Logarithmic and power law input-output relations in sensory systems with fold-change detection

Stress-induced failure of embodied cognition: A general model

We derive the classic, ubiquitous, but enigmatic Yerkes-Dodson effect of applied stress on real-world performance in a highly natural manner from fundamental assumptions on cognition and its dynamics, as constrained by the asymptotic limit theorems of information and control theories. We greatly extend the basic approach by showing how differences in an underlying probability model can affect the dynamics of decision across a broad range of cognitive enterprise. Most particularly, however, this development may help inform our understanding of the different expressions of human psychopathology. A 'thin tailed' underlying distribution appears to characterize expression of 'ordinary' situational depression/anxiety symptoms of conditions like burnout induced by toxic stress. A 'fat tailed' underlying distribution appears to be associated with brain structure and function abnormalities leading to serious mental illness and poor decision making where symptoms are not only emerging in the setting of severe stress but may also appear in a highly punctuated manner at relatively lower levels of stress. A simple hierarchical optimization shows how environmental 'shadow price' constraints can buffer or aggravate the effects of stress and arousal. Extension of the underlying theory to other patterns of pathology, like immune disorders and premature aging, seems apt. Applications to the punctuated dynamics of institutional cognition under stress also appear possible. Ultimately, the probability models studied here can be converted to new statistical tools for the analysis of observational and experimental data.

A quantitative systems pharmacology model of the pathophysiology and treatment of COVID-19 predicts optimal timing of pharmacological interventions

A quantitative systems pharmacology (QSP) model of the pathogenesis and treatment of SARS-CoV-2 infection can streamline and accelerate the development of novel medicines to treat COVID-19. Simulation of clinical trials allows in silico exploration of the uncertainties of clinical trial design and can rapidly inform their protocols. We previously published a preliminary model of the immune response to SARS-CoV-2 infection. To further our understanding of COVID-19 and treatment, we significantly updated the model by matching a curated dataset spanning viral load and immune responses in plasma and lung. We identified a population of parameter sets to generate heterogeneity in pathophysiology and treatment and tested this model against published reports from interventional SARS-CoV-2 targeting mAb and antiviral trials. Upon generation and selection of a virtual population, we match both the placebo and treated responses in viral load in these trials. We extended the model to predict the rate of hospitalization or death within a population. Via comparison of the in silico predictions with clinical data, we hypothesize that the immune response to virus is log-linear over a wide range of viral load. To validate this approach, we show the model matches a published subgroup analysis, sorted by baseline viral load, of patients treated with neutralizing Abs. By simulating intervention at different time points post infection, the model predicts efficacy is not sensitive to interventions within five days of symptom onset, but efficacy is dramatically reduced if more than five days pass post symptom onset prior to treatment.

Design principles of improving the dose-response alignment in coupled GTPase switches

"Dose-response alignment" (DoRA), where the downstream response of cellular signaling pathways closely matches the fraction of activated receptor, can improve the fidelity of dose information transmission. The negative feedback has been experimentally identified as a key component for DoRA, but numerical simulations indicate that negative feedback is not sufficient to achieve perfect DoRA, i.e., perfect match of downstream response and receptor activation level. Thus a natural question is whether there exist design principles for signaling motifs within only negative feedback loops to improve DoRA to near-perfect DoRA. Here, we investigated several model formulations of an experimentally validated circuit that couples two molecular switches-mGTPase (monomeric GTPase) and tGTPase (heterotrimeric GTPases) - with negative feedback loops. In the absence of feedback, the low and intermediate mGTPase activation levels benefit DoRA in mass action and Hill-function models, respectively. Adding negative feedback has versatile roles on DoRA: it may impair DoRA in the mass action model with low mGTPase activation level and Hill-function model with intermediate mGTPase activation level; in other cases, i.e., the mass action model with a high mGTPase activation level or the Hill-function model with a non-intermediate mGTPase activation level, it improves DoRA. Furthermore, we found that DoRA in a longer cascade (i.e., tGTPase) can be obtained using Hill-function kinetics under certain conditions. In summary, we show how ranges of activity of mGTPase, reaction kinetics, the negative feedback, and the cascade length affect DoRA. This work provides a framework for improving the DoRA performance in signaling motifs with negative feedback.

Synthetic neuromorphic computing in living cells

Computational properties of neuronal networks have been applied to computing systems using simplified models comprising repeated connected nodes, e.g., perceptrons, with decision-making capabilities and flexible weighted links. Analogously to their revolutionary impact on computing, neuro-inspired models can transform synthetic gene circuit design in a manner that is reliable, efficient in resource utilization, and readily reconfigurable for different tasks. To this end, we introduce the perceptgene, a perceptron that computes in the logarithmic domain, which enables efficient implementation of artificial neural networks in Escherichia coli cells. We successfully modify perceptgene parameters to create devices that encode a minimum, maximum, and average of analog inputs. With these devices, we create multi-layer perceptgene circuits that compute a soft majority function, perform an analog-to-digital conversion, and implement a ternary switch. We also create a programmable perceptgene circuit whose computation can be modified from OR to AND logic using small molecule induction. Finally, we show that our approach enables circuit optimization via artificial intelligence algorithms.

A Novel Method for Lung Image Processing Using Complex Networks

The High-Resolution Computed Tomography (HRCT) detection and diagnosis of diffuse lung disease is primarily based on the recognition of a limited number of specific abnormal findings, pattern combinations or their distributions, as well as anamnesis and clinical information. Since texture recognition has a very high accuracy percentage if a complex network approach is used, this paper aims to implement such a technique customized for diffuse interstitial lung diseases (DILD). The proposed procedure translates HRCT lung imaging into complex networks by taking samples containing a secondary lobule, converting them into complex networks and analyzing them in three dimensions: emphysema, ground glass opacity, and consolidation. This method was evaluated on a 60-patient lot and the results showed a clear, quantifiable difference between healthy and affected lungs. By deconstructing the image on three pathological axes, the method offers an objective way to quantify DILD details which, so far, have only been analyzed subjectively.

The dopamine circuit as a reward-taxis navigation system

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

The series of a four-node motif and coherent type-1 feed-forward loop can provide sensitive detection over arbitrary range of input signal, thereby explain Weber's law in higher-order sensory processes, and compute logarithm

Weber's law states that the ratio of the smallest perceptual change in an input signal and the background signal is constant. The law is observed across the perception of weight, light intensity, and sound intensity and pitch. To explain Weber's law observed in steady-state responses, two models of perception have been proposed, namely the logarithmic and the linear model. This paper argues in favour of the linear model, which requires the sensory system to generate linear input-output relationship over several orders of magnitude. To this end, a four-node motif (FNM) is constructed from first principles whose series provides almost linear relationship between input signal and the output over arbitrary range of input signal. Mathematical analysis into the origin of this quasi-linear relationship shows that the series of coherent type-1 feed-forward loop (C1-FFL) is able to provide perfectly linear input-output relationship over arbitrary range of input signal. FNM also reproduces the neuronal data of numerosity detection study on the monkey. The series of FNM also provides a mechanism for sensitive detection over arbitrary range of input signal when the output has an upper limit. Further, the series of FNM provides a general basis for a class of bow-tie architecture where the number of receptors is much lower than the range of input signal and the "decoded output". Besides (quasi-)linear input-output relationship, another example of this class of bow-tie architecture that the series of FNM is able to produce is absorption spectra of cone opsins of humans. Further, the series of FNM and C1-FFL, both, can compute logarithm over arbitrary range of input signal.

Root electrotropism in Arabidopsis does not depend on auxin distribution but requires cytokinin biosynthesis

Efficient foraging by plant roots relies on the ability to sense multiple physical and chemical cues in soil and to reorient growth accordingly (tropism). Root tropisms range from sensing gravity (gravitropism), light (phototropism), water (hydrotropism), touch (thigmotropism), and more. Electrotropism, also known as galvanotropism, is the phenomenon of aligning growth with external electric fields and currents. Although root electrotropism has been observed in a few species since the end of the 19th century, its molecular and physical mechanisms remain elusive, limiting its comparison with the more well-defined sensing pathways in plants. Here, we provide a quantitative and molecular characterization of root electrotropism in the model system Arabidopsis (Arabidopsis thaliana), showing that it does not depend on an asymmetric distribution of the plant hormone auxin, but instead requires the biosynthesis of a second hormone, cytokinin. We also show that the dose-response kinetics of the early steps of root electrotropism follows a power law analogous to the one observed in some physiological reactions in animals. Future studies involving more extensive molecular and quantitative characterization of root electrotropism would represent a step toward a better understanding of signal integration in plants and would also serve as an independent outgroup for comparative analysis of electroreception in animals and fungi.

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.

An opponent process for alcohol addiction based on changes in endocrine gland mass

Consuming addictive drugs is often initially pleasurable, but escalating drug intake eventually recruits physiological anti-reward systems called opponent processes that cause tolerance and withdrawal symptoms. Opponent processes are fundamental for the addiction process, but their physiological basis is not fully characterized. Here, we propose an opponent processes mechanism centered on the endocrine stress response, the hypothalamic-pituitary-adrenal (HPA) axis. We focus on alcohol addiction, where the HPA axis is activated and secretes β-endorphin, causing euphoria and analgesia. Using a mathematical model, we show that slow changes in the functional mass of HPA glands act as an opponent process for β-endorphin secretion. The model explains hormone dynamics in alcohol addiction and experiments on alcohol preference in rodents. The opponent process is based on fold-change detection (FCD) where β-endorphin responses are relative rather than absolute; FCD confers vulnerability to addiction but has adaptive roles for learning. Our model suggests gland mass changes as potential targets for intervention in addiction.

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Addiction involves tolerance and withdrawal over weeks

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Model of the HPA-axis and β-endorphins explains tolerance and withdrawal

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Effects due to changes in the functional mass of endocrine glands

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Fold-change detection makes circuit prone to addiction but boosts learning

Autonomous and Assisted Control for Synthetic Microbiology

The control of microbes and microbial consortia to achieve specific functions requires synthetic circuits that can reliably cope with internal and external perturbations. Circuits that naturally evolved to regulate biological functions are frequently robust to alterations in their parameters. As the complexity of synthetic circuits increases, synthetic biologists need to implement such robust control "by design". This is especially true for intercellular signaling circuits for synthetic consortia, where robustness is highly desirable, but its mechanisms remain unclear. Cybergenetics, the interface between synthetic biology and control theory, offers two approaches to this challenge: external (computer-aided) and internal (autonomous) control. Here, we review natural and synthetic microbial systems with robustness, and outline experimental approaches to implement such robust control in microbial consortia through population-level cybergenetics. We propose that harnessing natural intercellular circuit topologies with robust evolved functions can help to achieve similar robust control in synthetic intercellular circuits. A "hybrid biology" approach, where robust synthetic microbes interact with natural consortia and-additionally-with external computers, could become a useful tool for health and environmental applications.

Arrestin-3 scaffolding of the JNK3 cascade suggests a mechanism for signal amplification

Scaffold proteins tether and orient components of a signaling cascade to facilitate signaling. Although much is known about how scaffolds colocalize signaling proteins, it is unclear whether scaffolds promote signal amplification. Here, we used arrestin-3, a scaffold of the ASK1-MKK4/7-JNK3 cascade, as a model to understand signal amplification by a scaffold protein. We found that arrestin-3 exhibited >15-fold higher affinity for inactive JNK3 than for active JNK3, and this change involved a shift in the binding site following JNK3 activation. We used systems biochemistry modeling and Bayesian inference to evaluate how the activation of upstream kinases contributed to JNK3 phosphorylation. Our combined experimental and computational approach suggested that the catalytic phosphorylation rate of JNK3 at Thr-221 by MKK7 is two orders of magnitude faster than the corresponding phosphorylation of Tyr-223 by MKK4 with or without arrestin-3. Finally, we showed that the release of activated JNK3 was critical for signal amplification. Collectively, our data suggest a "conveyor belt" mechanism for signal amplification by scaffold proteins. This mechanism informs on a long-standing mystery for how few upstream kinase molecules activate numerous downstream kinases to amplify signaling.

Creative exploration as a scale-invariant search on a meaning landscape

Can knowledge accumulated in systems biology on mechanisms governing cell behavior help us to elucidate cognitive processes, such as human creative search? To address this, we focus on the property of scale invariance, which allows sensory systems to adapt to environmental signals spanning orders of magnitude. For example, bacteria search for nutrients, by responding to relative changes in nutrient concentration rather than absolute levels, via a sensory mechanism termed fold-change detection (FCD). Scale invariance is prevalent in cognition, yet the specific mechanisms are mostly unknown. Here, we screen many possible dynamic equation topologies, to find that an FCD model best describes creative search dynamics. The model further predicts robustness to variations in meaning perception, in agreement with behavioral data. We thus suggest FCD as a specific mechanism for scale invariant search, connecting sensory processes of cells and cognitive processes in human.

Fold-change Response of Photosynthesis to Step Increases of Light Level

Plants experience light intensity over several orders of magnitude. High light is stressful, and plants have several protective feedback mechanisms against this stress. Here we asked how plants respond to sudden rises at low ambient light, far below stressful levels. For this, we studied the fluorescence of excited chlorophyll a of photosystem II in Arabidopsis thaliana plants in response to step increases in light level at different background illuminations. We found a response at low-medium light with characteristics of a sensory system: fold-change detection (FCD), Weber law, and exact adaptation, in which the response depends only on relative, and not absolute, light changes. We tested various FCD circuits and provide evidence for an incoherent feedforward mechanism upstream of known stress response feedback loops. These findings suggest that plant photosynthesis may have a sensory modality for low light background that responds early to small light increases, to prepare for damaging high light levels.

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Chl a fluorescence responds to fold-change (FCD) in low-medium input light

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Identified fast feedforward (IFFL) regulation that depends on direct light input

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The direct sensing of input and FCD response are typical of sensory modules

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The IFFL precedes known feedback photoprotective regulation

Hilbert-Schmidt and Sobol sensitivity indices for static and time series Wnt signaling measurements in colorectal cancer - part A

Background

Ever since the accidental discovery of Wingless [Sharma R.P., Drosophila information service, 1973, 50, p 134], research in the field of Wnt signaling pathway has taken significant strides in wet lab experiments and various cancer clinical trials, augmented by recent developments in advanced computational modeling of the pathway. Information rich gene expression profiles reveal various aspects of the signaling pathway and help in studying different issues simultaneously. Hitherto, not many computational studies exist which incorporate the simultaneous study of these issues.

Results

This manuscript ∙ explores the strength of contributing factors in the signaling pathway, ∙ analyzes the existing causal relations among the inter/extracellular factors effecting the pathway based on prior biological knowledge and ∙ investigates the deviations in fold changes in the recently found prevalence of psychophysical laws working in the pathway. To achieve this goal, local and global sensitivity analysis is conducted on the (non)linear responses between the factors obtained from static and time series expression profiles using the density (Hilbert-Schmidt Information Criterion) and variance (Sobol) based sensitivity indices.

Conclusion

The results show the advantage of using density based indices over variance based indices mainly due to the former’s employment of distance measures & the kernel trick via Reproducing kernel Hilbert space (RKHS) that capture nonlinear relations among various intra/extracellular factors of the pathway in a higher dimensional space. In time series data, using these indices it is now possible to observe where in time, which factors get influenced & contribute to the pathway, as changes in concentration of the other factors are made. This synergy of prior biological knowledge, sensitivity analysis & representations in higher dimensional spaces can facilitate in time based administration of target therapeutic drugs & reveal hidden biological information within colorectal cancer samples.

Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration

Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.

Quantitative Systems Biology to decipher design principles of a dynamic cell cycle network: the "Maximum Allowable mammalian Trade-Off-Weight" (MAmTOW)

Network complexity is required to lend cellular processes flexibility to respond timely to a variety of dynamic signals, while simultaneously warranting robustness to protect cellular integrity against perturbations. The cell cycle serves as a paradigm for such processes; it maintains its frequency and temporal structure (although these may differ among cell types) under the former, but accelerates under the latter. Cell cycle molecules act together in time and in different cellular compartments to execute cell type-specific programs. Strikingly, the timing at which molecular switches occur is controlled by abundance and stoichiometry of multiple proteins within complexes. However, traditional methods that investigate one effector at a time are insufficient to understand how modulation of protein complex dynamics at cell cycle transitions shapes responsiveness, yet preserving robustness. To overcome this shortcoming, we propose a multidisciplinary approach to gain a systems-level understanding of quantitative cell cycle dynamics in mammalian cells from a new perspective. By suggesting advanced experimental technologies and dedicated modeling approaches, we present innovative strategies (i) to measure absolute protein concentration in vivo, and (ii) to determine how protein dosage, e.g., altered protein abundance, and spatial (de)regulation may affect timing and robustness of phase transitions. We describe a method that we name “Maximum Allowable mammalian Trade–Off–Weight” (MAmTOW), which may be realized to determine the upper limit of gene copy numbers in mammalian cells. These aspects, not covered by current systems biology approaches, are essential requirements to generate precise computational models and identify (sub)network-centered nodes underlying a plethora of pathological conditions.

Revisiting chemoaffinity theory: Chemotactic implementation of topographic axonal projection

Neural circuits are wired by chemotactic migration of growth cones guided by extracellular guidance cue gradients. How growth cone chemotaxis builds the macroscopic structure of the neural circuit is a fundamental question in neuroscience. I addressed this issue in the case of the ordered axonal projections called topographic maps in the retinotectal system. In the retina and tectum, the erythropoietin-producing hepatocellular (Eph) receptors and their ligands, the ephrins, are expressed in gradients. According to Sperry's chemoaffinity theory, gradients in both the source and target areas enable projecting axons to recognize their proper terminals, but how axons chemotactically decode their destinations is largely unknown. To identify the chemotactic mechanism of topographic mapping, I developed a mathematical model of intracellular signaling in the growth cone that focuses on the growth cone's unique chemotactic property of being attracted or repelled by the same guidance cues in different biological situations. The model presented mechanism by which the retinal growth cone reaches the correct terminal zone in the tectum through alternating chemotactic response between attraction and repulsion around a preferred concentration. The model also provided a unified understanding of the contrasting relationships between receptor expression levels and preferred ligand concentrations in EphA/ephrinA- and EphB/ephrinB-encoded topographic mappings. Thus, this study redefines the chemoaffinity theory in chemotactic terms.

A mathematical model of mechanotransduction reveals how mechanical memory regulates mesenchymal stem cell fate decisions

BACKGROUND

Mechanical and biophysical properties of the cellular microenvironment regulate cell fate decisions. Mesenchymal stem cell (MSC) fate is influenced by past mechanical dosing (memory), but the mechanisms underlying this process have not yet been well defined. We have yet to understand how memory affects specific cell fate decisions, such as the differentiation of MSCs into neurons, adipocytes, myocytes, and osteoblasts.

RESULTS

We study a minimal gene regulatory network permissive of multi-lineage MSC differentiation into four cell fates. We present a continuous model that is able to describe the cell fate transitions that occur during differentiation, and analyze its dynamics with tools from multistability, bifurcation, and cell fate landscape analysis, and via stochastic simulation. Whereas experimentally, memory has only been observed during osteogenic differentiation, this model predicts that memory regions can exist for each of the four MSC-derived cell lineages. We can predict the substrate stiffness ranges over which memory drives differentiation; these are directly testable in an experimental setting. Furthermore, we quantitatively predict how substrate stiffness and culture duration co-regulate the fate of a stem cell, and we find that the feedbacks from the differentiating MSC onto its substrate are critical to preserve mechanical memory. Strikingly, we show that re-seeding MSCs onto a sufficiently soft substrate increases the number of cell fates accessible.

CONCLUSIONS

Control of MSC differentiation is crucial for the success of much-lauded regenerative therapies based on MSCs. We have predicted new memory regions that will directly impact this control, and have quantified the size of the memory region for osteoblasts, as well as the co-regulatory effects on cell fates of substrate stiffness and culture duration. Taken together, these results can be used to develop novel strategies to better control the fates of MSCs in vitro and following transplantation.

Fold-change detection and scale invariance of cell-cell signaling in social amoeba

Cell-cell signaling is subject to variability in the extracellular volume, cell number, and dilution that potentially increase uncertainty in the absolute concentrations of the extracellular signaling molecules. To direct cell aggregation, the social amoebae Dictyostelium discoideum collectively give rise to oscillations and waves of cyclic adenosine 3',5'-monophosphate (cAMP) under a wide range of cell density. To date, the systems-level mechanism underlying the robustness is unclear. By using quantitative live-cell imaging, here we show that the magnitude of the cAMP relay response of individual cells is determined by fold change in the extracellular cAMP concentrations. The range of cell density and exogenous cAMP concentrations that support oscillations at the population level agrees well with conditions that support a large fold-change-dependent response at the single-cell level. Mathematical analysis suggests that invariance of the oscillations to density transformation is a natural outcome of combining secrete-and-sense systems with a fold-change detection mechanism.

Improving Metabolic Pathway Efficiency by Statistical Model-Based Multivariate Regulatory Metabolic Engineering

Metabolic engineering entails target modification of cell metabolism to maximize the production of a specific compound. For empowering combinatorial optimization in strain engineering, tools and algorithms are needed to efficiently sample the multidimensional gene expression space and locate the desirable overproduction phenotype. We addressed this challenge by employing design of experiment (DoE) models to quantitatively correlate gene expression with strain performance. By fractionally sampling the gene expression landscape, we statistically screened the dominant enzyme targets that determine metabolic pathway efficiency. An empirical quadratic regression model was subsequently used to identify the optimal gene expression patterns of the investigated pathway. As a proof of concept, our approach yielded the natural product violacein at 525.4 mg/L in shake flasks, a 3.2-fold increase from the baseline strain. Violacein production was further increased to 1.31 g/L in a controlled benchtop bioreactor. We found that formulating discretized gene expression levels into logarithmic variables (Linlog transformation) was essential for implementing this DoE-based optimization procedure. The reported methodology can aid multivariate combinatorial pathway engineering and may be generalized as a standard procedure for accelerating strain engineering and improving metabolic pathway efficiency.

Chemical reaction networks for computing logarithm

Living cells constantly process information from their living environment. It has recently been shown that a number of cell signaling mechanisms (e.g. G protein-coupled receptor and epidermal growth factor) can be interpreted as computing the logarithm of the ligand concentration. This suggests that logarithm is a fundamental computation primitive in cells. There is also an increasing interest in the synthetic biology community to implement analog computation and computing the logarithm is one such example. The aim of this article is to study how the computation of logarithm can be realized using chemical reaction networks (CRNs). CRNs cannot compute logarithm exactly. A standard method is to use power series or rational function approximation to compute logarithm approximately. Although CRNs can realize these polynomial or rational function computations in a straightforward manner, the issue is that in order to be able to compute logarithm accurately over a large input range, it is necessary to use high-order approximation that results in CRNs with a large number of reactions. This article proposes a novel method to compute logarithm accurately in CRNs while keeping the number of reactions in CRNs low. The proposed method can create CRNs that can compute logarithm to different levels of accuracy by adjusting two design parameters. In this article, we present the chemical reactions required to realize the CRNs for computing logarithm. The key contribution of this article is a novel method to create CRNs that can compute logarithm accurately over a wide input range using only a small number of chemical reactions.

Multi-phasic bi-directional chemotactic responses of the growth cone

The nerve growth cone is bi-directionally attracted and repelled by the same cue molecules depending on the situations, while other non-neural chemotactic cells usually show uni-directional attraction or repulsion toward their specific cue molecules. However, how the growth cone differs from other non-neural cells remains unclear. Toward this question, we developed a theory for describing chemotactic response based on a mathematical model of intracellular signaling of activator and inhibitor. Our theory was first able to clarify the conditions of attraction and repulsion, which are determined by balance between activator and inhibitor, and the conditions of uni- and bi-directional responses, which are determined by dose-response profiles of activator and inhibitor to the guidance cue. With biologically realistic sigmoidal dose-responses, our model predicted tri-phasic turning response depending on intracellular Ca²⁺ level, which was then experimentally confirmed by growth cone turning assays and Ca²⁺ imaging. Furthermore, we took a reverse-engineering analysis to identify balanced regulation between CaMKII (activator) and PP1 (inhibitor) and then the model performance was validated by reproducing turning assays with inhibitions of CaMKII and PP1. Thus, our study implies that the balance between activator and inhibitor underlies the multi-phasic bi-directional turning response of the growth cone.

Rescaling of Spatio-Temporal Sensing in Eukaryotic Chemotaxis

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient—an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies.

Processing Oscillatory Signals by Incoherent Feedforward Loops

From the timing of amoeba development to the maintenance of stem cell pluripotency, many biological signaling pathways exhibit the ability to differentiate between pulsatile and sustained signals in the regulation of downstream gene expression. While the networks underlying this signal decoding are diverse, many are built around a common motif, the incoherent feedforward loop (IFFL), where an input simultaneously activates an output and an inhibitor of the output. With appropriate parameters, this motif can exhibit temporal adaptation, where the system is desensitized to a sustained input. This property serves as the foundation for distinguishing input signals with varying temporal profiles. Here, we use quantitative modeling to examine another property of IFFLs—the ability to process oscillatory signals. Our results indicate that the system’s ability to translate pulsatile dynamics is limited by two constraints. The kinetics of the IFFL components dictate the input range for which the network is able to decode pulsatile dynamics. In addition, a match between the network parameters and input signal characteristics is required for optimal “counting”. We elucidate one potential mechanism by which information processing occurs in natural networks, and our work has implications in the design of synthetic gene circuits for this purpose.

From circadian clocks to ultradian rhythms, oscillatory signals are found ubiquitously in nature. These oscillations are crucial in the regulation of cellular processes. While the fundamental design principles underlying the generation of these oscillations are extensively studied, the mechanisms for decoding these signals are underappreciated. With implications in both the basic understanding of how cells process temporal signals and the design of synthetic systems, we use quantitative modeling to probe one mechanism, the counting of pulses. We demonstrate the capability of an Incoherent Feedforward Loop motif for the differentiation between sustained and oscillatory input signals.

Allosteric proteins as logarithmic sensors

Many sensory systems, from vision and hearing in animals to signal transduction in cells, respond to fold changes in signal relative to background. Responding to fold change requires that the system senses signal on a logarithmic scale, responding identically to a change in signal level from 1 to 3, or from 10 to 30. It is an ongoing search in the field to understand the ways in which a logarithmic sensor can be implemented at the molecular level. In this work, we present evidence that logarithmic sensing can be implemented with a single protein, by means of allosteric regulation. Specifically, we find that mathematical models show that allosteric proteins can respond to stimuli on a logarithmic scale. Next, we present evidence from measurements in the literature that some allosteric proteins do operate in a parameter regime that permits logarithmic sensing. Finally, we present examples suggesting that allosteric proteins are indeed used in this capacity: allosteric proteins play a prominent role in systems where fold-change detection has been proposed. This finding suggests a role as logarithmic sensors for the many allosteric proteins across diverse biological processes.

Quantitative measures for redox signaling

Redox signaling is now recognized as an important regulatory mechanism for a number of cellular processes including the antioxidant response, phosphokinase signal transduction and redox metabolism. While there has been considerable progress in identifying the cellular machinery involved in redox signaling, quantitative measures of redox signals have been lacking, limiting efforts aimed at understanding and comparing redox signaling under normoxic and pathogenic conditions. Here we have outlined some of the accepted principles for redox signaling, including the description of hydrogen peroxide as a signaling molecule and the role of kinetics in conferring specificity to these signaling events. Based on these principles, we then develop a working definition for redox signaling and review a number of quantitative methods that have been employed to describe signaling in other systems. Using computational modeling and published data, we show how time- and concentration- dependent analyses, in particular, could be used to quantitatively describe redox signaling and therefore provide important insights into the functional organization of redox networks. Finally, we consider some of the key challenges with implementing these methods.

Comparative Study of Regulatory Circuits in Two Sea Urchin Species Reveals Tight Control of Timing and High Conservation of Expression Dynamics

Accurate temporal control of gene expression is essential for normal development and must be robust to natural genetic and environmental variation. Studying gene expression variation within and between related species can delineate the level of expression variability that development can tolerate. Here we exploit the comprehensive model of sea urchin gene regulatory networks and generate high-density expression profiles of key regulatory genes of the Mediterranean sea urchin, Paracentrotus lividus (Pl). The high resolution of our studies reveals highly reproducible gene initiation times that have lower variation than those of maximal mRNA levels between different individuals of the same species. This observation supports a threshold behavior of gene activation that is less sensitive to input concentrations. We then compare Mediterranean sea urchin gene expression profiles to those of its Pacific Ocean relative, Strongylocentrotus purpuratus (Sp). These species shared a common ancestor about 40 million years ago and show highly similar embryonic morphologies. Our comparative analyses of five regulatory circuits operating in different embryonic territories reveal a high conservation of the temporal order of gene activation but also some cases of divergence. A linear ratio of 1.3-fold between gene initiation times in Pl and Sp is partially explained by scaling of the developmental rates with temperature. Scaling the developmental rates according to the estimated Sp-Pl ratio and normalizing the expression levels reveals a striking conservation of relative dynamics of gene expression between the species. Overall, our findings demonstrate the ability of biological developmental systems to tightly control the timing of gene activation and relative dynamics and overcome expression noise induced by genetic variation and growth conditions.