Molecular circuits for dynamic noise filtering

Advanced methods for gene network identification and noise decomposition from single-cell data

Central to analyzing noisy gene expression systems is solving the Chemical Master Equation (CME), which characterizes the probability evolution of the reacting species' copy numbers. Solving CMEs for high-dimensional systems suffers from the curse of dimensionality. Here, we propose a computational method for improved scalability through a divide-and-conquer strategy that optimally decomposes the whole system into a leader system and several conditionally independent follower subsystems. The CME is solved by combining Monte Carlo estimation for the leader system with stochastic filtering procedures for the follower subsystems. We demonstrate this method with high-dimensional numerical examples and apply it to identify a yeast transcription system at the single-cell resolution, leveraging mRNA time-course experimental data. The identification results enable an accurate examination of the heterogeneity in rate parameters among isogenic cells. To validate this result, we develop a noise decomposition technique exploiting time-course data but requiring no supplementary components, e.g., dual-reporters.

Effects of mRNA conformational switching on translational noise in gene circuits

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Bioenergetic costs and the evolution of noise regulation by microRNAs

Noise control, together with other regulatory functions facilitated by microRNAs (miRNAs), is believed to have played important roles in the evolution of multicellular eukaryotic organisms. miRNAs can dampen protein fluctuations via enhanced degradation of messenger RNA (mRNA), but this requires compensation by increased mRNA transcription to maintain the same expression levels. The overall mechanism is metabolically expensive, leading to questions about how it might have evolved in the first place. We develop a stochastic model of miRNA noise regulation, coupled with a detailed analysis of the associated metabolic costs. Additionally, we calculate binding free energies for a range of miRNA seeds, the short sequences which govern target recognition. We argue that natural selection may have fine-tuned the Michaelis-Menten constant [Formula: see text] describing miRNA-mRNA affinity and show supporting evidence from analysis of experimental data. [Formula: see text] is constrained by seed length, and optimal noise control (minimum protein variance at a given energy cost) is achievable for seeds of 6 to 7 nucleotides in length, the most commonly observed types. Moreover, at optimality, the degree of noise reduction approaches the theoretical bound set by the Wiener-Kolmogorov linear filter. The results illustrate how selective pressure toward energy efficiency has potentially shaped a crucial regulatory pathway in eukaryotes.

Bye bye, linearity, bye: quantification of the mean for linear CRNs in a random environment

Molecular reactions within a cell are inherently stochastic, and cells often differ in morphological properties or interact with a heterogeneous environment. Consequently, cell populations exhibit heterogeneity both due to these intrinsic and extrinsic causes. Although state-of-the-art studies that focus on dissecting this heterogeneity use single-cell measurements, the bulk data that shows only the mean expression levels is still in routine use. The fingerprint of the heterogeneity is present also in bulk data, despite being hidden from direct measurement. In particular, this heterogeneity can affect the mean expression levels via bimolecular interactions with low-abundant environment species. We make this statement rigorous for the class of linear reaction systems that are embedded in a discrete state Markov environment. The analytic expression that we provide for the stationary mean depends on the reaction rate constants of the linear subsystem, as well as the generator and stationary distribution of the Markov environment. We demonstrate the effect of the environment on the stationary mean. Namely, we show how the heterogeneous case deviates from the quasi-steady state (Q.SS) case when the embedded system is fast compared to the environment.

Systematic analysis of noise reduction properties of coupled and isolated feed-forward loops

Cells can maintain their homeostasis in a noisy environment since their signaling pathways can filter out noise somehow. Several network motifs have been proposed for biological noise filtering and, among these, feed-forward loops have received special attention. Specific feed-forward loops show noise reducing capabilities, but we notice that this feature comes together with a reduced signal transducing performance. In posttranslational signaling pathways feed-forward loops do not function in isolation, rather they are coupled with other motifs to serve a more complex function. Feed-forward loops are often coupled to other feed-forward loops, which could affect their noise-reducing capabilities. Here we systematically study all feed-forward loop motifs and all their pairwise coupled systems with activation-inactivation kinetics to identify which networks are capable of good noise reduction, while keeping their signal transducing performance. Our analysis shows that coupled feed-forward loops can provide better noise reduction and, at the same time, can increase the signal transduction of the system. The coupling of two coherent 1 or one coherent 1 and one incoherent 4 feed-forward loops can give the best performance in both of these measures.

Cellular behavior can be affected by noise in molecular interactions. Signaling pathways should process noisy input signals and support cellular decision making by properly transducing the signals, while removing noise from them. Three component networks of feed-forward loops (FFLs) have been proposed to serve as ideal noise reducers, while linear pathways were shown to be good signal transducers. These signaling units do not work in isolation, so there is a possibility that a combination of various feed-forward loops can provide good noise reduction, while maintaining good signal transduction. To test this hypothesis, we have systematically tested the noise reducing and signal transducing capabilities of all possible combinations of feed-forward loops and compared them with the performance of individual FFLs. We built mathematical models of all these systems and compared their capabilities at reducing noise in the input signal while maintaining responses to meaningful changes in the incoming signal. We found that a combination of two copies of a special type of fully positive signaling FFLs is the best noise reducer, while a combination of two incoherent (one positive, one negative signal) FFLs can provide the best signal transduction. The combination of these two FFLs could provide good signal processing where both noise reduction and signal transduction are achieved.

Cellular Signaling beyond the Wiener-Kolmogorov Limit

Accurate propagation of signals through stochastic biochemical networks involves significant expenditure of cellular resources. The same is true for regulatory mechanisms that suppress fluctuations in biomolecular populations. Wiener-Kolmogorov (WK) optimal noise filter theory, originally developed for engineering problems, has recently emerged as a valuable tool to estimate the maximum performance achievable in such biological systems for a given metabolic cost. However, WK theory has one assumption that potentially limits its applicability: it relies on a linear, continuum description of the reaction dynamics. Despite this, up to now no explicit test of the theory in nonlinear signaling systems with discrete molecular populations has ever seen performance beyond the WK bound. Here we report the first direct evidence of the bound being broken. To accomplish this, we develop a theoretical framework for multilevel signaling cascades, including the possibility of feedback interactions between input and output. In the absence of feedback, we introduce an analytical approach that allows us to calculate exact moments of the stationary distribution for a nonlinear system. With feedback, we rely on numerical solutions of the system's master equation. The results show WK violations in two common network motifs: a two-level signaling cascade and a negative feedback loop. However, the magnitude of the violation is biologically negligible, particularly in the parameter regime where signaling is most effective. The results demonstrate that while WK theory does not provide strict bounds, its predictions for performance limits are excellent approximations, even for nonlinear systems.

Connection between the Bacterial Chemotactic Network and Optimal Filtering

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.

Characterization and mitigation of gene expression burden in mammalian cells

Despite recent advances in circuit engineering, the design of genetic networks in mammalian cells is still painstakingly slow and fraught with inexplicable failures. Here, we demonstrate that transiently expressed genes in mammalian cells compete for limited transcriptional and translational resources. This competition results in the coupling of otherwise independent exogenous and endogenous genes, creating a divergence between intended and actual function. Guided by a resource-aware mathematical model, we identify and engineer natural and synthetic miRNA-based incoherent feedforward loop (iFFL) circuits that mitigate gene expression burden. The implementation of these circuits features the use of endogenous miRNAs as elementary components of the engineered iFFL device, a versatile hybrid design that allows burden mitigation to be achieved across different cell-lines with minimal resource requirements. This study establishes the foundations for context-aware prediction and improvement of in vivo synthetic circuit performance, paving the way towards more rational synthetic construct design in mammalian cells.

Kalman-like Self-Tuned Sensitivity in Biophysical Sensing

Living organisms need to be sensitive to a changing environment while also ignoring uninformative environmental fluctuations. Here, we argue that living cells can navigate these conflicting demands by dynamically tuning their environmental sensitivity. We analyze the circadian clock in Synechococcus elongatus, showing that clock-metabolism coupling can detect mismatch between clock predictions and the day-night light cycle, temporarily raise the clock's sensitivity to light changes, and thus re-entraining faster. We find analogous behavior in recent experiments on switching between slow and fast osmotic-stress-response pathways in yeast. In both cases, cells can raise their sensitivity to new external information in epochs of frequent challenging stress, much like a Kalman filter with adaptive gain in signal processing. Our work suggests a new class of experiments that probe the history dependence of environmental sensitivity in biophysical sensing mechanisms.

Molecular Filters for Noise Reduction

Living systems are inherently stochastic and operate in a noisy environment, yet despite all these uncertainties, they perform their functions in a surprisingly reliable way. The biochemical mechanisms used by natural systems to tolerate and control noise are still not fully understood, and this issue also limits our capacity to engineer reliable, quantitative synthetic biological circuits. We study how representative models of biochemical systems propagate and attenuate noise, accounting for intrinsic as well as extrinsic noise. We investigate three molecular noise-filtering mechanisms, study their noise-reduction capabilities and limitations, and show that nonlinear dynamics such as complex formation are necessary for efficient noise reduction. We further suggest that the derived molecular filters are widespread in gene expression and regulation and, particularly, that microRNAs can serve as such noise filters. To our knowledge, our results provide new insight into how biochemical networks control noise and could be useful to build robust synthetic circuits.

Genetic Circuit-Assisted Smart Microbial Engineering

Rapid advances in DNA synthesis, genetic manipulation, and biosensors have greatly improved the ability to engineer microorganisms with complex functions. By accurately integrating quality biosensors and complex genetic circuits, recently emerged smart microorganisms have enabled exciting opportunities for dissecting complex signaling networks and making responses without artificial intervention. However, because of the lack of design principles, developing such smart microorganisms remains challenging. In this review, we propose the concept of smart microbial engineering (SME) and describe the general features of basic SME, including the circuit architecture, components, and design process. We also summarize the latest SME achievements, remaining challenges, and potential solutions in this growing field.

Bounding the stationary distributions of the chemical master equation via mathematical programming

The stochastic dynamics of biochemical networks are usually modeled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with uncontrolled errors. Here, we introduce mathematical programming approaches that yield approximations of these distributions with computable error bounds which enable the verification of their accuracy. First, we use semidefinite programming to compute increasingly tighter upper and lower bounds on the moments of the stationary distributions for networks with rational propensities. Second, we use these moment bounds to formulate linear programs that yield convergent upper and lower bounds on the stationary distributions themselves, their marginals, and stationary averages. The bounds obtained also provide a computational test for the uniqueness of the distribution. In the unique case, the bounds form an approximation of the stationary distribution with a computable bound on its error. In the nonunique case, our approach yields converging approximations of the ergodic distributions. We illustrate our methodology through several biochemical examples taken from the literature: Schlögl's model for a chemical bifurcation, a two-dimensional toggle switch, a model for bursty gene expression, and a dimerization model with multiple stationary distributions.

Modeling the Growth of Organisms Validates a General Relation between Metabolic Costs and Natural Selection

Metabolism and evolution are closely connected: if a mutation incurs extra energetic costs for an organism, there is a baseline selective disadvantage that may or may not be compensated for by other adaptive effects. A long-standing, but to date unproven, hypothesis is that this disadvantage is equal to the fractional cost relative to the total resting metabolic expenditure. We validate this result from physical principles through a general growth model and show it holds to excellent approximation for experimental parameters drawn from a wide range of species.

Optimal Noise-Canceling Networks

Natural and artificial networks, from the cerebral cortex to large-scale power grids, face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant question of whether and how noise filtering can be hard wired directly into a network's architecture. By considering generic phase oscillator arrays under cost constraints, we explore here analytically and numerically the design, efficiency, and topology of noise-canceling networks. Specifically, we find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. More broadly, our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks.

Sources, propagation and consequences of stochasticity in cellular growth

Growth impacts a range of phenotypic responses. Identifying the sources of growth variation and their propagation across the cellular machinery can thus unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. Alongside we provide a theory to analyse stochastic chemical reactions coupled with cell divisions, enabling efficient parameter estimation, sensitivity analysis and hypothesis testing. The cell model recovers population-averaged data on growth-dependence of bacterial physiology and how growth variations in single cells change across conditions. We identify processes responsible for this variation and reconstruct the propagation of initial fluctuations to growth and other processes. Finally, we study drug-nutrient interactions and find that antibiotics can both enhance and suppress growth heterogeneity. Our results provide a predictive framework to integrate heterogeneous data and draw testable predictions with implications for antibiotic tolerance, evolutionary and synthetic biology.

The drivers of growth rate variability in bacteria are yet unknown. Here, the authors present a theory to predict the growth dynamics of individual cells and use a stochastic cell model integrating metabolism, gene expression and replication to identify the processes that underlie growth variation.

Multiscale effects of heating and cooling on genes and gene networks

Fluctuating environments such as changes in ambient temperature represent a fundamental challenge to life. Cells must protect gene networks that protect them from such stresses, making it difficult to understand how temperature affects gene network function in general. Here, we focus on single genes and small synthetic network modules to reveal four key effects of nonoptimal temperatures at different biological scales: (i) a cell fate choice between arrest and resistance, (ii) slower growth rates, (iii) Arrhenius reaction rates, and (iv) protein structure changes. We develop a multiscale computational modeling framework that captures and predicts all of these effects. These findings promote our understanding of how temperature affects living systems and enables more robust cellular engineering for real-world applications.

Most organisms must cope with temperature changes. This involves genes and gene networks both as subjects and agents of cellular protection, creating difficulties in understanding. Here, we study how heating and cooling affect expression of single genes and synthetic gene circuits in Saccharomyces cerevisiae. We discovered that nonoptimal temperatures induce a cell fate choice between stress resistance and growth arrest. This creates dramatic gene expression bimodality in isogenic cell populations, as arrest abolishes gene expression. Multiscale models incorporating population dynamics, temperature-dependent growth rates, and Arrhenius scaling of reaction rates captured the effects of cooling, but not those of heating in resistant cells. Molecular-dynamics simulations revealed how heating alters the conformational dynamics of the TetR repressor, fully explaining the experimental observations. Overall, nonoptimal temperatures induce a cell fate decision and corrupt gene and gene network function in computationally predictable ways, which may aid future applications of engineered microbes in nonstandard temperatures.

Making sense of snapshot data: ergodic principle for clonal cell populations

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations.

Selected-node stochastic simulation algorithm

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

Heritable stress response dynamics revealed by single-cell genealogy

Cells often respond to environmental stimuli by activating specific transcription factors. Upon exposure to glucose limitation stress, it is known that yeast Saccharomyces cerevisiae cells dephosphorylate the general stress response factor Msn2, leading to its nuclear localization, which in turn activates the expression of many genes. However, the precise dynamics of Msn2 nucleocytoplasmic translocations and whether they are inherited over multiple generations in a stress-dependent manner are not well understood. Tracking Msn2 localization events in yeast lineages grown on a microfluidic chip, here we report how cells modulate the amplitude, duration, frequency, and dynamic pattern of the localization events in response to glucose limitation stress. Single yeast cells were found to modulate the amplitude and frequency of Msn2 nuclear localization, but not its duration. Moreover, the Msn2 localization frequency was epigenetically inherited in descendants of mother cells, leading to a decrease in cell-to-cell variation in localization frequency. An analysis of the time dynamic patterns of nuclear localizations between genealogically related cell pairs using an information theory approach found that the magnitude of pattern similarity increased with stress intensity and was strongly inherited by the descendant cells at the highest stress level. By dissecting how general stress response dynamics is contributed by different modulation schemes over long time scales, our work provides insight into which scheme evolution might have acted on to optimize fitness in stressful environments.

A Miniaturized Escherichia coli Green Light Sensor with High Dynamic Range

Genetically engineered photoreceptors enable unrivaled control over gene expression. Previously, we ported the Synechocystis PCC 6803 CcaSR two-component system, which is activated by green light and deactivated by red, into Escherichia coli, resulting in a sensor with a sixfold dynamic range. Later, we optimized pathway protein expression levels and the output promoter sequence to decrease transcriptional leakiness and to increase the dynamic range to approximately 120-fold. These CcaSR v 1.0 and v 2.0 systems have been used for precise quantitative, temporal, and spatial control of gene expression for a variety of applications. Recently, other workers deleted two PAS domains of unknown function from the CcaS sensor histidine kinase in a system similar to CcaSR v 1.0. Here we apply these deletions to CcaSR v 2.0, resulting in a v 3.0 light sensor with an output four times less leaky and a dynamic range of nearly 600-fold. We demonstrate that the PAS domain deletions have no deleterious effect on CcaSR green light sensitivity or response dynamics. CcaSR v 3.0 is the best-performing engineered bacterial green light sensor available, and should have broad applications in fundamental and synthetic biology studies.

Engineering an E. coli Near-Infrared Light Sensor

Optogenetics is a technology wherein researchers combine light and genetically engineered photoreceptors to control biological processes with unrivaled precision. Near-infrared (NIR) wavelengths (>700 nm) are desirable optogenetic inputs due to their low phototoxicity and spectral isolation from most photoproteins. The bacteriophytochrome photoreceptor 1 (BphP1), found in several purple photosynthetic bacteria, senses NIR light and activates transcription of photosystem promoters by binding to and inhibiting the transcriptional repressor PpsR2. Here, we examine the response of a library of output promoters to increasing levels of Rhodopseudomonas palustris PpsR2 expression, and we identify that of Bradyrhizobium sp. BTAi1 crtE as the most strongly repressed in Escherichia coli. Next, we optimize Rps. palustris bphP1 and ppsR2 expression in a strain engineered to produce the required chromophore biliverdin IXα in order to demonstrate NIR-activated transcription. Unlike a previously engineered bacterial NIR photoreceptor, our system does not require production of a second messenger, and it exhibits rapid response dynamics. It is also the most red-shifted bacterial optogenetic tool yet reported by approximately 50 nm. Accordingly, our BphP1-PpsR2 system has numerous applications in bacterial optogenetics.

The importance of thermodynamics for molecular systems, and the importance of molecular systems for thermodynamics

Improved understanding of molecular systems has only emphasised the sophistication of networks within the cell. Simultaneously, the advance of nucleic acid nanotechnology, a platform within which reactions can be exquisitely controlled, has made the development of artificial architectures and devices possible. Vital to this progress has been a solid foundation in the thermodynamics of molecular systems. In this pedagogical review and perspective, we discuss how thermodynamics determines both the overall potential of molecular networks, and the minute details of design. We then argue that, in turn, the need to understand molecular systems is helping to drive the development of theories of thermodynamics at the microscopic scale.

System identification of signaling dependent gene expression with different time-scale data

Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we used compressed sensing technology and developed a system identification method using data of different time scales by recovering signals of missing time points. We measured phosphorylation of ERK and CREB, immediate early gene expression products, and mRNAs of decoder genes for neurite elongation in PC12 cell differentiation and performed system identification, revealing the input-output relationships between signaling and gene expression with sensitivity such as graded or switch-like response and with time delay and gain, representing signal transfer efficiency. We predicted and validated the identified system using pharmacological perturbation. Thus, we provide a versatile method for system identification using data with different time scales.

Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise

Stochastic fluctuations in gene expression trigger both beneficial and harmful consequences for cell behavior. Therefore, achieving a desired mean protein expression level while minimizing noise is of interest in many applications, including robust protein production systems in industrial biotechnology. Here, we consider a synthetic gene circuit combining intracellular negative feedback and cell-to-cell communication based on quorum sensing. Accounting for both intrinsic and extrinsic noise, stochastic simulations allow us to analyze the capability of the circuit to reduce noise strength as a function of its parameters. We obtain mean expression levels and noise strengths for all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in Escherichia coli. Our in silico experiments, validated by preliminary in vivo results, reveal significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback and highlight the differential role that they play in regard to intrinsic and extrinsic noise.

Ultrasensitivity in signaling cascades revisited: Linking local and global ultrasensitivity estimations

Ultrasensitive response motifs, capable of converting graded stimuli into binary responses, are well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive modules can enhance the system's ultrasensitivity, how a given combination of layers affects a cascade's ultrasensitivity remains an open question for the general case. Here, we introduce a methodology that allows us to determine the presence of sequestration effects and to quantify the relative contribution of each module to the overall cascade's ultrasensitivity. The proposed analysis framework provides a natural link between global and local ultrasensitivity descriptors and it is particularly well-suited to characterize and understand mathematical models used to study real biological systems. As a case study, we have considered three mathematical models introduced by O'Shaughnessy et al. to study a tunable synthetic MAPK cascade, and we show how our methodology can help modelers better understand alternative models.

Universal signal generator for dynamic cell stimulation

Dynamic cell stimulation is a powerful technique for probing gene networks and for applications in stem cell differentiation, immunomodulation and signaling. We developed a robust and flexible method and associated microfluidic devices to generate a wide-range of precisely formulated dynamic chemical signals to stimulate live cells and measure their dynamic response. This signal generator is capable of digital to analog conversion (DAC) through combinatoric selection of discrete input concentrations, and outperforms existing methods by both achievable resolution, dynamic range and simplicity in design. It requires no calibration, has minimal space requirements and can be easily integrated into microfluidic cell culture devices. The signal generator hardware and software we developed allows to choose the waveform, period and amplitude of chemical input signals and features addition of well-defined chemical noise to study the role of stochasticity in cellular information processing.

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.