Accurate encoding and decoding by single cells: amplitude versus frequency modulation

Biological physics to uncover cell signaling

In this report, I describe some of the subjects and problems that we have addressed over the last 25 years in the area of cell signaling using the tools of biological physics. The report covers part of our work on intracellular Ca2 + signals, pattern formation, transport of messengers in the interior of cells, quantification of biophysical parameters from experiments, and information transmission. The description includes both our modeling and experimental work highlighting how the tools of physics can give useful insights into the workings of biological systems.

Amplitude and frequency encoding result in qualitatively distinct informational landscapes in cell signaling

Cells continuously sense their surroundings to detect modifications and generate responses. Very often changes in extracellular concentrations initiate signaling cascades that eventually result in changes in gene expression. Increasing stimulus strengths can be encoded in increasing concentration amplitudes or increasing activation frequencies of intermediaries of the pathway. In this paper we show that the different way in which amplitude and frequency encoding map environmental changes endow cells with qualitatively different information transmission capabilities. While amplitude encoding is optimal for a limited range of stimuli strengths, frequency encoding can transmit information with equal reliability over much broader ranges. The qualitative difference between the two strategies stems from the scale invariant discriminating power of the first transducing step in frequency codification. The apparently redundant combination of both strategies in some cell types may then serve the purpose of expanding the span over which stimulus strengths can be reliably discriminated. In this paper we discuss a possible example of this mechanism in yeast.

Fluorescent biosensors illuminate the spatial regulation of cell signaling across scales

As cell signaling research has advanced, it has become clearer that signal transduction has complex spatiotemporal regulation that goes beyond foundational linear transduction models. Several technologies have enabled these discoveries, including fluorescent biosensors designed to report live biochemical signaling events. As genetically encoded and live-cell compatible tools, fluorescent biosensors are well suited to address diverse cell signaling questions across different spatial scales of regulation. In this review, methods of examining spatial signaling regulation and the design of fluorescent biosensors are introduced. Then, recent biosensor developments that illuminate the importance of spatial regulation in cell signaling are highlighted at several scales, including membranes and organelles, molecular assemblies, and cell/tissue heterogeneity. In closing, perspectives on how fluorescent biosensors will continue enhancing cell signaling research are discussed.

Oscillatory ERK Signaling and Morphology Determine Heterogeneity of Breast Cancer Cell Chemotaxis via MEK-ERK and p38-MAPK Signaling Pathways

Chemotaxis, regulated by oscillatory signals, drives critical processes in cancer metastasis. Crucial chemoattractant molecules in breast cancer, CXCL12 and EGF, drive the activation of ERK and Akt. Regulated by feedback and crosstalk mechanisms, oscillatory signals in ERK and Akt control resultant changes in cell morphology and chemotaxis. While commonly studied at the population scale, metastasis arises from small numbers of cells that successfully disseminate, underscoring the need to analyze processes that cancer cells use to connect oscillatory signaling to chemotaxis at single-cell resolution. Furthermore, little is known about how to successfully target fast-migrating cells to block metastasis. We investigated to what extent oscillatory networks in single cells associate with heterogeneous chemotactic responses and how targeted inhibitors block signaling processes in chemotaxis. We integrated live, single-cell imaging with time-dependent data processing to discover oscillatory signal processes defining heterogeneous chemotactic responses. We identified that short ERK and Akt waves, regulated by MEK-ERK and p38-MAPK signaling pathways, determine the heterogeneous random migration of cancer cells. By comparison, long ERK waves and the morphological changes regulated by MEK-ERK signaling, determine heterogeneous directed motion. This study indicates that treatments against chemotaxis in consider must interrupt oscillatory signaling.

Soluble cyclase-mediated nuclear cAMP synthesis is sufficient for cell proliferation

cAMP, a key player in many physiological processes, was classically considered to originate solely from the plasma membrane (PM). This view was recently challenged by observations showing that upon internalization GsPCRs can sustain signaling from endosomes and/or the trans-Golgi network (TGN). In this new view, after the first PM-generated cAMP wave, the internalization of GsPCRs and ACs generates a second wave that was strictly associated with nuclear transcriptional events responsible for triggering specific biological responses. Here, we report that the endogenously expressed TSHR, a canonical GsPCR, triggers an internalization-dependent, calcium-mediated nuclear sAC activation that drives PKA activation and CREB phosphorylation. Both pharmacological and genetic sAC inhibition, which did not affect the cytosolic cAMP levels, blunted nuclear cAMP accumulation, PKA activation, and cell proliferation, while an increase in nuclear sAC expression significantly enhanced cell proliferation. Furthermore, using novel nuclear-targeted optogenetic actuators, we show that light-stimulated nuclear cAMP synthesis can mimic the proliferative action of TSH by activating PKA and CREB. Therefore, based on our results, we propose a novel three-wave model in which the "third" wave of cAMP is generated by nuclear sAC. Despite being downstream of events occurring at the PM (first wave) and endosomes/TGN (second wave), the nuclear sAC-generated cAMP (third wave) is sufficient and rate-limiting for thyroid cell proliferation.

A closed-loop multi-scale model for intrinsic frequency-dependent regulation of axonal growth

This article develops a closed-loop multi-scale model for axon length regulation based on a frequency-dependent negative feedback mechanism. It builds on earlier models by linking molecular motor dynamics to signaling delays that then determine signal oscillation period. The signal oscillation is treated as a front end for a signaling pathway that modulates axonal length. This model is used to demonstrate the feasibility of such a mechanism and is tested against two previously published reports in which experimental manipulations were performed that resulted in axon growth. The model captures these observations and yields an expression for equilibrium axonal length. One major prediction of the model is that increasing motor density in the body of an axon results in axonal growth-this idea has not yet been explored experimentally.

Electrically synchronizing and modulating the dynamics of ERK activation to regulate cell fate

Intracellular signaling dynamics play fundamental roles in cell biology. Precise modulation of the amplitude, duration, and frequency of signaling activation will be a powerful approach to investigate molecular mechanisms as well as to engineer signaling to control cell behaviors. Here, we showed a practical approach to achieve precise amplitude modulation (AM), frequency modulation (FM), and duration modulation (DM) of MAP kinase activation. Alternating current (AC) electrical stimulation induced synchronized ERK activation. Amplitude and duration of ERK activation were controlled by varying stimulation strength and duration. ERK activation frequencies were arbitrarily modulated with trains of short AC applications with accurately defined intervals. Significantly, ERK dynamics coded by well-designed AC can rewire PC12 cell fate independent of growth factors. This technique can be used to synchronize and modulate ERK activation dynamics, thus would offer a practical way to control cell behaviors in vivo without the use of biochemical agents or genetic manipulation.

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Alternating-current (AC) electric field activates ERK independently of growth factors

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AC stimulation length modulates the amplitude and duration of ERK activation

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On-off time interval of AC modulates the frequency of ERK activation peaks

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Electrical modulation of ERK dynamics promotes neuronal differentiation of PC12 cells

Information transmission from NFkB signaling dynamics to gene expression

The dynamic signal encoding paradigm suggests that information flows from the extracellular environment into specific signaling patterns (encoding) that are then read by downstream effectors to control cellular behavior. Previous work empirically quantified the information content of dynamic signaling patterns. However, whether this information can be faithfully transmitted to the gene expression level is unclear. Here we used NFkB signaling as a model to understand the accuracy of information transmission from signaling dynamics into gene expression. Using a detailed mathematical model, we simulated realistic NFkB signaling patterns with different degrees of variability. The NFkB patterns were used as an input to a simple gene expression model. Analysis of information transmission between ligand and NFkB and ligand and gene expression allows us to determine information loss in transmission between receptors to dynamic signaling patterns and between signaling dynamics to gene expression. Information loss could occur due to biochemical noise or due to a lack of specificity. We found that noise-free gene expression has very little information loss suggesting that gene expression can preserve specificity in NFkB patterns. As expected, the addition of noise to the gene expression model results in information loss. Interestingly, this effect can be mitigated by a specific choice of parameters that can substantially reduce information loss due to biochemical noise during gene expression. Overall our results show that the cellular capacity for information transmission from dynamic signaling patterns to gene expression can be high enough to preserve ligand specificity and thereby the accuracy of cellular response to environmental cues.

Network Motifs Capable of Decoding Transcription Factor Dynamics

Transcription factors (TFs) can encode the information of upstream signal in terms of its temporal activation dynamics. However, it remains unclear how different types of TF dynamics are decoded by downstream signalling networks. In this work, we studied all three-node transcriptional networks for their ability to distinguish two types of TF dynamics: amplitude modulation (AM), where the TF is activated with a constant amplitude, and frequency modulation (FM), where the TF activity displays an oscillatory behavior. We found two sets of network topologies: one set can differentially respond to AM TF signal but not to FM; the other set to FM signal but not to AM. Interestingly, there is little overlap between the two sets. We identified the prevalent topological features in each set and gave a mechanistic explanation as to why they can differentially respond to only one type of TF signal. We also found that some network topologies have a weak (not robust) ability to differentially respond to both AM and FM input signals by using different values of parameters for AM and FM cases. Our results provide a novel network mechanism for decoding different TF dynamics.

Extracellular Electrophysiological Measurements of Cooperative Signals in Astrocytes Populations

Astrocytes are neuroglial cells that exhibit functional electrical properties sensitive to neuronal activity and capable of modulating neurotransmission. Thus, electrophysiological recordings of astroglial activity are very attractive to study the dynamics of glial signaling. This contribution reports on the use of ultra-sensitive planar electrodes combined with low noise and low frequency amplifiers that enable the detection of extracellular signals produced by primary cultures of astrocytes isolated from mouse cerebral cortex. Recorded activity is characterized by spontaneous bursts comprised of discrete signals with pronounced changes on the signal rate and amplitude. Weak and sporadic signals become synchronized and evolve with time to higher amplitude signals with a quasi-periodic behavior, revealing a cooperative signaling process. The methodology presented herewith enables the study of ionic fluctuations of population of cells, complementing the single cells observation by calcium imaging as well as by patch-clamp techniques.

Developmental ERK Signaling Goes Digital

Reporting in Developmental Cell, de la Cova et al. (2017) present a biosensor to measure ERK activity dynamics in C. elegans larvae. They find that fate decision signaling involves frequency-modulated, digital ERK activity pulses. These findings may explain how graded morphogen signals are converted into precise and robust cell fate patterns.

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. This underlies a new challenge to the experimentalist because neither intuition nor pre-existing methods work well for identifying oscillatory activity in noisy biological time series. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here, we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live-cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a Hes1 promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5’ LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.

Technological advances now allow us to observe gene expression in real-time at a single-cell level. In a wide variety of biological contexts this new data has revealed that gene expression is highly dynamic and possibly oscillatory. It is thought that periodic gene expression may be useful for keeping track of time and space, as well as transmitting information about signalling cues. Classifying a time series as periodic from single cell data is difficult because it is necessary to distinguish whether peaks and troughs are generated from an underlying oscillator or whether they are aperiodic fluctuations. To this end, we present a novel tool to classify live-cell data as oscillatory or non-oscillatory that accounts for inherent biological noise. We first demonstrate that the method outperforms a competing scheme in classifying computationally simulated single-cell data, and we subsequently analyse live-cell imaging time series. Our method is able to successfully detect oscillations in a known genetic oscillator, but it classifies data from a constitutively expressed gene as aperiodic. The method forms a basis for discovering new gene expression oscillators and quantifying how oscillatory activity alters in response to changes in cell fate and environmental or genetic perturbations.

The dynamic mechanism of noisy signal decoding in gene regulation

Experimental evidence supports that signaling pathways can induce different dynamics of transcription factor (TF) activation, but how an input signal is encoded by such a dynamic, noisy TF and further decoded by downstream genes remains largely unclear. Here, using a system of stochastic transcription with signal regulation, we show that (1) keeping the intensity of the signal noise invariant but prolonging the signal duration can both enhance the mutual information (MI) and reduce the energetic cost (EC); (2) if the signal duration is fixed, the larger MI needs the larger EC, but if the signal period is fixed, there is an optimal time that the signal spends at one lower branch, such that MI reaches the maximum; (3) if both the period and the duration are simultaneously fixed, increasing the input noise can always enhance MI in the case of transcription regulation rather than in the case of degradation regulation. In addition, we find that the input noise can induce stochastic focusing in a regulation-dependent manner. These results reveal not only the dynamic mechanism of noisy signal decoding in gene regulation but also the essential role of external noise in controlling gene expression levels.

Systematic Characterization of Dynamic Parameters of Intracellular Calcium Signals

Dynamic processes, such as intracellular calcium signaling, are hallmark of cellular biology. As real-time imaging modalities become widespread, a need for analytical tools to reliably characterize time-series data without prior knowledge of the nature of the recordings becomes more pressing. The goal of this study is to develop a signal-processing algorithm for MATLAB that autonomously computes the parameters characterizing prominent single transient responses (TR) and/or multi-peaks responses (MPR). The algorithm corrects for signal contamination and decomposes experimental recordings into contributions from drift, TRs, and MPRs. It subsequently provides numerical estimates for the following parameters: time of onset after stimulus application, activation time (time for signal to increase from 10 to 90% of peak), and amplitude of response. It also provides characterization of the (i) TRs by quantifying their area under the curve (AUC), response duration (time between 1/2 amplitude on ascent and descent of the transient), and decay constant of the exponential decay region of the deactivation phase of the response, and (ii) MPRs by quantifying the number of peaks, mean peak magnitude, mean periodicity, standard deviation of periodicity, oscillatory persistence (time between first and last discernable peak), and duty cycle (fraction of period during which system is active) for all the peaks in the signal, as well as coherent oscillations (i.e., deterministic spikes). We demonstrate that the signal detection performance of this algorithm is in agreement with user-mediated detection and that parameter estimates obtained manually and algorithmically are correlated. We then apply this algorithm to study how metabolic acidosis affects purinergic (P2) receptor-mediated calcium signaling in osteoclast precursor cells. Our results reveal that acidosis significantly attenuates the amplitude and AUC calcium responses at high ATP concentrations. Collectively, our data validated this algorithm as a general framework for comprehensively analyzing dynamic time-series.

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.

Mechanisms of information decoding in a cascade system of gene expression

Biotechnology advances have allowed investigation of heterogeneity of cellular responses to stimuli on the single-cell level. Functionally, this heterogeneity can compromise cellular responses to environmental signals, and it can also enlarge the repertoire of possible cellular responses and hence increase the adaptive nature of cellular behaviors. However, the mechanism of how this response heterogeneity is generated remains elusive. Here, by systematically analyzing a representative cellular signaling system, we show that (1) the upstream activator always amplifies the downstream burst frequency (BF) but the noiseless activator performs better than the noisy one, remarkably for small or moderate input signal strengths, and the repressor always reduces the downstream BF but the difference in the reducing effect between noiseless and noise repressors is very small; (2) both the downstream burst size and mRNA mean are a monotonically increasing function of the activator strength but a monotonically decreasing function of the repressor strength; (3) for repressor-type input, there is a noisy signal strength such that the downstream mRNA noise arrives at an optimal level, but for activator-type input, the output noise intensity is fundamentally a monotonically decreasing function of the input strength. Our results reveal the essential mechanisms of both signal information decoding and cellular response heterogeneity, whereas our analysis provides a paradigm for analyzing dynamics of noisy biochemical signaling systems.

Know the Single-Receptor Sensing Limit? Think Again

How cells reliably infer information about their environment is a fundamentally important question. While sensing and signaling generally start with cell-surface receptors, the degree of accuracy with which a cell can measure external ligand concentration with even the simplest device-a single receptor-is surprisingly hard to pin down. Recent studies provide conflicting results for the fundamental physical limits. Comparison is made difficult as different studies either suggest different readout mechanisms of the ligand-receptor occupancy, or differ on how ligand diffusion is implemented. Here we critically analyse these studies and present a unifying perspective on the limits of sensing, with wide-ranging biological implications.