Analysis of Homeostatic Mechanisms in Biochemical Networks

A Minimalistic Covalent Bond-Forming Chemical Reaction Cycle that Consumes Adenosine Diphosphate

The development of synthetic active matter requires the ability to design materials capable of harnessing energy from a source to carry out work. Nature achieves this using chemical reaction cycles in which energy released from an exergonic chemical reaction is used to drive biochemical processes. Although many chemically fuelled synthetic reaction cycles that control transient responses, such as self-assembly, have been reported, the generally high complexity of the reported systems hampers a full understanding of how the available chemical energy is actually exploited by these systems. This lack of understanding is a limiting factor in the design of chemically fuelled active matter. Here, we report a minimalistic synthetic responsive reaction cycle in which adenosine diphosphate (ADP) triggers the formation of a catalyst for its own hydrolysis. This establishes an interdependence between the concentrations of the network components resulting in the transient formation of the catalyst. The network is sufficiently simple that all kinetic and thermodynamic parameters governing its behaviour can be characterised, allowing kinetic models to be built that simulate the progress of reactions within the network. While the current network does not enable the ADP-hydrolysis reaction to populate a non-equilibrium composition, these models provide insight into the way the network dissipates energy. Furthermore, essential design principles are revealed for constructing driven systems, in which the network composition is driven away from equilibrium through the consumption of chemical energy.

Time-dependent homeostatic mechanisms underlie brain-derived neurotrophic factor action on neural circuitry

Plasticity and homeostatic mechanisms allow neural networks to maintain proper function while responding to physiological challenges. Despite previous work investigating morphological and synaptic effects of brain-derived neurotrophic factor (BDNF), the most prevalent growth factor in the central nervous system, how exposure to BDNF manifests at the network level remains unknown. Here we report that BDNF treatment affects rodent hippocampal network dynamics during development and recovery from glutamate-induced excitotoxicity in culture. Importantly, these effects are not obvious when traditional activity metrics are used, so we delve more deeply into network organization, functional analyses, and in silico simulations. We demonstrate that BDNF partially restores homeostasis by promoting recovery of weak and medium connections after injury. Imaging and computational analyses suggest these effects are caused by changes to inhibitory neurons and connections. From our in silico simulations, we find that BDNF remodels the network by indirectly strengthening weak excitatory synapses after injury. Ultimately, our findings may explain the difficulties encountered in preclinical and clinical trials with BDNF and also offer information for future trials to consider.

Developing the genotype-to-phenotype relationship in evolutionary theory: A primer of developmental features

For decades, there have been repeated calls for more integration across evolutionary and developmental biology. However, critiques in the literature and recent funding initiatives suggest this integration remains incomplete. We suggest one way forward is to consider how we elaborate the most basic concept of development, the relationship between genotype and phenotype, in traditional models of evolutionary processes. For some questions, when more complex features of development are accounted for, predictions of evolutionary processes shift. We present a primer on concepts of development to clarify confusion in the literature and fuel new questions and approaches. The basic features of development involve expanding a base model of genotype-to-phenotype to include the genome, space, and time. A layer of complexity is added by incorporating developmental systems, including signal-response systems and networks of interactions. The developmental emergence of function, which captures developmental feedbacks and phenotypic performance, offers further model elaborations that explicitly link fitness with developmental systems. Finally, developmental features such as plasticity and developmental niche construction conceptualize the link between a developing phenotype and the external environment, allowing for a fuller inclusion of ecology in evolutionary models. Incorporating aspects of developmental complexity into evolutionary models also accommodates a more pluralistic focus on the causal importance of developmental systems, individual organisms, or agents in generating evolutionary patterns. Thus, by laying out existing concepts of development, and considering how they are used across different fields, we can gain clarity in existing debates around the extended evolutionary synthesis and pursue new directions in evolutionary developmental biology. Finally, we consider how nesting developmental features in traditional models of evolution can highlight areas of evolutionary biology that need more theoretical attention.

Quantitative Systems Pharmacology and Machine Learning: A Match Made in Heaven or Hell?

As pharmaceutical development moves from early-stage in vitro experimentation to later in vivo and subsequent clinical trials, data and knowledge are acquired across multiple time and length scales, from the subcellular to whole patient cohort scale. Realizing the potential of this data for informing decision making in pharmaceutical development requires the individual and combined application of machine learning (ML) and mechanistic multiscale mathematical modeling approaches. Here we outline how these two approaches, both individually and in tandem, can be applied at different stages of the drug discovery and development pipeline to inform decision making compound development. The importance of discerning between knowledge and data are highlighted in informing the initial use of ML or mechanistic quantitative systems pharmacology (QSP) models. We discuss the application of sensitivity and structural identifiability analyses of QSP models in informing future experimental studies to which ML may be applied, as well as how ML approaches can be used to inform mechanistic model development. Relevant literature studies are highlighted and we close by discussing caveats regarding the application of each approach in an age of constant data acquisition. SIGNIFICANCE STATEMENT: We consider when best to apply machine learning (ML) and mechanistic quantitative systems pharmacology (QSP) approaches in the context of the drug discovery and development pipeline. We discuss the importance of prior knowledge and data available for the system of interest and how this informs the individual and combined application of ML and QSP approaches at each stage of the pipeline.

Development of a model for the prediction of biological age

BACKGROUND AND OBJECTIVE

Rates of aging vary markedly among individuals, and biological age serves as a more reliable predictor of current health status than does chronological age. As such, the ability to predict biological age can support appropriate and timely active interventions aimed at improving coping with the aging process. However, the aging process is highly complex and multifactorial. Therefore, it is more scientific to construct a prediction model for biological age from multiple dimensions systematically.

METHODS

Physiological and biochemical parameters were evaluated to gage individual health status. Then, age-related indices were screened for inclusion in a model capable of predicting biological age. For subsequent modeling analyses, samples were divided into training and validation sets for subsequent deep learning model-based analyses (e.g. linear regression, lasso model, ridge regression, bayesian ridge regression, elasticity network, k-nearest neighbor, linear support vector machine, support vector machine, and decision tree models, and so on), with the model exhibiting the best ability to predict biological age thereby being identified.

RESULTS

First, we defined the individual biological age according to the individual health status. Then, after 22 candidate indices (DNA methylation, leukocyte telomere length, and specific physiological and biochemical indicators) were screened for inclusion in a model capable of predicting biological age, 14 age-related indices and gender were used to construct a model via the Bagged Trees method, which was found to be the most reliable qualitative prediction model for biological age (accuracy=75.6%, AUC=0.84) by comparing 30 different classification algorithm models. The most reliable quantitative predictive model for biological age was found to be the model developed using the Rational Quadratic method (R2=0.85, RMSE=8.731 years) by comparing 24 regression algorithm models.

CONCLUSIONS

Both qualitative model and quantitative model of biological age were successfully constructed from a multi-dimensional and systematic perspective. The predictive performance of our models was similar in both smaller and larger datasets, making it well-suited to predicting a given individual's biological age.

Reliability and robustness of oscillations in some slow-fast chaotic systems

A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal conditions. Motivated by the subtle dynamics of cell activity in a crustacean central pattern generator (CPG), this paper proposes a refinement of the notion of chaos that reconciles homeostasis and chaos in systems with multiple timescales. We show that systems displaying relaxation cycles while going through chaotic attractors generate chaotic dynamics that are regular at macroscopic timescales and are, thus, consistent with physiological function. We further show that this relative regularity may break down through global bifurcations of chaotic attractors such as crises, beyond which the system may also generate erratic activity at slow timescales. We analyze these phenomena in detail in the chaotic Rulkov map, a classical neuron model known to exhibit a variety of chaotic spike patterns. This leads us to propose that the passage of slow relaxation cycles through a chaotic attractor crisis is a robust, general mechanism for the transition between such dynamics. We validate this numerically in three other models: a simple model of the crustacean CPG neural network, a discrete cubic map, and a continuous flow.

Advancing physiology education by understanding the multiple dimensions of homeostasis

Homeostasis of the internal environment has been considered the central organizing concept of physiology. However, current definitions of it in textbooks and online teaching sources do not sufficiently reflect how homeostasis serves its central unifying role. Meanwhile, scientific understanding of the functions of the body's structures at multiple levels (molecular, cell, tissue, organ, organ system, and organism) has advanced significantly, but the understanding of homeostasis is still in the same place. In this article, the author describes some issues and insufficiencies in teaching about homeostasis in physiology education and proposes that homeostasis needs to be understood in terms of four dimensions rather than a simple definition: internal, functional organization; functional manifestation; mechanism; and effect or consequence. Each dimension has two subdimensions or sides. Throughout the elucidation of these dimensions and subdimensions, the original meaning of homeostasis is reinforced, what is lost in current understanding of homeostasis becomes clear, some insufficiencies mentioned above are supplemented, new insights into homeostasis develop, and how the four dimensions of homeostasis can be applied to physiology education is exampled. This new, comprehensive conceptualization advances the understanding of homeostasis and can facilitate teaching and learning about homeostasis and physiology.

Functional advantages of building nanosystems using multiple molecular components

Over half of all the natural nanomachines in living organisms are multimeric and likely exploit the self-assembly of their components to provide functional benefits. However, the advantages and disadvantages of building nanosystems using multiple molecular components remain relatively unexplored at the thermodynamic, kinetic and functional levels. In this study we used theory and a simple DNA-based model that forms the same nanostructures with different numbers of components to advance our knowledge in this area. Despite its lower assembly rate, we found that a system built with three components may undergo a more cooperative assembly transition from less preorganized components, which facilitates the emergence of functionalities. Using simple variations of its components, we also found that trimeric nanosystems display a much higher level of programmability than their dimeric counterparts because they can assemble with various levels of cooperativity, self-inhibition and time-dependent properties. We show here how two simple strategies (for example, cutting and adding components) can be employed to efficiently programme the regulatory function of a more complex, artificially selected, RNA-cleaving catalytic nanosystem.

Homeostasis and injectivity: a reaction network perspective

Homeostasis represents the idea that a feature may remain invariant despite changes in some external parameters. We establish a connection between homeostasis and injectivity for reaction network models. In particular, we show that a reaction network cannot exhibit homeostasis if a modified version of the network (which we call homeostasis-associated network) is injective. We provide examples of reaction networks which can or cannot exhibit homeostasis by analyzing the injectivity of their homeostasis-associated networks.

Feedback from nuclear RNA on transcription promotes robust RNA concentration homeostasis in human cells

RNA concentration homeostasis involves coordinating RNA abundance and synthesis rates with cell size. Here, we study this in human cells by combining genome-wide perturbations with quantitative single-cell measurements. Despite relative ease in perturbing RNA synthesis, we find that RNA concentrations generally remain highly constant. Perturbations that would be expected to increase nuclear mRNA levels, including those targeting nuclear mRNA degradation or export, result in downregulation of RNA synthesis. This is associated with reduced abundance of transcription-associated proteins and protein states that are normally coordinated with RNA production in single cells, including RNA polymerase II (RNA Pol II) itself. Acute perturbations, elevation of nuclear mRNA levels, and mathematical modeling indicate that mammalian cells achieve robust mRNA concentration homeostasis by the mRNA-based negative feedback on transcriptional activity in the nucleus. This ultimately acts to coordinate RNA Pol II abundance with nuclear mRNA degradation and export rates and may underpin the scaling of mRNA abundance with cell size.

How an information perspective helps overcome the challenge of biology to physics

Living systems have long been a puzzle to physics, leading some to claim that new laws of physics are needed to explain them. Separating physical reality into the general (laws) and the particular (location of particles in space and time), it is possible to see that the combination of these amounts to efficient causation, whereby forces are constrained by patterns that constitute embodied information which acts as formal cause. Embodied information can only be produced by correlation with existing patterns, but sets of patterns can be arranged to form reflexive relations in which constraints on force are themselves formed by the pattern that results from action of those same constrained forces. This inevitably produces a higher level of pattern which reflexively reinforces itself. From this, multi-level hierarchies and downward causation by information are seen to be patterns of patterns that constrain forces. Such patterns, when causally cyclical, are closed to efficient causation. But to be autonomous, a system must also have its formative information accumulated by repeated cycles of selection until sufficient is obtained to represent the information content of the whole (which is the essential purpose of information oligomers such as DNA). Living systems are the result of that process and therefore cannot exist unless they are both closed to efficient causation and capable of embodying an independent supply of information sufficient to constitute their causal structure. Understanding this is not beyond the scope of standard physics, but it does recognise the far greater importance of information accumulation in living than in non-living systems and, as a corollary, emphasises the dependence of biological systems on the whole history of life, leading up to the present state of any and all organisms.

A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves

Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J Math Biol 74(1-2):387-407, 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the average of a quantity taken around the limit cycle. We apply the "infinitesimal shape response curve" (iSRC) introduced by Wang et al. (SIAM J Appl Dyn Syst 82(7):1-43, 2021) to study infinitesimal homeostasis for limit-cycle systems in terms of the mean value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized shape displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.

Testing Theoretical Minimal Genomes Using Whole-Cell Models

The minimal gene set for life has often been theorized, with at least ten produced for Mycoplasma genitalium (M. genitalium). Due to the difficulty of using M. genitalium in the lab, combined with its long replication time of 12-15 h, none of these theoretical minimal genomes have been tested, even with modern techniques. The publication of the M. genitalium whole-cell model provided the first opportunity to test them, simulating the genome edits in silico. We simulated minimal gene sets from the literature, finding that they produced in silico cells that did not divide. Using knowledge from previous research, we reintroduced specific essential and low essential genes in silico; enabling cellular division. This reinforces the need to identify species-specific low essential genes and their interactions. Any genome designs created using the currently incomplete and fragmented gene essentiality information will very likely require in vivo reintroductions to correct issues and produce dividing cells.

A description of the relationship in healthy longevity and aging-related disease: from gene to protein

Human longevity is a complex phenotype influenced by both genetic and environmental factors. It is also known to be associated with various types of age-related diseases, such as Alzheimer's disease (AD) and cardiovascular disease (CVD). The central dogma of molecular biology demonstrates the conversion of DNA to RNA to the encoded protein. These proteins interact to form complex cell signaling pathways, which perform various biological functions. With prolonged exposure to the environment, the in vivo homeostasis adapts to the changes, and finally, humans adopt the phenotype of longevity or aging-related diseases. In this review, we focus on two different states: longevity and aging-related diseases, including CVD and AD, to discuss the relationship between genetic characteristics, including gene variation, the level of gene expression, regulation of gene expression, the level of protein expression, both genetic and environmental influences and homeostasis based on these phenotypes shown in organisms.

Infinitesimal homeostasis in three-node input-output networks

Homeostasis occurs in a system where an output variable is approximately constant on an interval on variation of an input variable [Formula: see text]. Homeostasis plays an important role in the regulation of biological systems, cf.  Ferrell (Cell Syst 2:62-67, 2016), Tang and McMillen (J Theor Biol 408:274-289, 2016), Nijhout et al. (BMC Biol 13:79, 2015), and Nijhout et al. (Wiley Interdiscip Rev Syst Biol Med 11:e1440, 2018). A method for finding homeostasis in mathematical models is given in the control theory literature as points where the derivative of the output variable with respect to [Formula: see text] is identically zero. Such points are called perfect homeostasis or perfect adaptation. Alternatively, Golubitsky and Stewart (J Math Biol 74:387-407, 2017) use an infinitesimal notion of homeostasis (namely, the derivative of the input-output function is zero at an isolated point) to introduce singularity theory into the study of homeostasis. Reed et al. (Bull Math Biol 79(9):1-24, 2017) give two examples of infinitesimal homeostasis in three-node chemical reaction systems: feedforward excitation and substrate inhibition. In this paper we show that there are 13 different three-node networks leading to 78 three-node input-output network configurations, under the assumption that there is one input node, one output node, and they are distinct. The different configurations are based on which node is the input node and which node is the output node. We show nonetheless that there are only three basic mechanisms for three-node input-output networks that lead to infinitesimal homeostasis and we call them structural homeostasis, Haldane homeostasis, and null-degradation homeostasis. Substantial parts of this classification are given in Ma et al. (Cell 138:760-773, 2009) and Ferrell (2016) among others. Our contributions include giving a complete classification using general admissible systems (Golubitsky and Stewart in Bull Am Math Soc 43:305-364, 2006) rather than specific biochemical models, relating the types of infinitesimal homeostasis to the graph theoretic existence of simple paths, and providing the basis to use singularity theory to study higher codimension homeostasis singularities such as the chair singularities introduced in Nijhout and Reed (Integr Comp Biol 54(2):264-275, 2014. https://doi.org/10.1093/icb/icu010) and Nijhout et al. (Math Biosci 257:104-110, 2014). See Golubitsky and Stewart (2017). The first two of these mechanisms are illustrated by feedforward excitation and substrate inhibition. Structural homeostasis occurs only when the network has a feedforward loop as a subnetwork; that is, when there are two distinct simple paths connecting the input node to the output node. Moreover, when the network is just the feedforward loop motif itself, one of the paths must be excitatory and one inhibitory to support infinitesimal homeostasis. Haldane homeostasis occurs when there is a single simple path from the input node to the output node and then only when one of the couplings along this path has strength 0. Null-degradation homeostasis is illustrated by a biochemical example from Ma et al. (2009); this kind of homeostasis can occur only when the degradation constant of the third node is 0. The paper ends with an analysis of Haldane homeostasis infinitesimal chair singularities.

Homeostasis in a feed forward loop gene regulatory motif

The internal state of a cell is affected by inputs from the extra-cellular environment such as external temperature. If some output, such as the concentration of a target protein, remains approximately constant as inputs vary, the system exhibits homeostasis. Special sub-networks called motifs are unusually common in gene regulatory networks (GRNs), suggesting that they may have a significant biological function. Potentially, one such function is homeostasis. In support of this hypothesis, we show that the feed-forward loop GRN produces homeostasis. Here the inputs are subsumed into a single parameter that affects only the first node in the motif, and the output is the concentration of a target protein. The analysis uses the notion of infinitesimal homeostasis, which occurs when the input-output map has a critical point (zero derivative). In model equations such points can be located using implicit differentiation. If the second derivative of the input-output map also vanishes, the critical point is a chair: the output rises roughly linearly, then flattens out (the homeostasis region or plateau), and then starts to rise again. Chair points are a common cause of homeostasis. In more complicated equations or networks, numerical exploration would have to augment analysis. Thus, in terms of finding chairs, this paper presents a proof of concept. We apply this method to a standard family of differential equations modeling the feed-forward loop GRN, and deduce that chair points occur. This function determines the production of a particular mRNA and the resulting chair points are found analytically. The same method can potentially be used to find homeostasis regions in other GRNs. In the discussion and conclusion section, we also discuss why homeostasis in the motif may persist even when the rest of the network is taken into account.

Serine synthesis through PHGDH coordinates nucleotide levels by maintaining central carbon metabolism

Phosphoglycerate dehydrogenase (PHGDH) catalyzes the committed step in de novo serine biosynthesis. Paradoxically, PHGDH and serine synthesis are required in the presence of abundant environmental serine even when serine uptake exceeds the requirements for nucleotide synthesis. Here, we establish a mechanism for how PHGDH maintains nucleotide metabolism. We show that inhibition of PHGDH induces alterations in nucleotide metabolism independent of serine utilization. These changes are not attributable to defects in serine-derived nucleotide synthesis and redox maintenance, another key aspect of serine metabolism, but result from disruption of mass balance within central carbon metabolism. Mechanistically, this leads to simultaneous alterations in both the pentose phosphate pathway and the tri-carboxylic acid cycle, as we demonstrate based on a quantitative model. These findings define a mechanism whereby disruption of one metabolic pathway induces toxicity by simultaneously affecting the activity of multiple related pathways.

Serine synthesis from glucose is required even when serine is available from the environment. Here, the authors explain this paradox by showing that the enzyme PHGDH enables nucleotide synthesis by coordinating anabolic fluxes related to central carbon metabolism, independent of its role in serine production.