Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Wherefore Art Thou, Homeo(stasis)? Functional Diversity in Homeostatic Synaptic Plasticity

Homeostatic plasticity has emerged as a fundamental regulatory principle that strives to maintain neuronal activity within optimal ranges by altering diverse aspects of neuronal function. Adaptation to network activity is often viewed as an essential negative feedback restraint that prevents runaway excitation or inhibition. However, the precise importance of these homeostatic functions is often theoretical rather than empirically derived. Moreover, a remarkable multiplicity of homeostatic adaptations has been observed. To clarify these issues, it may prove useful to ask: why do homeostatic mechanisms exist, what advantages do these adaptive responses confer on a given cell population, and why are there so many seemingly divergent effects? Here, we approach these questions by applying the principles of control theory to homeostatic synaptic plasticity of mammalian neurons and suggest that the varied responses observed may represent distinct functional classes of control mechanisms directed toward disparate physiological goals

Uncompensated and compensated backgrounds in homeostatic controllers: Analogies to retinal light adaptation

Integral controllers with single negative feedbacks were subjected to a step-perturbation at constant but different backgrounds. Response amplitudes of the controlled variable, here called A, decreased monotonically with increasing backgrounds, which was opposed and corrected for by compensatory actions of the manipulated variable E. The controllers divided equally into two classes, in which the compensatory fluxes were either based on derepression or activation. Controllers with derepression-based compensatory fluxes showed decreased sensitivity but accelerated response kinetics, which is analogous to the resetting kinetics seen in vertebrate photoreceptors. Retinal light adaptation also involves compensating backgrounds according to remarks in the literature. We therefore became interested in understanding the underlying feedback mechanisms of background compensation. As such, we created controllers or oscillators that show robust background compensation independent of the applied background. These controllers need a second feedback layer, where the additional integral controllers (I1 and I2) feed directly or coherently back to the controlled variable. These feedback conditions were termed "coherent feedback" in analogy to a similar feedback mechanism used in quantum control theory and optics. Finally, simple three-neuron retinal light adapation (RLA) models, representing the retina as a whole, were subjected to the same perturbations. It was the feedback organization in the two-layered oscillator that was responsible for eliminating backgrounds. Robust background compensation, here described theoretically, could be of interest in terms of regulatory properties. Although, no biological relevanse of the concept has been identified

Perfusion bioreactor for liver bioengineering

End-stage organ failure has grown to become one of the key challenges for the medical community because of the high number of patients in waiting list for a transplant and the severe shortage of suitable organ donors. These, together with population ageing, have created an accumulation phenomenon of patients which increases the severity of the problem. New techniques for organ preservation, organ recovery from organs not suitable for transplant, and organ recellularization attempt to tackle this problem, appearing as some of the most promising solutions. The aim of this bachelor thesis is to continue the development of a complex liver perfusion bioreactor in order to design and develop an efficient and repeatable method for organ perfusion, decellularization and recellularization, with the final objective being the creation of a perfusion bioreactor for liver bioengineering able to be used for organ perfusion and preservation, organ decellularization and organ recellularization, able to preserve cell structure, functionality, growth and control differentiation for up to 4 weeks, while avoiding contamination and automating as much as possible the process. In order to do this, the bioreactor will include many sensors and data acquisition systems as well as control systems for pressure, flow rate, and temperature among others.Ingeniería Biomédic

Normothermic perfusion ofan isolated liver: control software implementation

The current concern about the shortage of available liver donors for transplantation poses different possibilities that help overcoming this problem. New techniques for organ preservation, organ recovery methods of those organs classified as non viable in the first place, or the still under development method of decellularization followed by the recellularization of organs, stand as the most promising solutions nowadays. Along with the primary objective, these approaches also have in common a perfusion step of the organ. This study proposes a newly developed normothermic perfusion machine with a PC control. It provides a user-friendly platform for liver perfusion with the implementation of a software control that accomplishes an autonomous and homogeneous system able to adapt and adjust to the characteristics of the organ. The circuit is constituted by a whole set of devices that are electronically interconnected in order to work one depending on each other, resembling the physiology that interacts with the liver in a real body. These allow an instant measurement of meaningful values and blood parameters of the current state of the system. Results show a stable and constant-parameter control able to work independently of human surveillance during 24 hours while maintaining organ function and viability. It becomes an easier and more accurate system that will improve and make more reliable perfusion experiments in these lines of research that work against the actual lack of liver donors. It offers not only an improved method over the actual ones, but also presents a design able to implement future clinical evaluations into the software environment.Ingeniería Biomédic

The Daisyworld control system

The original Gaia Hypothesis proposed that life on Earth, along with the oceans, atmosphere and crust, forms a homeostatic system which reduces the effects of external perturbations, so that conditions are maintained to within the range that allows widespread life. Daisyworld is a simple mathematical model intended to demonstrate certain aspects of this planetary homeostasis. There have been a considerable number of extensions and developments to the original Daisyworld model. Some of this work has been produced in response to criticism of the Gaia Hypothesis and Daisyworld specifically and some has been produced by using Daisyworld as a testbed to explore a range of issues. This thesis examines the Daisyworld control system and in doing so explains how Daisyworld performs homeostasis. The control system is classified as a rein control system which is potentially applicable to a wide range of scenarios from physiological and environmental homeostasis to robotic control. A series of simple Daisyworld models are produced and aspects of the original Daisyworld are explained, in particular the inverse response to forcing: why temperature goes down on Daisyworld when the brightness of the star increases. The Daisyworld control system is evaluated within an evolutionary context. A key result is that environmental regulation emerges not despite of Darwinian evolution but because of it. Within an ecological context, it is found that increasing the complexity of a self-regulating ecosystem can increase its stability. An energy balance climate model is developed to assess the effects of non-equilibrium thermodynamic processes on the Daisyworld control system. Results are presented that support the hypothesis that when the system is in a state of maximum entropy production, homeostasis is maximised

Modelling endocrine regulation of glycaemic control in animal models of diabetes

This thesis is concerned with mathematical modelling of the glucose-insulin homeostatic system, with the specific aim of mathematically modelling diabetes and diabetes-like conditions in animals. Existing models were examined and critiqued in this thesis. Additionally, structural identifiability analysis of the most widely-used model in the field, the Minimal Model, was performed using Taylor series and similarity transformation approaches. It was shown under certain assumptions that it was theoretically possible to obtain a unique set of parameters for the model from only measuring glucose. C-peptide deconvolution was performed using the WinNonLin algorithm and Maximum Entropy technique implemented in MATLAB. This was used to calculate insulin secretion, the percentage of insulin appearing in the periphery and insulin clearance rate. This was then further developed to model insulin appearance and clearance based on hepatic blood flow changes. A short-term model of the glucose-insulin and C-peptide system was initially formulated using a PID controller concept and later refined to reduce the number of model parameters. Structural identifiability analysis was performed using the Lie symmetries approach, followed by parameter estimation on rat and mice data from IVGTTs, OGTTs and hyperglycaemic clamps and sensitivity analysis. This short-term model was integrated into a long-term model to analyse Zucker and ZDF rat data to create a single model to cater for both short- and long-term dynamics. Finally, a software tool was developed to allow non-mathematical scientists to use and access the benefits of the model

(Im) Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis

Background: Metabolic control analysis (MCA) and supply–demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply–demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect. Results: This study integrates control engineering and classical MCA augmented with supply–demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the ‘integral control’ (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of ‘integral control’ should rarely be expected to lead to the ‘perfect adaptation’: although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily. Conclusions: A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the ‘perfect’ regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering