Feedback Loop Structure Research Articles

A mathematical model for the role of dopamine-D2 self-regulation in the production of ultradian rhythms.

Many self-motivated and goal-directed behaviours display highly flexible, approximately 4 hour ultradian (shorter than a day) oscillations. Despite lacking direct correspondence to physical cycles in the environment, these ultradian rhythms may be involved in optimizing functional interactions with the environment and reflect intrinsic neural dynamics. Current evidence supports a role of mesostriatal dopamine (DA) in the expression and propagation of ultradian rhythmicity, however, the biochemical processes underpinning these oscillations remain to be identified. Here, we use a mathematical model to investigate D2 autoreceptor-dependent DA self-regulation as the source of ultradian behavioural rhythms. DA concentration at the midbrain-striatal synapses is governed through a dual-negative feedback-loop structure, which naturally gives rise to rhythmicity. This model shows the propensity of striatal DA to produce an ultradian oscillation characterized by a flexible period that is highly sensitive to parameter variations. Circadian (approximately 24 hour) regulation consolidates the ultradian oscillations and alters their response to the phase-dependent, rapid-resetting effect of a transient excitatory stimulus. Within a circadian framework, the ultradian rhythm orchestrates behavioural activity and enhances responsiveness to an external stimulus. This suggests a role for the circadian-ultradian timekeeping hierarchy in governing organized behaviour and shaping daily experience through coordinating the motivation to engage in recurring, albeit not highly predictable events, such as social interactions.

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.

309 Dairy Cow Response to Heat Stress Modeled with a System Dynamics Approach

Abstract Modeling the individual animal response to heat stress (HS) conditions is challenging because of the complex interactions that characterize the system behavior. In explaining the resulting animal behavior, the dynamicity, nonlinearity, and delays in the HS response are often unaccounted for or misinterpreted. The system dynamics (SD) methodology, a mathematical modeling approach based on feedback loop structures, allows for modeling and understanding the behavior of complex systems over time. By applying SD methodology, this study developed a preliminary conceptual model to capture the cow response and observed milk yield (MY) under HS. The data on the temperature-humidity index (THI) and MY used for model development were collected from a dairy cattle farm in August 2021. The parameters related to the HS response of 20 selected cows were used for calibration and parameterization of the model. To minimize the effect of the lactation stage on milk production and model results, 20 cows were selected for days in milk (DIM) to be between 70 and 220 d. After the parameter calibration using MY data, it was found that the historical data pattern of 13 out of 20 cows followed the expected behavioral pattern generated by the model. In contrast, the behavior of the remaining seven cows did not align with that generated by the model. Therefore, based on their patterns, the cows were identified as fitting or non-fitting the model’s structure. The structure of the model captured the effect of HS on fitting cows with high accuracy (mean absolute percentage error, MAPE < 5%; R2 > 0.6; concordance correlation coefficient, CCC > 0.6). At the same time, the behavior of the non-fitting cows could not be explained by the defined parameter space. We believe they either had heat-resistant behavior or experienced different biological delays than average. Based on the obtained results, the evaluation of parameter values should be done only for the fitting cows, as the work aimed to develop a model to understand the HS response. The behaviors generated by the model can help farmers and decision-makers distinguish heat-sensitive from heat-tolerant cows and quantify the animal response in terms of MY so that mitigation strategies can be implemented.

All-optical reservoir computing system based on polarization dynamics

Reservoir computing (RC) is a simplified recurrent neural network and can be implemented by using a nonlinear system with delay feedback, thus it is called delay-based RC. Various nonlinear nodes and feedback loop structures have been proposed. Most of existing researches are based on the dynamical responses in intensity of the nonlinear systems. There are also a photoelectric RC system based on wavelength dynamics and an all-optical RC based on the phase dynamics of a semiconductor laser with optical feedback, as well as so-called polarization dynamics of a vertical cavity surface emitting laser (VCSEL). However, these VCSEL-RCs actually are based on the intensity dynamics of two mutually orthogonal polarization modes, or polarization-resolved intensity dynamics. The RC based on rich dynamical responses in polarization has not yet been found. A semiconductor optical amplifier (SOA) fiber ring laser can produce rich dynamical states in polarization, and is used in optical chaotic secure communication and distributed optical fiber sensing. To further expand the application of polarization dynamics of the SOA fiber ring laser and open up a new direction for the research of optical RC neural network, an all-optical RC system based on polarization dynamics of the ring laser is proposed. The ring laser is used as the reservoir, and the SOA as the nonlinear node. After the input signal is masked according to a synchronization scheme, it is injected into the reservoir by intensity modulation for a continuous wave generated by a superluminescent light emitting diode (SLED). The dynamical response in polarization of the ring laser is detected by a polarizer and a photodetector. The influences of the SOA operation current, output power of the SLED and attenuation of a variable optical attenuator (VOA) in the fiber loop on the polarization dynamic characteristic (mainly referring to the output degree of polarization) of the laser are analyzed experimentally. The fading memory and nonlinear response of the RC system based on the polarization dynamic response and intensity dynamic response are compared experimentally. The influences of output power of the SLED and attenuation of the VOA on fading memory, consistency and separation of the RC system based on the two kinds of dynamic responses are investigated experimentally. Thus the range of the VOA attenuation is determined. The network performance of the polarization dynamics RC system is evaluated by processing a Santa Fe time series prediction task and a multi-waveform recognition task. The normalized mean square error can be as low as 0.0058 for the time series prediction task, and the identification rate can be as high as 100% for the recognition task under the appropriate system parameters and only 30 virtual nodes. The experimental results show that the polarization dynamics RC system has good prediction performance and classification capability, which are comparable to the existing RC system based on intensity dynamics of the ring laser. The system can be expected to process two tasks in parallel when the polarization dynamics and intensity dynamics are used at the same time.

Hydropolitical System Archetypes: Feedback Structures, Physical Environments, Unintended Behaviors, and a Diagnostic Checklist

Hydropolitics is defined as the systematic study of conflict and cooperation in transboundary water basins, affecting around 40% of the world’s population. There has been great advancement in studies endeavoring to explore linkages between hydropolitical drivers and hydropolitical situations in transboundary basins. To add to this, we posit that hydropolitics would benefit from a system thinking approach that has remained less addressed in the literature. For this purpose, considering a transboundary basin as a system, this study is built on the main principle of system dynamics, which implies that a system’s structure determines its behavior. Incorporating system archetypes into hydropolitics can provide a framework for assessing hydropolitical behavior according to the potential structure of archetypes. In this paper, we discuss five hydropolitical system archetypes and their feedback loop structures, the required physical environments, and potential unintended behavior over time. Finally, an example of a diagnostic checklist is presented that will help riparian states recognize patterns of behavior they may face in the future. This paper lays the groundwork for gaining insight into using system archetypes in projecting plausible hydropolitical behaviors and understanding past behaviors in transboundary basins.

Dynamical Mechanism Analysis of Three Neuroregulatory Strategies on the Modulation of Seizures.

This paper attempts to explore and compare the regulatory mechanisms of optogenetic stimulation (OS), deep brain stimulation (DBS) and electromagnetic induction on epilepsy. Based on the Wilson-Cowan model, we first demonstrate that the external input received by excitatory and inhibitory neural populations can induce rich dynamic bifurcation behaviors such as Hopf bifurcation, and make the system exhibit epileptic and normal states. Then, both OS and DBS are shown to be effective in controlling the epileptic state to a normal low-level state, and the stimulus parameters have a broad effective range. However, electromagnetic induction cannot directly control epilepsy to this desired state, even if it can significantly reduce the oscillation frequency of neural populations. One main difference worth noting is that the high spatiotemporal specificity of OS allows it to target inhibitory neuronal populations, whereas DBS and electromagnetic induction can only stimulate excitatory as well as inhibitory neuronal populations together. Next, the propagation behavior of epilepsy is explored under a typical three-node feedback loop structure. An increase in coupling strength accelerates and exacerbates epileptic activity in other brain regions. Finally, OS and DBS applied to the epileptic focus play similar positive roles in controlling the behavior of the area of seizure propagation, while electromagnetic induction still only achieves unsatisfactory effects. It is hoped that these dynamical results can provide insights into the treatment of epilepsy as well as other neurological disorders.

FLAM-PUF: A Response–Feedback-Based Lightweight Anti-Machine-Learning-Attack PUF

Physical unclonable functions (PUFs) have been adopted in many resource-constrained Internet of Things (IoT) applications to provide effective and lightweight solutions for device authentication. However, an attacker can collect challenge–response pairs (CRPs) of a strong PUF, to build a machine learning (ML) model and mimic its behavior, i.e., predicting the responses of unseen challenges with high accuracy. Although several PUFs have been proposed to resist such modeling attacks, they incur high hardware overhead. Developing a PUF primitive with low hardware cost and high resistance to ML attacks is thus a crucial task. In this article, we propose the first response–feedback-based lightweight anti-ML-attack PUF (FLAM-PUF). It is only composed of one arbiter PUF (APUF) and one Galois linear-feedback shift register (LFSR), with some basic logic gates, reducing more than 62% hardware cost compared with the state-of-the-art robust strong PUFs. Specifically, FLAM-PUF leverages a cost-effective feedback loop structure to dynamically control and update the LFSR configuration. FLAM-PUF has two main characteristics: 1) it feeds back a 1-bit response in every cycle to intentionally poison the data of the CRP set for training. To resist ML-based modeling attacks, the 1-bit response can randomly update one coefficient of the feedback polynomial to implant more complex correlations into the model built by attackers and 2) it takes advantage of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n-$ </tex-math></inline-formula> bit response feedback-controlled reconfigurable Galois LFSR to enlarge the original challenge space of the APUF. Extensive experimental results show that the proposed FLAM-PUF achieves near-optimal uniformity, uniqueness, and reliability. Our scheme works well under standard attack models with public crucial initial information. In particular, the prediction accuracy of modeling attacks against FLAM-PUF is nearly 50% under the four widely used ML algorithms, i.e., support vector machines (SVMs), logistic regression (LR), covariance matrix adaptation evolution strategy (CMA-ES), and deep neural networks (DNNs), indicating excellent resistance against these ML attacks.

Hepatitis C virus risk among young people who inject drugs.

BackgroundInjection drug use (IDU) is the leading risk factor for hepatitis C virus (HCV) transmission in the U.S. While the general risk factors for HCV transmission are known, there is limited work on how these factors interact and impact young people who inject drugs (YPWID).MethodsProject data were drawn from a study of 539 New York City (NYC) residents ages 18-29 who were recruited via Respondent-Driven Sampling and, reported past-month non-medical use of prescription opioids and/or heroin. Analyses are based on a subsample of 337 (62%) who reported injecting any drug in the past 12 months. All variables were assessed via self-report, except HCV status, which was established via rapid antibody testing. Integrating the observed statistical associations with extant literature on HCV risk, we also developed a qualitative system dynamics (SD) model to use as a supplemental data visualization tool to explore plausible pathways and interactions among key risk and protective factors for HCV.ResultsResults showed a 31% HCV antibody prevalence with an overall incidence of 10 per 100 person-years. HCV status was independently correlated with having shared cookers with two or more people (AOR = 2.17); injected drugs 4–6 years (AOR = 2.49) and 7 or more years (AOR = 4.95); lifetime homelessness (AOR = 2.52); and having been incarcerated two or more times (AOR = 1.99). These outcomes along with the extant literature on HCV risk were used to develop the qualitative SD model, which describes a causal hypothesis around non-linearities and feedback loop structures underlying the spread of HCV among YPWID.ConclusionsDespite ongoing harm reduction efforts, close to a third of YPWID in the community sample have been exposed to HCV, have risks for injection drug use, and face challenges with structural factors that may be preventing adequate intervention. The qualitative SD model explores these issues and contributes to a better understanding of how these various risk factors interact and what policies could potentially be effective in reducing HCV infections.

Order‐dependent LMI‐based stability and stabilization conditions for fractional‐order time‐delay systems using small gain theorem

AbstractIn this article, based on small gain theorem, the stability, and stabilization problems for fractional‐order time‐delay systems are investigated. First, one order‐dependent and delay‐independent stability condition, and two order‐dependent and delay‐dependent stability conditions of nominal fractional‐order time‐delay systems are derived by developing different feedback loop structures. Then, by employing the proposed order‐dependent stability conditions, the robust stability conditions for fractional‐order time‐delay systems with norm‐bounded uncertainties are given. Moreover, state feedback controllers that robustly stabilize fractional‐order time‐delay systems with norm‐bounded uncertainties are obtained. The proposed results are in terms of linear matrix inequalities. With the help of LMI solvers, these criteria can be easily verified. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones.

Quantifying the optimal strategy of population control of quorum sensing network in Escherichia coli

Biological functions of bacteria can be regulated by monitoring their own population density induced by the quorum sensing system. However, quantitative insight into the system’s dynamics and regulatory mechanism remain challenging. Here, we construct a comprehensive mathematical model of the synthetic quorum sensing circuit that controls population density in Escherichia coli. Simulations agree well with experimental results obtained under different ribosome-binding site (RBS) efficiencies. We present a quantitative description of the component dynamics and show how the components respond to isopropyl-β-D-1-thiogalactopyranoside (IPTG) induction. The optimal IPTG-induction range for efficiently controlling population density is quantified. The controllable area of population density by acyl-homoserine lactone (AHL) permeability is quantified as well, indicating that high AHL permeability should be treated with a high dose of IPTG, while low AHL permeability should be induced with low dose for efficiently controlling. Unexpectedly, an oscillatory behavior of the growth curve is observed with proper RBS-binding strengths and the oscillation is greatly restricted by the bacterial death induced by toxic metabolic by-products. Moreover, we identify that the mechanism underlying the emergence of oscillation is determined by the negative feedback loop structure within the signaling. Bifurcation analysis and landscape theory are further employed to study the stochastic dynamic and global stability of the system, revealing two faces of toxic metabolic by-products in controlling oscillatory behavior. Overall, our study presents a quantitative basis for understanding and new insights into the control mechanism of quorum sensing system, providing possible clues to guide the development of more rational control strategy.

Simulation of Steady‐State Temperature Rise of Electric Heating Field of Wireless Sensor Circuit Fault Current Trigger

This article analyzes the structure of the wireless sensor circuit, considering the balance of power consumption, integration, area, noise, etc., and adopts a radio frequency wireless sensor circuit with a low‐IF structure. Through the analysis and comparison of traditional analog current trigger and digital current trigger structure, the feed‐forward current trigger structure is selected, which is composed of received signal strength indicator (RSSI) and variable gain amplifier (VGA), which achieves low power consumption, fast stabilization time, and wide dynamic range design. The received signal strength indicator adopts the form of approximate logarithmic amplifier, five‐stage double feedback loop structure, and realizes lower power consumption. In order to prevent the load current trigger from entering the speed saturation zone, a gain unit structure in which the superimposed current trigger is connected to the NMOS tube as the load is proposed. The test results show that the circuit has a good power consumption performance (1 mW) and at the same time 56.8 dB/m sensitivity. In this paper, through the analysis of the current trigger system and the analysis and comparison of the existing variable gain amplifiers, the variable gain amplifier structure composed of the folded wireless sensing unit and the index control unit is adopted. In order to reduce the power consumption of the circuit and increase the output swing, a structure in which the two‐stage folding wireless sensor unit shares the controlled voltage‐to‐current part of the circuit is proposed. Aiming at the design requirements of the system, this article discussed in detail the architecture of the entire temperature measurement node and the design parameters of the chip and completed the overall architecture design of the chip. The simulation results of the steady‐state temperature rise of the electric heating field show that the circuit has achieved an input dynamic adjustment range of more than 60 dB, the maximum power consumption is 1 mW, and the linearity error is less than 0.5 dB. The designed automatic gain control circuit is implemented in SMIC 0.18 cape CMOS process. The simulation results of the steady‐state temperature rise of the electric heating field show that the circuit has a 56 dB input dynamic adjustment range within a linear error of 1.25 dB, and the time constant is 7.55 ms, and power consumption is 2.84 mW. Through the steady‐state temperature rise simulation and test results of the electric heating field, the correctness of the design is verified and it meets the system requirements.

The dynamics of wine tourism adoption in Chile

The aim of this paper is to identify the key drivers of wine tourism adoption in Chile and their feedback loop structures through an extensive literature review supplemented by in-depth semistructured interviews of Chilean wine managers. We develop a model to quantitatively assess the impacts of these drivers on wine tourism adoption over time. We use a system dynamics modeling approach to simulate the effectiveness of wine adoption drivers based on data from 69 Chilean wine firms. To different degrees, five drivers affect wine tourists: word-of-mouth recommendations, product attractiveness, tourism services, information available on the internet, and tour operators’ recommendations. Tour operators and tourism services are critical drivers in increasing the number of wine tourists, but product attractiveness has a stronger influence over the long term.

A novel demodulation algorithm for VHF Data Broadcast signals in multi-sources augmentation navigation system

The augmentation navigation system based on multi-source information fusion can significantly improve position accuracy, and the multi-source information is usually transmitted through VHF Data Broadcast . Aiming at the burst characteristics of VHF Data Broadcast, this article proposed a novel demodulation algorithm based on open-loop structure. When a VHF Data Broadcast burst is detected, the timing recovery should be finished first, and the value of cross-correlation between the timing-recovered signal and the local training symbol is calculated to complete the frame synchronization. Then, the data-aided and non-data-aided algorithms are used to estimate the frequency offset. Finally, the phase offset is estimated and the carrier synchronization is accomplished. The simulation results demonstrate that the proposed algorithm can quickly accomplished carrier synchronization without using feedback-loop structure, and the bit error rate is less than 10−4 when the signal-to-noise ratio is greater than 17 dB, which satisfy the requirement of receiving VHF Data Broadcast signals in augmentation navigation system. Therefore, the proposed algorithm can be used for receiving VHF Data Broadcast signals.

Understanding entrepreneurial competence and capability product innovation management in agriculture: a qualitative system dynamics perspective

There are insights to be gained from the examination of innovation processes conducted by entrepreneurs in low and medium technology (LMT) sectors such as agricultural production. The research question addressed in this paper is: How can agricultural entrepreneurs innovate with largely undifferentiated and low-margin products? The research objective is to better understand the emerging articulation of factors regarding competencies and capabilities agricultural production entrepreneurs can mobilise to innovate in LMT. The syntax of qualitative system dynamics (QSD) is used to present a dynamic hypothesis of competence and capability development by agricultural entrepreneurs. The contribution is an analysis of the underlying feedback loop structure in support of knowledge management practice in LMT product, characteristic and process innovation by agricultural entrepreneurs, and could generally be useful to understand innovation management in other LMT sectors more generally.

Understanding entrepreneurial competence and capability product innovation management in agriculture: a qualitative system dynamics perspective

There are insights to be gained from the examination of innovation processes conducted by entrepreneurs in low and medium technology (LMT) sectors such as agricultural production. The research question addressed in this paper is: How can agricultural entrepreneurs innovate with largely undifferentiated and low-margin products? The research objective is to better understand the emerging articulation of factors regarding competencies and capabilities agricultural production entrepreneurs can mobilise to innovate in LMT. The syntax of qualitative system dynamics (QSD) is used to present a dynamic hypothesis of competence and capability development by agricultural entrepreneurs. The contribution is an analysis of the underlying feedback loop structure in support of knowledge management practice in LMT product, characteristic and process innovation by agricultural entrepreneurs, and could generally be useful to understand innovation management in other LMT sectors more generally.

Contrast inversion of O adatom on rutile TiO2(1 1 0)-(1 × 1) surface by atomic force microscopy imaging

Oxygen adatom on rutile TiO2(1 1 0)-(1 × 1) surface was imaged by atomic force microscopy (AFM) with atomic resolution. The atomic contrast inversion of oxygen adatom is dependent on tip-sample distance and can be obtained in both constant frequency shift and constant height mode. The origin of contrast inversion was analyzed, combining the effect of adsorbed species, feedback loop and tip apex structure. Experimental frequency shift versus distance curves around O adatom show that there is a turning-point in the constant frequency shift mode and a cross-point in the constant height mode. The repulsive force is thought to contribute to the contrast inversion of oxygen adatom. The present results show the origin of contrast inversion of oxygen adatom on rutile TiO2(1 1 0)-(1 × 1) surface and illustrate the importance of tip-height for the atomic contrast inversion of the surface adsorbate on the metal oxide surface.

A System Dynamics Approach to Mitigate Waterlog due to Urban Flood in Jorhat Town, Assam

Waterlog due to urban flood is a great threat to the urban population now-a-days. An unplanned city with illegitimate constructions and without proper drainage planning has led to this problem. Problems associated with urban floods range from relatively localized incidents to major incidents, resulting in cities being inundated from a few hours to several days. Therefore, the impact can also be widespread, including temporary relocation of people, damage to civic amenities, deterioration of water quality and risk of epidemics. The study undertakes the waterlog problem of Jorhat town, Assam, India. The paper presents a System Dynamics approach based on the cause and effect analysis and feedback loop structures. Ten factors Rainfall, Water Log, Population, Urbanisation, Cost (health and economy), Waste Material Production, Drainage Construction and Maintenance, Encroachment, Ground Percolation and Drain Capacity are considered for the causal loop diagram. The model runs in Vensim PLE software and the simulated results suggest to construct the poorly developed drains of the town and to minimise drain blockage to mitigate water log for now and coming future.

High-speed optical secure communication with an external noise source and an internal time-delayed feedback loop

We propose and experimentally demonstrate a novel physical layer encryption scheme for high-speed optical communication. A 10 Gb/s on-off keying signal is secretly transmitted over 100 km standard single-mode fiber. The intensity-modulated message is secured by the encryption mechanism, which is composed of an external noise source and an internal time-delayed feedback loop. The external noise serves as an entropy source with sufficient randomness. The feedback loop structure in the transmitter introduces a time-domain encryption key space, and a corresponding open-loop configuration at the receiver side is used for synchronization and decryption. Experiment results show the effectiveness of the proposed scheme. For a legitimate terminal, bit error rate below 10−8 can be obtained. Decryption degradations with the mismatch of different hardware parameters are researched. The time delay in the feedback loop provides a sensitive encryption key. For other hardware parameters, the system is robust enough for synchronization. Meanwhile, the time-delay signature of the loop is able to be well concealed by the external noise. Moreover, the proposed scheme can support density wavelength division multiplexing transmission with a relatively simple structure. This work also provides a new concept to establish optical secure communication by combining a time-delayed feedback chaotic system and random noise.

Homeostatic controllers compensating for growth and perturbations.

Cells and organisms have developed homeostatic mechanisms which protect them against a changing environment. How growth and homeostasis interact is still not well understood, but of increasing interest to the molecular and synthetic biology community to recognize and design control circuits which can oppose the diluting effects of cell growth. In this paper we describe the performance of selected negative feedback controllers in response to different applied growth laws and time dependent outflow perturbations of a controlled variable. The approach taken here is based on deterministic mass action kinetics assuming that cell content is instantaneously mixed. All controllers behave ideal in the sense that they for step-wise perturbations in volume and a controlled compound A are able to drive A precisely back to the controllers’ theoretical set-points. The applied growth kinetics reflect experimentally observed growth laws, which range from surface to volume ratio growth to linear and exponential growth. Our results show that the kinetic implementation of integral control and the structure of the negative feedback loop are two properties which affect controller performance. Best performance is observed for controllers based on derepression kinetics and controllers with an autocatalytic implementation of integral control. Both are able to defend exponential growth and perturbations, although the autocatalytic controller shows an offset from its theoretical set-point. Controllers with activating signaling using zero-order or bimolecular (antithetic) kinetics for integral control behave very similar but less well. Their performance can be improved by implementing negative feedback structures having repression/derepression steps or by increasing controller aggressiveness. Our results provide a guide what type of feedback structures and integral control kinetics are suitable to oppose the dilution effects by different growth laws and time dependent perturbations on a deterministic level.

Modeling Biological Oscillations: Integration of Short Reaction Pauses into a Stationary Model of a Negative Feedback Loop Generates Sustained Long Oscillations.

Sustained oscillations are frequently observed in biological systems consisting of a negative feedback loop, but a mathematical model with two ordinary differential equations (ODE) that has a negative feedback loop structure fails to produce sustained oscillations. Only when a time delay is introduced into the system by expanding to a three-ODE model, transforming to a two-delay differential equations (DDE) model, or introducing a bistable trigger do stable oscillations present themselves. In this study, we propose another mechanism for producing sustained oscillations based on periodic reaction pauses of chemical reactions in a negative feedback system. We model the oscillatory system behavior by allowing the coefficients in the two-ODE model to be periodic functions of time-called pulsate functions-to account for reactions with go-stop pulses. We find that replacing coefficients in the two-ODE system with pulsate functions with microscale (several seconds) pauses can produce stable system-wide oscillations that have periods of approximately 1 to several hours long. We also compare our two-ODE and three-ODE models with the two-DDE, three-ODE, and three-DDE models without the pulsate functions. Our numerical experiments suggest that sustained long oscillations in biological systems with a negative feedback loop may be an intrinsic property arising from the slow diffusion-based pulsate behavior of biochemical reactions.