Adaptation with transcriptional regulation

Homeostasis in input-output networks: Structure, Classification and Applications

Homeostasis is concerned with regulatory mechanisms, present in biological systems, where some specific variable is kept close to a set value as some external disturbance affects the system. Many biological systems, from gene networks to signaling pathways to whole tissue/organism physiology, exhibit homeostatic mechanisms. In all these cases there are homeostatic regions where the variable is relatively to insensitive external stimulus, flanked by regions where it is sensitive. Mathematically, the notion of homeostasis can be formalized in terms of an input-output function that maps the parameter representing the external disturbance to the output variable that must be kept within a fairly narrow range. This observation inspired the introduction of the notion of infinitesimal homeostasis, namely, the derivative of the input-output function is zero at an isolated point. This point of view allows for the application of methods from singularity theory to characterize infinitesimal homeostasis points (i.e. critical points of the input-output function). In this paper we review the infinitesimal approach to the study of homeostasis in input-output networks. An input-output network is a network with two distinguished nodes 'input' and 'output', and the dynamics of the network determines the corresponding input-output function of the system. This class of dynamical systems provides an appropriate framework to study homeostasis and several important biological systems can be formulated in this context. Moreover, this approach, coupled to graph-theoretic ideas from combinatorial matrix theory, provides a systematic way for classifying different types of homeostasis (homeostatic mechanisms) in input-output networks, in terms of the network topology. In turn, this leads to new mathematical concepts, such as, homeostasis subnetworks, homeostasis patterns, homeostasis mode interaction. We illustrate the usefulness of this theory with several biological examples: biochemical networks, chemical reaction networks (CRN), gene regulatory networks (GRN), Intracellular metal ion regulation and so on.

Regulatory Effects of Cooperativity and Signal Profile on Adaptive Dynamics in Incoherent Feedforward Loop Networks

Cellular adaptation to external signals is essential for biological functions, and it is an important field of interest in systems biology. This study examines the impact of cooperativity on the adaptation response of the Incoherent Feedforward Loop (IFFL) network motif to various signal profiles. Through comprehensive simulations, we studied how the IFFL motif responds to constant and pulse-type signals under varying levels of cooperativity. The results of our study demonstrate that positive cooperativity generally enhances the system's ability to adapt to different signal profiles. Nevertheless, given specific signal profiles, higher levels of cooperativity may decrease the system's adaptability. On the other hand, the adaptive response breaks down for negative cooperativity. For constant signals, increased positive cooperativity leads to a response with higher amplitude, and it accelerates the response time but delays the return time required to settle back down to the pre-stimulus state. Upon signal cessation, high positive cooperativity not only slows the system's response and return times but, in some cases, can lead to a complete temporary halt in response. For the pulse-like signal, cooperativity increases the maximum amplitude of the oscillatory response. These insights highlight the delicate balance between cooperativity and signal profile in cellular adaptation mechanisms involving the IFFL network motif.

Feed-forward loop improves the transient dynamics of an antithetic biological controller

Integral controller is widely used in industry for its capability of endowing perfect adaptation to disturbances. To harness such capability for precise gene expression regulation, synthetic biologists have endeavoured in building biomolecular (quasi-)integral controllers, such as the antithetic integral controller. Despite demonstrated successes, challenges remain with designing the controller for improved transient dynamics and adaptation. Here, we explore and investigate the design principles of alternative RNA-based biological controllers, by modifying an antithetic integral controller with prevalently found natural feed-forward loops (FFL), to improve its transient dynamics and adaptation performance. With model-based analysis, we demonstrate that while the base antithetic controller shows excellent responsiveness and adaptation to system disturbances, incorporating the type-1 incoherent FFL into the base antithetic controller could attenuate the transient dynamics caused by changes in the stimuli, especially in mitigating the undesired overshoot in the output gene expression. Further analysis on the kinetic parameters reveals similar findings to previous studies that the degradation and transcription rates of the circuit RNA species would dominate in shaping the performance of the controllers.

Chicken GLUT4 function via enhancing mitochondrial oxidative phosphorylation and inhibiting ribosome pathway in skeletal muscle satellite cells

Glucose Transporter 4 (GLUT4) is a crucial protein facilitating glucose uptake and metabolism across cell membranes in mammals. However, information on GLUT4 in birds has historically been limited. In this study, we investigated the dynamic expression profile of chicken GLUT4 using real-time quantitative PCR (RT-qPCR) and examined its potential effects and mechanisms via GLUT4 overexpression and RNA sequencing (RNA-seq) in chicken primary skeletal muscle satellite cells (CP-SMSCs). Our results demonstrated that chicken GLUT4 is differentially expressed across tissues, with predominant expression in skeletal muscles, and across developmental stages of CP-SMSCs, with notable upregulation during the phases of cell proliferation and early differentiation. Notably, 0.1 μM insulin for 60 min significantly elevated the expression of GLUT4 in CP-SMSCs (P < 0.05). GLUT4 overexpression in CP-SMSCs promoted cell proliferation, as evidenced by Cell Counting Kit-8 (CCK-8) (P < 0.05) and 5-Ethynyl-2'-Deoxyuridine (EDU) assays (P < 0.05), and enhanced glucose consumption following 0.1 μM insulin treatment (P < 0.05). However, it inhibited glucose consumption 12 h after the addition of 5 g/L glucose (P < 0.05). After overexpressing GLUT4, we identified 302 differentially expressed genes (DEGs) in CP-SMSCs, with 134 upregulated and 168 downregulated. These DEGs are primarily enriched in pathways such as oxidative phosphorylation, ribosome, cardiac muscle contraction, ATP metabolic processes, and mitochondrial protein complexes. Specifically, in the enriched oxidative phosphorylation pathway, the upregulated DEGs (12) encode mitochondrial proteins, while the downregulated DEGs (6) are nuclear genome-derived. The ribosomal pathway is predominantly inhibited, accompanying with the downregulation of the translocase of outer mitochondrial membrane 7 (TOMM7)/translocase of inner mitochondrial membrane 8 (TIMM8A) complex responsible for mitochondrial protein transport, and a reduction in 28S (LOC121106978) and 18S (LOC112533601) ribosomal rRNAs. In conclusion, chicken GLUT4 is dynamically modulated during development and acts as an insulin responder that significantly regulates cellular glucose uptake and cell proliferation. This regulation occurs mainly through enhancing the mitochondrial oxidative phosphorylation and inhibiting ribosomal pathway.

The dynamic-process characterization and prediction of synthetic gene circuits by dynamic delay model

Differential equation models are widely used to describe genetic regulations, predict multicomponent regulatory circuits, and provide quantitative insights. However, it is still challenging to quantitatively link the dynamic behaviors with measured parameters in synthetic circuits. Here, we propose a dynamic delay model (DDM) which includes two simple parts: the dynamic determining part and the doses-related steady-state-determining part. The dynamic determining part is usually supposed as the delay time but without a clear formula. For the first time, we give the detail formula of the dynamic determining function and provide a method for measuring all parameters of synthetic elements (include 8 activators and 5 repressors) by microfluidic system. Three synthetic circuits were built to show that the DDM can notably improve the prediction accuracy and can be used in various synthetic biology applications.

Exogenous Hydrogen Sulfide Induces A375 Melanoma Cell Apoptosis Through Overactivation of the Unfolded Protein Response

Purpose

Melanomas are highly malignant and rapidly develop drug resistance due to dysregulated apoptosis. Therefore, pro-apoptotic agents could be effective for the management of melanoma. Hydrogen sulfide is ubiquitous in the body, and exogenous hydrogen sulfide has been reported to show inhibitory and pro-apoptotic effects on cancer cells. However, whether high concentrations of exogenous hydrogen sulfide have pro-apoptotic effects on melanoma and its mechanisms remain unknown. Hence, this study aimed to explore the pro-apoptotic effects and mechanisms of exogenous hydrogen sulfide on the A375 melanoma cell line treated with a hydrogen sulfide donor (NaHS).

Methods

The cell proliferation test, flow cytometric analysis, Hoechst 33258 staining, and Western blotting of B-cell lymphoma 2 and cleaved caspase-3 were used to explore the pro-apoptotic effects of hydrogen sulfide on A375 cells. The transcriptional profile of NaHS-treated A375 cells was further explored via high-throughput sequencing. Western blotting of phosphorylated inositol-requiring enzyme 1α (p-IRE1α), phosphorylated protein kinase R-like ER kinase (p-PERK), phosphorylated eukaryotic translation initiation factor 2α (p-eIF2α), C/EBP homologous protein, glucose-regulating protein 78, IRE1α, PERK, and eIF2α was performed to verify the changes in the transcriptional profile.

Results

NaHS inhibited A375 melanoma cell proliferation and induced apoptosis. The endoplasmic reticulum stress unfolded protein response and apoptosis-associated gene expression was upregulated in NaHS-treated A375 melanoma cells. The overactivation of the unfolded protein response and increase in endoplasmic reticulum stress was verified at the protein level.

Conclusion

Treatment with NaHS increased endoplasmic reticulum stress, which triggered the overactivation of the unfolded protein response and ultimately lead to melanoma cell apoptosis. The pro-apoptotic effect of NaHS suggests that it can be explored as a potential therapeutic agent in melanoma.

Evolutionary Stability of Small Molecular Regulatory Networks That Exhibit Near-Perfect Adaptation

Large-scale protein regulatory networks, such as signal transduction systems, contain small-scale modules ('motifs') that carry out specific dynamical functions. Systematic characterization of the properties of small network motifs is therefore of great interest to molecular systems biologists. We simulate a generic model of three-node motifs in search of near-perfect adaptation, the property that a system responds transiently to a change in an environmental signal and then returns near-perfectly to its pre-signal state (even in the continued presence of the signal). Using an evolutionary algorithm, we search the parameter space of these generic motifs for network topologies that score well on a pre-defined measure of near-perfect adaptation. We find many high-scoring parameter sets across a variety of three-node topologies. Of all possibilities, the highest scoring topologies contain incoherent feed-forward loops (IFFLs), and these topologies are evolutionarily stable in the sense that, under 'macro-mutations' that alter the topology of a network, the IFFL motif is consistently maintained. Topologies that rely on negative feedback loops with buffering (NFLBs) are also high-scoring; however, they are not evolutionarily stable in the sense that, under macro-mutations, they tend to evolve an IFFL motif and may-or may not-lose the NFLB motif.

Two-Layered Microfluidic Devices for High-Throughput Dynamic Analysis of Synthetic Gene Circuits in E. coli

Escherichia coli is a common chassis for synthetic gene circuit studies. In addition to the dose-response of synthetic gene circuits, the analysis of dynamic responses is also an important part of the future design of more complicated synthetic systems. Recently, microfluidic-based methods have been widely used for the analysis of gene expression dynamics. Here, we established a two-layered microfluidic platform for the systematic characterization of synthetic gene circuits (eight strains in eight different culture environments could be observed simultaneously with a 5 min time resolution). With this platform, both dose responses and dynamic responses with a high temporal resolution could be easily derived for further analysis. A controlled environment ensures the stability of the bacterial growth rate, excluding changes in gene expression dynamics caused by changes of the growth dilution rate. The precise environmental switch and automatic micrograph shooting ensured that there was nearly no time lag between the inducer addition and the data recording. We studied four four-node incoherent-feedforward-loop (IFFL) networks with different operators using this device. The experimental results showed that as the effect of inhibition increased, two of the IFFL networks generated pulselike dynamic gene expressions in the range of the inducer concentrations, which was different from the dynamics of the two other circuits with only a simple pattern of rising to the platform. Through fitting the dose-response curves and the dynamic response curves, corresponding parameters were derived and introduced to a simple model that could qualitatively explain the generation of pulse dynamics.

Network design principle for robust oscillatory behaviors with respect to biological noise

Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus, a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive autoregulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive autoregulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive autoregulation—improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Designing Biological Circuits: From Principles to Applications

Genetic circuit design is a well-studied problem in synthetic biology. Ever since the first genetic circuits─the repressilator and the toggle switch─were designed and implemented, many advances have been made in this area of research. The current review systematically organizes a number of key works in this domain by employing the versatile framework of generalized morphological analysis. Literature in the area has been mapped on the basis of (a) the design methodologies used, ranging from brute-force searches to control-theoretic approaches, (b) the modeling techniques employed, (c) various circuit functionalities implemented, (d) key design characteristics, and (e) the strategies used for the robust design of genetic circuits. We conclude our review with an outlook on multiple exciting areas for future research, based on the systematic assessment of key research gaps that have been readily unravelled by our analysis framework.

Synthetic robust perfect adaptation achieved by negative feedback coupling with linear weak positive feedback

Unlike their natural counterparts, synthetic genetic circuits are usually fragile in the face of environmental perturbations and genetic mutations. Several theoretical robust genetic circuits have been designed, but their performance under real-world conditions has not yet been carefully evaluated. Here, we designed and synthesized a new robust perfect adaptation circuit composed of two-node negative feedback coupling with linear positive feedback on the buffer node. As a key feature, the linear positive feedback was fine-tuned to evaluate its necessity. We found that the desired function was robustly achieved when genetic parameters were varied by systematically perturbing all interacting parts within the topology, and the necessity of the completeness of the topological structures was evaluated by destroying key circuit features. Furthermore, different environmental perturbances were imposed onto the circuit by changing growth rates, carbon metabolic strategies and even chassis cells, and the designed perfect adaptation function was still achieved under all conditions. The successful design of a robust perfect adaptation circuit indicated that the top-down design strategy is capable of predictably guiding bottom-up engineering for robust genetic circuits. This robust adaptation circuit could be integrated as a motif into more complex circuits to robustly implement more sophisticated and critical biological functions.

Glucocorticoid-Mediated Developmental Programming of Vertebrate Stress Responsivity

Glucocorticoids, vertebrate steroid hormones produced by cells of the adrenal cortex or interrenal tissue, function dynamically to maintain homeostasis under constantly changing and occasionally stressful environmental conditions. They do so by binding and thereby activating nuclear receptor transcription factors, the Glucocorticoid and Mineralocorticoid Receptors (MR and GR, respectively). The GR, by virtue of its lower affinity for endogenous glucocorticoids (cortisol or corticosterone), is primarily responsible for transducing the dynamic signals conveyed by circadian and ultradian glucocorticoid oscillations as well as transient pulses produced in response to acute stress. These dynamics are important determinants of stress responsivity, and at the systemic level are produced by feedforward and feedback signaling along the hypothalamus-pituitary-adrenal/interrenal axis. Within receiving cells, GR signaling dynamics are controlled by the GR target gene and negative feedback regulator fkpb5. Chronic stress can alter signaling dynamics via imperfect physiological adaptation that changes systemic and/or cellular set points, resulting in chronically elevated cortisol levels and increased allostatic load, which undermines health and promotes development of disease. When this occurs during early development it can "program" the responsivity of the stress system, with persistent effects on allostatic load and disease susceptibility. An important question concerns the glucocorticoid-responsive gene regulatory network that contributes to such programming. Recent studies show that klf9, a ubiquitously expressed GR target gene that encodes a Krüppel-like transcription factor important for metabolic plasticity and neuronal differentiation, is a feedforward regulator of GR signaling impacting cellular glucocorticoid responsivity, suggesting that it may be a critical node in that regulatory network.

Control of tissue homeostasis, tumorigenesis, and degeneration by coupled bidirectional bistable switches

The Hippo-YAP/TAZ signaling pathway plays a critical role in tissue homeostasis, tumorigenesis, and degeneration disorders. The regulation of YAP/TAZ levels is controlled by a complex regulatory network, where several feedback loops have been identified. However, it remains elusive how these feedback loops contain the YAP/TAZ levels and maintain the system in a healthy physiological state or trap the system in pathological conditions. Here, a mathematical model was developed to represent the YAP/TAZ regulatory network. Through theoretical analyses, three distinct states that designate the one physiological and two pathological outcomes were found. The transition from the physiological state to the two pathological states is mechanistically controlled by coupled bidirectional bistable switches, which are robust to parametric variation and stochastic fluctuations at the molecular level. This work provides a mechanistic understanding of the regulation and dysregulation of YAP/TAZ levels in tissue state transitions.

Tissue development and homeostasis require well-controlled cell proliferation. Lack of this control could lead to degenerative or tumorigenic diseases. Signaling pathways have been explored in promoting or inhibiting these diseases. The Hippo signaling pathway is one of these, which has been found to control tissue homeostasis and organ size through cell proliferation and apoptosis, as evidenced by extensive experimental data. However, the question remains of how tissue can transition from a homeostatic state to either a degenerative or tumorigenic state. By theoretically analyzing a mathematical model of its regulatory network, we present a mechanism that underlies Hippo signaling to control tissue transition from a homeostatic state to a disease state. This provides us with a mechanistic understanding of how the parts of the regulatory network are coordinated for the transitions between the homeostasis state and the disease states. In addition, we looked at the role of system noise and found that it could promote the transition to one of the disease states. Our model allows for experimental hypotheses to be generated and could lead to the development of therapeutic strategies by targeting the Hippo signaling pathway.

Differences in evolutionary accessibility determine which equally effective regulatory motif evolves to generate pulses

Transcriptional regulatory networks (TRNs) are enriched for certain "motifs." Motif usage is commonly interpreted in adaptationist terms, i.e., that the optimal motif evolves. But certain motifs can also evolve more easily than others. Here, we computationally evolved TRNs to produce a pulse of an effector protein. Two well-known motifs, type 1 incoherent feed-forward loops (I1FFLs) and negative feedback loops (NFBLs), evolved as the primary solutions. The relative rates at which these two motifs evolve depend on selection conditions, but under all conditions, either motif achieves similar performance. I1FFLs generally evolve more often than NFBLs. Selection for a tall pulse favors NFBLs, while selection for a fast response favors I1FFLs. I1FFLs are more evolutionarily accessible early on, before the effector protein evolves high expression; when NFBLs subsequently evolve, they tend to do so from a conjugated I1FFL-NFBL genotype. In the empirical S. cerevisiae TRN, output genes of NFBLs had higher expression levels than those of I1FFLs. These results suggest that evolutionary accessibility, and not relative functionality, shapes which motifs evolve in TRNs, and does so as a function of the expression levels of particular genes.

Glucocorticoid-Responsive Transcription Factor Krüppel-Like Factor 9 Regulates fkbp5 and Metabolism

Krüppel-like factor 9 (Klf9) is a feedforward regulator of glucocorticoid receptor (GR) signaling. Here we show that in zebrafish klf9 is expressed with GR-dependent oscillatory dynamics in synchrony with fkbp5, a GR target that encodes a negative feedback regulator of GR signaling. We found that fkbp5 transcript levels are elevated in klf9 -/- mutants and that Klf9 associates with chromatin at the fkbp5 promoter, which becomes hyperacetylated in klf9 -/ - mutants, suggesting that the GR regulates fkbp5 via an incoherent feedforward loop with klf9. As both the GR and Fkbp5 are known to regulate metabolism, we asked how loss of Klf9 affects metabolic rate and gene expression. We found that klf9 -/- mutants have a decreased oxygen consumption rate (OCR) and upregulate glycolytic genes, the promoter regions of which are enriched for potential Klf9 binding motifs. Our results suggest that Klf9 functions downstream of the GR to regulate cellular glucocorticoid responsivity and metabolic homeostasis.

Coexistence of Hopf-born rotation and heteroclinic cycling in a time-delayed three-gene auto-regulated and mutually-repressed core genetic regulation network

In this work, we study the behavior of a time-delayed mutually repressive auto-activating three-gene system. Delays are introduced to account for the location difference between DNA transcription that leads to production of messenger RNA and its translation that result in protein synthesis. We study the dynamics of the system using numerical simulations, computational bifurcation analysis and mathematical analysis. We find Hopf bifurcations leading to stable and unstable rotation in the system, and we study the rotational behavior as a function of cyclic mutual repression parameter asymmetry between each gene pair in the network. We focus on how rotation co-exists with a stable heteroclinic flow linking the three saddles in the system. We find that this coexistence allows for a transition between two markedly different types of rotation leading to strikingly different phenotypes. One type of rotation belongs to Hopf-induced rotation while the other type, belongs to heteroclinic cycling between three saddle nodes in the system. We discuss the evolutionary and biological implications of our findings.

Finding gene network topologies for given biological function with recurrent neural network

Searching for possible biochemical networks that perform a certain function is a challenge in systems biology. For simple functions and small networks, this can be achieved through an exhaustive search of the network topology space. However, it is difficult to scale this approach up to larger networks and more complex functions. Here we tackle this problem by training a recurrent neural network (RNN) to perform the desired function. By developing a systematic perturbative method to interrogate the successfully trained RNNs, we are able to distill the underlying regulatory network among the biological elements (genes, proteins, etc.). Furthermore, we show several cases where the regulation networks found by RNN can achieve the desired biological function when its edges are expressed by more realistic response functions, such as the Hill-function. This method can be used to link topology and function by helping uncover the regulation logic and network topology for complex tasks.

Networks are useful ways to describe interactions between molecules in a cell, but predicting the real topology of large networks can be challenging. Here, the authors use deep learning to predict the topology of networks that perform biologically-plausible functions.

How Retroactivity Affects the Behavior of Incoherent Feedforward Loops

An incoherent feedforward loop (IFFL) is a network motif known for its ability to accelerate responses and generate pulses. It remains an open question to understand the behavior of IFFLs in contexts with high levels of retroactivity, where an upstream transcription factor binds to numerous downstream binding sites. Here we study the behavior of IFFLs by simulating and comparing ODE models with different levels of retroactivity. We find that increasing retroactivity in an IFFL can increase, decrease, or keep the network's response time and pulse amplitude constant. This suggests that increasing retroactivity, traditionally considered an impediment to designing robust synthetic systems, could be exploited to improve the performance of IFFLs. In contrast, we find that increasing retroactivity in a negative autoregulated circuit can only slow the response. The ability of an IFFL to flexibly handle retroactivity may have contributed to its significant abundance in both bacterial and eukaryotic regulatory networks.

A theoretical model of neural maturation in the developing chick spinal cord

Cellular differentiation is a tightly regulated process under the control of intricate signaling and transcription factors interaction network working in coordination. These interactions make the systems dynamic, robust and stable but also difficult to dissect. In the spinal cord, recent work has shown that a network of FGF, WNT and Retinoic Acid (RA) signaling factors regulate neural maturation by directing the activity of a transcription factor network that contains CDX at its core. Here we have used partial and ordinary (Hill) differential equation based models to understand the spatiotemporal dynamics of the FGF/WNT/RA and the CDX/transcription factor networks, alone and in combination. We show that in both networks, the strength of interaction among network partners impacts the dynamics, behavior and output of the system. In the signaling network, interaction strength determine the position and size of discrete regions of cell differentiation and small changes in the strength of the interactions among networking partners can result in a signal overriding, balancing or oscillating with another signal. We also show that the spatiotemporal information generated by the signaling network can be conveyed to the CDX/transcription network to produces a transition zone that separates regions of high cell potency from regions of cell differentiation, in agreement with most in vivo observations. Importantly, one emerging property of the networks is their robustness to extrinsic disturbances, which allows the system to retain or canalize NP cells in developmental trajectories. This analysis provides a model for the interaction conditions underlying spinal cord cell maturation during embryonic axial elongation.

Chronic stress, physiological adaptation and developmental programming of the neuroendocrine stress system

Chronic stress undermines physical and mental health, in part via dysregulation of the neuroendocrine stress system. Key to understand this dysregulation is recognizing that the problem is not stress per se, but rather its chronicity. The optimally functioning stress system is highly dynamic, and negative feedback regulation enforces transient responses to acute stressors. Chronic stress overrides this, and adaptation to the chronicity can result in persistent dysregulation by altering sensitivity thresholds critical for control of system dynamics. Such adaptation involves plasticity within the central nervous system (CNS) as well as epigenetic regulation. When it occurs during development, it can have persistent effects on neuroendocrine regulation. Understanding how chronic stress programs development of the neuroendocrine stress system requires elucidation of stress-responsive gene regulatory networks that control CNS plasticity and development.

Network Topologies That Can Achieve Dual Function of Adaptation and Noise Attenuation

Many signaling systems execute adaptation under circumstances that require noise attenuation. Here, we identify an intrinsic trade-off existing between sensitivity and noise attenuation in the three-node networks. We demonstrate that although fine-tuning timescales in three-node adaptive networks can partially mediate this trade-off in this context, it prolongs adaptation time and imposes unrealistic parameter constraints. By contrast, four-node networks can effectively decouple adaptation and noise attenuation to achieve dual function without a trade-off, provided that these functions are executed sequentially. We illustrate ideas in seven biological examples, including Dictyostelium discoideum chemotaxis and the p53 signaling network and find that adaptive networks are often associated with a noise attenuation module. Our approach may be applicable to finding network design principles for other dual and multiple functions.

A quantitative method for estimating the adaptedness in a physiological study

Background

Existed mathematical models of individual adaptation are mostly reductionist by nature. Researchers usually a priori consider the subject adapted basing only on the fact of continued or prolonged influence of the harmful factor. This paper describes a method that allows assessing the physiological adaptedness to experimental challenges on the basis of holistic approach and quantitative criteria.

Methods

The suggested method comprises simple equations and incorporates into the model an indicator that differentiates functions in regard to their significance for determining physiological adaptedness considered as an outcome of the adaptive process.

Results

The proposed empirical model affords the possibility of comparing subjects in respect to their resistance to several loads. Physiological parameters were differentiated with regard to their significance for assessing adaptedness. Two examples of animal adaptation to exercise after physical training and plant adaptogen administration are considered.

Conclusion

The calculated index of adaptedness is useful in that it replaces wordy descriptions of large tables that reveal alterations in numerous parameters of many subjects under study.

Constructing network topologies for multiple signal-encoding functions

Background

Cells use signaling protein networks to sense their environment and mediate specific responses. Information about environmental stress is usually encoded in the dynamics of the signaling molecules, and qualitatively distinct dynamics of the same signaling molecule can lead to dramatically different cell fates. Exploring the design principles of networks with multiple signal-encoding functions is important for understanding how distinct dynamic patterns are shaped and integrated by real cellular networks, and for building cells with targeted sensing–response functions via synthetic biology.

Results

In this paper, we investigate multi-node enzymatic regulatory networks with three signal-encoding functions, i.e., dynamic responses of oscillation, transient activation, and sustained activation upon step stimulation by three different inducers, respectively. Taking into account competition effects of the substrates for the same enzyme in the enzymatic reactions, we searched for robust subnetworks for each signal-encoding function by three-node-network enumeration and then integrated the three subnetworks together via node-merging. The obtained tri-functional networks consisted of four to six nodes, and the core structures of these networks were hybrids of the motifs for the subfunctions.

Conclusions

The simplest but relatively robust tri-functional networks demonstrated that the three functions were compatible within a simple negative feedback loop. Depending on the network structure, the competition effects of the substrates for the same enzyme within the networks could promote or hamper the target functions, and can create implicit functional motifs. Overall, the networks we obtained could in principle be synthesized to construct dynamic control circuits with multiple target functions.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0676-5) contains supplementary material, which is available to authorized users.

Bi-functional biochemical networks

Understanding the relationship between the topology of a network and its function remains an important question in biological physics. However, this is not a one-to-one mapping. Often the behavior of a signaling system varies with the input signal it receives. For example, some biological systems show adaptation when they receive a low input signal while they show oscillation with a high input signal. We therefore set out to find all possible two-node and three-node networks that can perform both adaptation and oscillation with transcriptional regulation and enzymatic reactions. For two-node networks, we identified all bi-functional topologies by analyzing the Jacobean matrix. For three-node networks, they were identified by enumeration. We further investigated how the system can be transformed between these two functions. We found that the switching of functions can be achieved through changing anyone of the several key parameters, including the input signal level.