Dynamic Processes in Regulation and Some Implications for Biofeedback and Biobehavioral Interventions

Systems theory has long been used in psychology, biology, and sociology. This paper applies newer methods of control systems modeling for assessing system stability in health and disease. Control systems can be characterized as open or closed systems with feedback loops. Feedback produces oscillatory activity, and the complexity of naturally occurring oscillatory patterns reflects the multiplicity of feedback mechanisms, such that many mechanisms operate simultaneously to control the system. Unstable systems, often associated with poor health, are characterized by absence of oscillation, random noise, or a very simple pattern of oscillation. This modeling approach can be applied to a diverse range of phenomena, including cardiovascular and brain activity, mood and thermal regulation, and social system stability. External system stressors such as disease, psychological stress, injury, or interpersonal conflict may perturb a system, yet simultaneously stimulate oscillatory processes and exercise control mechanisms. Resonance can occur in systems with negative feedback loops, causing high-amplitude oscillations at a single frequency. Resonance effects can be used to strengthen modulatory oscillations, but may obscure other information and control mechanisms, and weaken system stability. Positive as well as negative feedback loops are important for system function and stability. Examples are presented of oscillatory processes in heart rate variability, and regulation of autonomic, thermal, pancreatic and central nervous system processes, as well as in social/organizational systems such as marriages and business organizations. Resonance in negative feedback loops can help stimulate oscillations and exercise control reflexes, but also can deprive the system of important information. Empirical hypotheses derived from this approach are presented, including that moderate stress may enhance health and functioning.     

On the functional diversity of dynamical behaviour in genetic and metabolic feedback systems

Background  

Feedback regulation plays crucial roles in the robust control and maintenance of many cellular systems. Negative feedbacks are found to underline both stable and unstable, often oscillatory, behaviours. We explore the dynamical characteristics of systems with single as well as coupled negative feedback loops using a combined approach of analytical and numerical techniques. Particularly, we emphasise how the loop's characterising factors (strength and cooperativity levels) affect system dynamics and how individual loops interact in the coupled-loop systems.     

Chemical oscillations and multiple steady states due to variable boundary permeability

An analysis is made of isothermal chemical reactions occurring in a volume bounded by a membrane and immersed in a reservoir of reactants and products at fixed concentrations. The permeability of the membrane to a given species is taken to be a function of the concentration of that species or of another species. This coupling between reaction and permeation provides feedback and, even for extremely simple (one or two step) reaction mechanisms, shows the following phenomena: (i) multiple steady states, some of which are stable, some unstable; (ii) hysteresis effects; (iii) reversible and irreversible transitions between stable branches of steady states induced by variation of one parameter and dependent on the values of other parameters; (iv) oscillatory temporal approach to a stable steady state; and (v) limit cycles. A method is given for predicting in certain limiting conditions the presence of unstable permeation-reaction feedback loops; the procedure is essentially independent of the details of the reaction mechanism. The theory is proposed as an appropriate construct for certain cellular phenomena, and as one example, is compared with some experiments on glycolysis in yeast cells.     

A concept of hemopoietic regulation and its biomathematical realization

Although the amount of experimental data on the behavior of the hemopoietic system after various perturbations is considerable, a conclusive understanding of hemopoietic regulation is still absent. In the last years, we have examined murine erythropoiesis, thrombopoiesis, granulopoiesis, and stem cell hemopoiesis by means of mathematical modeling in order to identify some of the underlying principles. Our results can be summarized in four hypotheses. 1) The regulation of hemopoiesis is governed by three interrelated control loops: autoregulation of stem cells, feedback from progenitors and precursors to the stem cells, and feedback from mature cells to progenitor and precursor cells. 2) The feedback from mature cells to the progenitor and precursor cells predominantly varies the number of cell divisions taking place during hemopoietic maturation. 3) Two distinct properties of the stem cells are regulated: their cyclic activity and their self-renewal. Both are under the control of stem cell autoregulation and the feedback from progenitors and precursors. 4) A large variance in the maturation time from the stem cells to the mature cells stabilizes the hemopoietic control. The mathematical formulation of these assumptions allows us to understand a broad range of experimental observations including recovery from stem cell damage, hypoproliferative and hyperproliferative situations, and interactions between different cell lines.     

A Robust Structural PGN Model for Control of Cell-Cycle Progression Stabilized by Negative Feedbacks

The cell division cycle comprises a sequence of phenomena controlled by a stable and robust genetic network. We applied a probabilistic genetic network (PGN) to construct a hypothetical model with a dynamical behavior displaying the degree of robustness typical of the biological cell cycle. The structure of our PGN model was inspired in well-established biological facts such as the existence of integrator subsystems, negative and positive feedback loops, and redundant signaling pathways. Our model represents genes interactions as stochastic processes and presents strong robustness in the presence of moderate noise and parameters fluctuations. A recently published deterministic yeast cell-cycle model does not perform as well as our PGN model, even upon moderate noise conditions. In addition, self stimulatory mechanisms can give our PGN model the possibility of having a pacemaker activity similar to the observed in the oscillatory embryonic cell cycle.     

Overlaid positive and negative feedback loops shape dynamical properties of PhoPQ two-component system

Bacteria use two-component systems (TCSs) to sense environmental conditions and change gene expression in response to those conditions. To amplify cellular responses, many bacterial TCSs are under positive feedback control, i.e. increase their expression when activated. Escherichia coli Mg²⁺ -sensing TCS, PhoPQ, in addition to the positive feedback, includes a negative feedback loop via the upregulation of the MgrB protein that inhibits PhoQ. How the interplay of these feedback loops shapes steady-state and dynamical responses of PhoPQ TCS to change in Mg²⁺ remains poorly understood. In particular, how the presence of MgrB feedback affects the robustness of PhoPQ response to overexpression of TCS is unclear. It is also unclear why the steady-state response to decreasing Mg²⁺ is biphasic, i.e. plateaus over a range of Mg²⁺ concentrations, and then increases again at growth-limiting Mg²⁺. In this study, we use mathematical modeling to identify potential mechanisms behind these experimentally observed dynamical properties. The results make experimentally testable predictions for the regime with response robustness and propose a novel explanation of biphasic response constraining the mechanisms for modulation of PhoQ activity by Mg²⁺ and MgrB. Finally, we show how the interplay of positive and negative feedback loops affects the network’s steady-state sensitivity and response dynamics. In the absence of MgrB feedback, the model predicts oscillations thereby suggesting a general mechanism of oscillatory or pulsatile dynamics in autoregulated TCSs. These results improve the understanding of TCS signaling and other networks with overlaid positive and negative feedback.     

A minimal model of light-induced circadian rhythms of nitrate reductase activity in leaves of barley

Observed circadian rhythms of nitrate reductase (NR) (EC 1.6.6.1) activity in leaves of barley ( Hordeum vulgare L. cv. Herta) under continuous light conditions are described by a simple kinetic model. The oscillatory mechanism has been decomposed into the negative and positive feedback loops which are necessary according to present theories of chemical oscillating systems. Our results indicate that the decrease of NR activity in darkness can be considered as a reversible unimolecular conversion of the active form of NR into an inactive form, forming a negative stabilizing feedback loop. The light-induced increase of NR activity is related to a positive destabilizing feedback loop. In our treatment this process is represented as an autocatalytical reaction.     

Introducing temperature‐compensation in any reaction kinetic oscillator model

Abstract

The positive and negative feedback loops in oscillatory reactions provide a basis for obtaining temperature‐compensation in any reaction‐kinetic model of chemical or biological oscillators. The present paper shows that positive and negative feedback reactions play the role of “opposing reactions”; whose existence was suggested by Hastings and Sweeney for more than 30 years ago. The principle is illustrated with the Brusselator model.     

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.     

Frequency domain analysis reveals external periodic fluctuations can generate sustained p53 oscillation

p53 is a well-known tumor suppressor protein that regulates many pathways, such as ones involved in cell cycle and apoptosis. The p53 levels are known to oscillate without damping after DNA damage, which has been a focus of many recent studies. A negative feedback loop involving p53 and MDM2 has been reported to be responsible for this oscillatory behavior, but questions remain as how the dynamics of this loop alter in order to initiate and maintain the sustained or undamped p53 oscillation. Our frequency domain analysis suggests that the sustained p53 oscillation is not completely dictated by the negative feedback loop; instead, it is likely to be also modulated by periodic DNA repair-related fluctuations that are triggered by DNA damage. According to our analysis, the p53-MDM2 feedback mechanism exhibits adaptability in different cellular contexts. It normally filters noise and fluctuations exerted on p53, but upon DNA damage, it stops performing the filtering function so that DNA repair-related oscillatory signals can modulate the p53 oscillation. Furthermore, it is shown that the p53-MDM2 feedback loop increases its damping ratio allowing p53 to oscillate at a frequency more synchronized with the other cellular efforts to repair the damaged DNA, while suppressing its inherent oscillation-generating capability. Our analysis suggests that the overexpression of MDM2, observed in many types of cancer, can disrupt the operation of this adaptive mechanism by making it less responsive to the modulating signals after DNA damage occurs.     

The regulatory circuits for hysteretic switching in cellular signal transduction pathways

Hysteresis can be found in many physical systems, and a hysteretic switch has been used for various mechanical and electrical systems. Such a hysteretic switch can be created by using a single positive feedback loop, as often used in engineering systems. It is, however, intriguing that various cellular signaling systems use coupled positive feedback loops to implement the hysteretic switch. A question then arises about the advantage of using coupled positive feedback loops instead of simple isolated positive feedback for an apparently equivalent hysteretic switch. Through mathematical simulations, we determined that cellular systems with coupled positive feedback loops show enhanced hysteretic switching, and can thereby make a more reliable decision under conditions of noisy signaling. As most intracellular processes are accompanied by intrinsic noise, important cellular decisions such as differentiation and apoptosis need to be highly robust to such noises. The coupled positive feedback loops might have been evolutionarily acquired to enable correct cell fate decisions to be made through enhanced hysteretic switching in noisy cellular environments.     

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

For many biological networks, the topology of the network constrains its dynamics. In particular, feedback loops play a crucial role. The results in this paper quantify the constraints that (unsigned) feedback loops exert on the dynamics of a class of discrete models for gene regulatory networks. Conjunctive (resp. disjunctive) Boolean networks, obtained by using only the AND (resp. OR) operator, comprise a subclass of networks that consist of canalyzing functions, used to describe many published gene regulation mechanisms. For the study of feedback loops, it is common to decompose the wiring diagram into linked components each of which is strongly connected. It is shown that for conjunctive Boolean networks with strongly connected wiring diagram, the feedback loop structure completely determines the long-term dynamics of the network. A formula is established for the precise number of limit cycles of a given length, and it is determined which limit cycle lengths can appear. For general wiring diagrams, the situation is much more complicated, as feedback loops in one strongly connected component can influence the feedback loops in other components. This paper provides a sharp lower bound and an upper bound on the number of limit cycles of a given length, in terms of properties of the partially ordered set of strongly connected components.     

Design principles of biochemical oscillators

Cellular rhythms are generated by complex interactions among genes, proteins and metabolites. They are used to control every aspect of cell physiology, from signalling, motility and development to growth, division and death. We consider specific examples of oscillatory processes and discuss four general requirements for biochemical oscillations: negative feedback, time delay, sufficient 'nonlinearity' of the reaction kinetics and proper balancing of the timescales of opposing chemical reactions. Positive feedback is one mechanism to delay the negative-feedback signal. Biological oscillators can be classified according to the topology of the positive- and negative-feedback loops in the underlying regulatory mechanism.     

Simulation of the Ras/cAMP/PKA pathway in budding yeast highlights the establishment of stable oscillatory states

In the yeast Saccharomyces cerevisiae, the Ras/cAMP/PKA pathway plays a major role in the regulation of metabolism, stress resistance and cell cycle progression. We extend here a mechanistic model of the Ras/cAMP/PKA pathway that we previously defined by describing the molecular interactions and post-translational modifications of proteins, and perform a computational analysis to investigate the dynamical behaviors of the components of this pathway, regulated by different control mechanisms. We carry out stochastic simulations to consider, in particular, the effect of the negative feedback loops on the activity of both Ira2 (a Ras-GAP) and Cdc25 (a Ras-GEF) proteins. Our results show that stable oscillatory regimes for the dynamics of cAMP can be obtained only through the activation of these feedback mechanisms, and when the amount of Cdc25 is within a specific range. In addition, we highlight that the levels of guanine nucleotides pools are able to regulate the pathway, by influencing the transition between stable steady states and oscillatory regimes.