency–time domain method for nonlinear aeroelastic systems with initial conditions

The frequency–time domain method is a very powerful tool for analyzing nonlinear aeroelastic systems; however, it is limited to obtaining steady-state solutions. To investigate nonlinear dynamic behaviors with initial conditions, a modified frequency–time domain method is proposed. Initial conditions, represented as pseudo forces, are introduced into the nonlinear feedback loops and are subsequently transformed from the time domain into the frequency domain. Hence, the proposed method allows nonlinear responses with initial conditions. Owing to the characteristics and limitations of this method, certain skills are presented to simulate both accurately and efficiently. Numerical results are provided for, in addition to the Van Der Pol equation, a two-degree-of-freedom airfoil section, and a three-degree-of-freedom aeroelastic typical section with control surface freeplay. Consequently, the feasibility of introducing initial conditions is validated. The comparison with the Runge–Kutta algorithm demonstrates the accuracy and efficiency of the proposed method, as an alternative to time-marching approaches. Furthermore, several key parameters, such as the sampling frequency and ending time of convolution integral, are investigated to explore the efficiency. The sensitivity of parameters and calculation methods of convolution integral is observed, which contributes to the strategies for adequate accuracy.

The Butterfly Effect and its Implications for Resilience in Complex Socio-Ecological Systems

This study delves into the intriguing concept of the Butterfly Effect and its implications for resilience in complex socio-ecological systems. Drawing upon chaos theory, the Butterfly Effect posits that minute initial changes can yield substantial and unforeseen outcomes in dynamic systems. The research investigates how the Butterfly Effect influences the resilience of intricate systems, such as urban ecosystems, global supply chains, and social networks, when confronted with environmental, economic, or social disruptions. By scrutinizing case studies and employing mathematical modeling, this study seeks to unveil the nonlinear dynamics, tipping points, and feedback loops that amplify or mitigate the effects of minor perturbations in complex systems. Moreover, it explores how comprehending the Butterfly Effect can inform strategies for augmenting the resilience of socio-ecological systems, including adaptive management, scenario planning, and community engagement. The study also explores the ethical and governance considerations arising from the unpredictability and interconnectedness inherent in complex systems. It highlights the need for inclusive decision-making processes that account for diverse perspectives and values. Additionally, it emphasizes the importance of adaptive governance approaches that allow for flexible responses to changing circumstances and evolving knowledge. By delving into the Butterfly Effect and its implications, this research endeavors to contribute to the development of strategies and policies that foster resilience in the face of uncertainty and promote sustainable development in complex socio-ecological systems. It recognizes the need for integrated approaches that consider the interdependencies and feedbacks between social, economic, and environmental dimensions. Ultimately, this study underscores the significance of understanding the Butterfly Effect as a lens through which to view and manage complex systems. By acknowledging the potential for cascading effects from minor changes, decision-makers and practitioners can adopt proactive measures to enhance system resilience. This research calls for further exploration of the Butterfly Effect across different scales and contexts to better grasp its implications and potential applications. In conclusion, the Butterfly Effect serves as a powerful concept for understanding the dynamics of complex socio-ecological systems. This research contributes to the existing body of knowledge by shedding light on its implications for resilience and providing guidance for decision-making and policy development in an uncertain and interconnected world.

Human recognition with the optoelectronic reservoir-computing-based micro-Doppler radar signal processing.

Current perception and monitoring systems, such as human recognition, are affected by several environmental factors, such as limited light intensity, weather changes, occlusion of targets, and public privacy. Human recognition using radar signals is a promising direction to overcome these defects; however, the low signal-to-noise ratio of radar signals still makes this task challenging. Therefore, it is necessary to use suitable tools that can efficiently deal with radar signals to identify targets. Reservoir computing (RC) is an efficient machine learning scheme that is easy to train and demonstrates excellent performance in processing complex time-series signals. The RC hardware implementation structure based on nonlinear nodes and delay feedback loops endows it with the potential for real-time fast signal processing. In this paper, we numerically study the performance of the optoelectronic RC composed of optical and electrical components in the task of human recognition with noisy micro-Doppler radar signals. A single-loop optoelectronic RC is employed to verify the application of RC in this field, and a parallel dual-loop optoelectronic RC scheme with a dual-polarization Mach-Zehnder modulator (DPol-MZM) is also used for performance comparison. The result is verified to be comparable with other machine learning tools, which demonstrates the ability of the optoelectronic RC in capturing gait information and dealing with noisy radar signals; it also indicates that optoelectronic RC is a powerful tool in the field of human target recognition based on micro-Doppler radar signals.

The Complexity Effect in U.S.-Turkey Relations: The Restructuring of the Middle East Regional Security

This paper proposes a discussion of its core theoretical argument that the international order is more complex than the theories generated by traditionalist state-centric approaches and critical approaches, including the regional security complex approach. The complexity approach highlights the sensitive dependency of complex systems on the nonlinear feedback loops and dynamic interactions by which the longer term reactions to the behavior of actors could set off actions-reaction spirals. This path dependency is evident in the erosion of U.S.-Turkey relations which is a cause and a consequence of the realignment in the international system and the Middle East regional system.

Physiological significance of bistable circuit design in metabolic homeostasis: role of integrated insulin-glucagon signalling network.

Insulin and glucagon signalling pathways operate in a synchronised manner to regulate metabolic homeostasis in different physiological conditions (like postprandial, fasting & exercise). Non-linear positive feedback loops involving effector molecules such as AKT and PKA in anabolic and catabolic signalling modules have a key role in eliciting bistable response in these networks. We have reviewed literature on insulin and glucagon signaling pathways in metabolic regulation along with the relevance of bistability in homeostasis. An ODE-based integrated signalling network model is used to simulate insulin and glucagon resistance conditions. Modifications in homeostatic to anabolic and catabolic switch activation thresholds are analyzed, indicating the effectiveness of insulin and glucagon signalling pathways in normal and diseased conditions. Perturbation analysis of the kinetic model provides valuable insights on bistability and its characterization with respect to endocrine inputs. Disturbance in bistability is linked with dysregulation of plasma macronutrient levels (glucose, fatty acids and amino acids) in abnormal conditions like insulin and glucagon resistance, which is associated with obesity, type 2 diabetes mellitus and non-alcoholic fatty liver disease. This article highlights the role of Systems biology approach in explaining plausible mechanisms underlying metabolic abnormalities. It captures essential crosstalk and feedback mechanisms that play a key role in inducing bistable response in a variety of physiological situations, as well as hints at how to reverse insulin and glucagon resistance.

Mapping farmer perceptions, Conservation Agriculture practices and on-farm measurements: The role of systems thinking in the process of adoption

CONTEXTConservation Agriculture (CA) usage, particularly in Southern Africa, has remained low with lower yield, higher weed pressure and lower soil quality cited as reasons for ‘disadoption’. OBJECTIVEUsing a detailed case study of 50 farmers in two villages in Cabo Delgado (Northern Mozambique), this study seeks to test the hypothesis that farmers' perceptions of CA are associated with distinctly different ‘mental models’ and if these "ways of thinking" overlap with farmers' identified/self-identified groupings (e.g. CA users, ‘disadopters’ and conventional tillage users). Secondly, we examine whether these different mental models (perceptions) are associated with actual differences in on-farm measurements. Finally, we explore the hypothesis that ‘systems thinking’ (i.e., understanding nonlinear causal relationships and internal feedback loops that drive a complex system) and CA usage are positively associated. METHODSFuzzy Cognitive Mapping (FCM) was used to elicit representations of farmers' mental models. To explore the association between farmers' mental models of CA/conventional practices and on-farm measurements we evaluated cowpea aboveground biomass, yield, weed cover, and soil quality parameters from the farmer's main plot. We drew on network analysis to measure structural metrics of cognitive maps that provide important information about a person's mental model (perceptions) of causal interdependencies of farming dynamics. RESULTS AND CONCLUSIONSWe find evidence of two data-driven distinct clusters of farmers' mental models that are in relative alignment with farmers' identified/self-identified groupings. Cluster 1 mainly consists of conventional users and cluster 2 mainly consists of CA users/disadopters. While no significant differences in socio-demographic variables were observed, clusters of mental models were associated with key differences in on-farm measurements. Importantly, cluster 1, who tended to be conventional users, had lower yields, lower soil cover, significantly lower carbon stock and higher weed coverage than cluster 2. Soil quality indicators were higher in cluster 2 as were farmers' overall revenue per hectare. Moreover, cluster 2 had significantly higher degrees of ‘systems thinking’ (measured through complex network analysis of graphical mental models) than cluster 1 which had higher forms of linear thinking. We argue that higher forms of experiential learning and practice of CA relate to higher degrees of systems thinking and stronger positive perceptions of CA, even among the CA ‘disadopters’. SIGNIFICANCEOur findings highlight the importance of systems thinking abilities and inclusion of biophysical, socio-economic and mental modelling variables rather than simple binary measurements which may have led to erroneous conclusions on CA and thus has implications for how CA is understood and promoted in future.

Integrating watershed and ecosystem service models to assess best management practice efficiency: guidelines for Lake Erie managers and watershed modellers

Lake Erie is the shallowest and most biologically productive system of the Great Lakes, surrounded by large urban, industrial, and agricultural areas. This combination prompted extensive efforts to promote best management practices (BMPs) to mitigate non-point source pollution in Lake Erie’s watershed. Recent technical and conceptual advancements caution that significant variability exists in the BMP efficiency to reduce the severity of runoff and nutrient concentrations due to differences in implementation, the dependence of operational performance on local soil and climatic conditions, storm events and seasonality, and declining performance over time owing to imperfect maintenance. Given the uncertainty surrounding the design and efficiency of BMPs in abating non-point source pollution, our primary objective is to review the critical strengths and potential weaknesses of nine agricultural BMPs promoted for use in the Lake Erie watershed. We examine the capacity of the current generation of watershed process-based models to recreate possible BMP-mediated changes in the water and nutrient cycles. After reviewing modelling strategies (dynamic, external forcing, and empirical) to recreate non-linear watershed responses and feedback loops to BMP efficiency, our study recommends adopting dynamic representations of the interplay among key mechanisms, like soil moisture, water table, nutrient availability, plant uptake, and subsequent growth. Notwithstanding the increased sophistication of complex mathematical models, their learning capacity is usually compromised by the coarse resolution of environmental data and limited empirical knowledge to accurately parameterize environmental properties and partially understood biogeochemical processes. Moreover, BMPs may differentially affect the provisions of an ecosystem (e.g., a BMP may amplify one ecosystem service while dampening another). In this context, we highlight the expression of the value of ecosystem services in monetary and non-monetary terms as a critical information piece when considering trade-offs among costly and diverse policy decisions. Our study also examines the degree to which different types of valuation methods, socioeconomic models, and data have been operationalized in Lake Erie. Consistent with the Integrated Watershed Management framework, we advocate the adoption of a rigorous mass-balance approach to assess the impact of BMPs on nutrient cycles, as well as the integration of the projected environmental improvements with terrestrial ecosystem services, beneficial use impairments, and aquatic ecosystem services. The proposed strategy has the potential to improve the decision-making process by identifying cost-effective management actions and balancing different goods and services provided by the agroecosystems at different time scales.

Enhancing adoption of climate services through an innovation systems approach

Recent years have marked the emergence of the innovation systems approach as a shift from the conventional linear models of technology transfer. Linear technology diffusion models hinder participatory approaches of local actors such as smallholder farmers and regards them as spectators in the development process, which impedes wide adoption of technology by the intended beneficiary. This article sought to understand the potential of the innovations systems approach as an incentive to enhance the adoption of climate services by smallholder farmers through regarding them and other relevant stakeholders as part of the process, fostering knowledge sharing and interactive learning. The methodology included stakeholder/actor identification, mapping of stakeholder linkages, capacity building and active involvement of stakeholders through the climate services process. The results showed that unlike the conventional linear knowledge delivery process, the innovation systems approach takes into consideration the complex processes that are highlighted by non-linear processes, feedback loops, and other complex interactions that occur among heterogeneous actors. As such in place of the linear knowledge delivery approach, a more systems approach is necessary to help mobilize science and technology such as climate services to deliver benefits, which has the potential to enhance access, salience, credibility and legitimacy of the scientific information.

Continuous Dynamic Modeling of Regulated Cell Adhesion: Sorting, Intercalation, and Involution

Cell-cell adhesion is essential for tissue growth and multicellular pattern formation and crucial for the cellular dynamics during embryogenesis and cancer progression. Understanding the dynamical gene regulation of cell adhesion molecules (CAMs) responsible for the emerging spatial tissue behaviors is a current challenge because of the complexity of these nonlinear interactions and feedback loops at different levels of abstraction—from genetic regulation to whole-organism shape formation. To extend our understanding of cell and tissue behaviors due to the regulation of adhesion molecules, here we present a novel, to our knowledge, model for the spatial dynamics of cellular patterning, growth, and shape formation due to the differential expression of CAMs and their regulation. Capturing the dynamic interplay between genetic regulation, CAM expression, and differential cell adhesion, the proposed continuous model can explain the complex and emergent spatial behaviors of cell populations that change their adhesion properties dynamically because of inter- and intracellular genetic regulation. This approach can demonstrate the mechanisms responsible for classical cell-sorting behaviors, cell intercalation in proliferating populations, and the involution of germ layer cells induced by a diffusing morphogen during gastrulation. The model makes predictions on the physical parameters controlling the amplitude and wavelength of a cellular intercalation interface, as well as the crucial role of N-cadherin regulation for the involution and migration of cells beyond the gradient of the morphogen Nodal during zebrafish gastrulation. Integrating the emergent spatial tissue behaviors with the regulation of genes responsible for essential cellular properties such as adhesion will pave the way toward understanding the genetic regulation of large-scale complex patterns and shapes formation in developmental, regenerative, and cancer biology.

System Dynamic Model for Simulating Demand-Supply Interaction of Railway Express Freight System

Express freight transportation is a rich seam of profit for China railway, and railway express freight system is a complex system with multiple variables and nonlinear feedback loops. This paper presents a System Dynamic Model for simulating the interaction between demand and supply of railway express freight system in China. The model consists of three submodels including economic environment, demand, supply, and investment, and its validity is verified by running in Vensim DDS software using historical data. In the simulation of period 2000–2025, the three variables are taken as control variables including growth rate of the national economy, railway express freight rate, and investment in fixed railway assets. Three scenarios for each control variable are simulated, and their effects are analyzed to provide beneficial reference for regulating the demand-supply gap of railway express freight. The simulation demonstrated that raising freight rate, adding investment in fixed railway assets, and decelerating economic growth rate are all effective ways to shrink the demand-supply gap of railway express freight. The model can be used to forecast the transport demand of railway express freight and test the outcomes of demand-supply regulating measures.

Dynamic Aeroservoelastic Response with Nonlinear Structural Elements

Linear structural dynamics, unsteady aerodynamics, control system, and actuator models are combined for linear aeroservoelastic equations of motion that are augmented with nonlinear feedback loops based on the increased-order modeling approach. Although the linear equations are formulated in the frequency domain for best combined efficiency, accuracy, and robustness in industrial environment, the nonlinear feedback loops are modeled in the time domain to provide maximal flexibility in adding nonlinear effects in all the involved disciplines. The linear equations are solved first to provide a baseline response to deterministic or stochastic gusts, maneuver commands, or direct-force excitations using fast Fourier transform techniques. Nonlinear effects are then added in a time-marching process that modifies the linear solution using convolution integrals. The numerical process was used in the Dynresp code that was recently developed as a framework for industrial applications and research in the area of nonlinear structural dynamics. The procedure is outlined with emphasis on structural nonlinearities using a fictitious-mass technique. The numerical example exhibits limit-cycle oscillations due to actuator nonlinearities.

Challenges in the Identification of Discrete Time Block Oriented Models for Continuous Time Nonlinear Systems

Block oriented nonlinear models capture the dynamics of a nonlinear system with linear dynamic sub-systems (L), the nonlinear behavior is modeled using static nonlinear subblocks (N). In this paper we focus on three important theoretical and practical challenges that need to be addressed when the class of systems is generalized from the simple but very popular Wiener, Hammerstein, Hammerstein-Wiener or Wiener-Hammerstein systems to more complex nonlinear systems, including nonlinear feedback loops: 1) Dealing with complex blockoriented models: initial (structure revealing) tests; 2) Testing of candidate semi-physical blockoriented models; and 3) Approximating continuous time nonlinear systems by a discrete time recursive model. Experimental illustrations and verifications are shown.

The agriculture’s role for sustainable and inclusive development

Sustainable development is characterized by interconnected social, economic, and ecological aspects and it is at the core value of the worldwide economy. A participatory and accountable framework is a prerequisite for inclusive and sustainable development; so power is redistributed, reducing uncertainty, inequality and promoting shared prosperity. Despite its crucial importance and relevance, barriers remain in making progress towards its implementation, in particular for the agricultural sector. The purpose of this paper is to investigate the role of agriculture for sustainable and inclusive development, highlighting environmental, economic and social dimensions. Then, we aim at providing policy-makers more accessible results on trade-offs of alternative measures for greening the agri-food system. The research is based on method of analysis based on an extensive review of research evidence related in particular to Climate Smart Agriculture (CSA). Focusing on CSA role, a set of priority actions for greening systems are drawn up. Results of analysis provide an insight on a new System Dynamics model able to represent the complex causal relations and non-linear feedback loops among key dimensions and actors of sustainable development. Furthermore investments/ measures coordination in agriculture and higher farmers’ knowledge are crucial driver in reaching this ambition.

Logarithmic and power law input-output relations in sensory systems with fold-change detection.

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.

Structural Identification of Nonlinear Dynamic Biomolecular Feedback and Feedforward Loops

Many biomolecular networks are still widely unknown. With high structural uncertainties, bottom-up identification based on model discrimination tends to fail because of combinatorially many possible model structures. Top-down approaches, in contrast, describe general signal processing properties, rather than specific mechanisms. Most of these approaches originated in engineering disciplines where linearity is commonly (approximately) given, but naturally evolved networks exhibit a rather high degree of nonlinearity. Here, we present a top-down structural identification method that is not only applicable to nonlinear biomolecular networks, but indeed requires the network under study to be nonlinear. Similar to traditional frequency domain analysis, we apply an oscillatory input signal to a biomolecular network. However, instead of varying the frequency, we vary the mean value of the oscillatory signal to detect, discriminate, and partly characterize single feedback and feedforward loops in nonlinear networks.