Temporal signals drive the emergence of multicellular information networks.

Coordinated responses to environmental stimuli are critical for multicellular organisms. To overcome the obstacles of cell-to-cell heterogeneity and noisy signaling dynamics within individual cells, cells must effectively exchange information with peers. However, the dynamics and mechanisms of collective information transfer driven by external signals are poorly understood. Here we investigate the calcium dynamics of neuronal cells that form confluent monolayers and respond to cyclic ATP stimuli in microfluidic devices. Using Granger inference to reconstruct the underlying causal relations between the cells, we find that the cells self-organize into spatially decentralized and temporally stationary networks to support information transfer via gap junction channels. The connectivity of the causal networks depends on the temporal profile of the external stimuli, where short periods, or long periods with small duty fractions, lead to reduced connectivity and fractured network topology. We build a theoretical model based on communicating excitable units that reproduces our observations. The model further predicts that connectivity of the causal network is maximal at an optimal communication strength, which is confirmed by the experiments. Together, our results show that information transfer between neuronal cells is externally regulated by the temporal profile of the stimuli and internally regulated by cell-cell communication.

Temporally regulated cell migration is sensitive to variation in body size.

Few studies have measured the robustness to perturbations of the final position of a long-range migrating cell. In the nematode Caenorhabditis elegans, the QR neuroblast migrates anteriorly, while undergoing three division rounds. We study the final position of two of its great-granddaughters, the end of migration of which was previously shown to depend on a timing mechanism. We find that the variance in their final position is similar to that of other long-range migrating neurons. As expected from the timing mechanism, the position of QR descendants depends on body size, which we varied by changing maternal age or using body size mutants. Using a mathematical model, we show that body size variation is partially compensated for. Applying environmental perturbations, we find that the variance in final position increased following starvation at hatching. The mean position is displaced upon a temperature shift. Finally, highly significant variation was found among C. elegans wild isolates. Overall, this study reveals that the final position of these neurons is quite robust to stochastic variation, shows some sensitivity to body size and to external perturbations, and varies in the species.This article has an associated 'The people behind the papers' interview.

Effects of Molecular Noise on Cell Size Control.

Cells employ control strategies to maintain a stable size. Dividing at a target size (the "sizer" strategy) is thought to produce the tightest size distribution. However, this result follows from phenomenological models that ignore the molecular mechanisms required to implement the strategy. Here we investigate a simple mechanistic model for exponentially growing cells whose division is triggered at a molecular abundance threshold. We find that size noise inherits the molecular noise and is consequently minimized not by the sizer but by the "adder" strategy, where a cell divides after adding a target amount to its birth size. We derive a lower bound on size noise that agrees with publicly available data from six microfluidic studies on Escherichia coli bacteria.

Signaling in microbial communities with open boundaries.

Microbial communities such as swarms or biofilms often form at the interfaces of solid substrates and open fluid flows. At the same time, in laboratory environments these communities are commonly studied using microfluidic devices with media flows and open boundaries. Extracellular signaling within these communities is therefore subject to different constraints than signaling within classic, closed-boundary systems such as developing embryos or tissues, yet is understudied by comparison. Here, we use mathematical modeling to show how advective-diffusive boundary flows and population geometry impact cell-cell signaling in monolayer microbial communities. We reveal conditions where the intercellular signaling lengthscale depends solely on the population geometry and not on diffusion or degradation, as commonly expected. We further demonstrate that diffusive coupling with the boundary flow can produce signal gradients within an isogenic population, even when there is no flow within the population. We use our theory to provide new insights into the signaling mechanisms of published experimental results, and we make several experimentally verifiable predictions. Our research highlights the importance of carefully evaluating boundary dynamics and environmental geometry when modeling microbial cell-cell signaling and informs the study of cell behaviors in both natural and synthetic systems.

Precision of Protein Thermometry.

Temperature sensing is a ubiquitous cell behavior, but the fundamental limits to the precision of temperature sensing are poorly understood. Unlike in chemical concentration sensing, the precision of temperature sensing is not limited by extrinsic fluctuations in the temperature field itself. Instead, we find that precision is limited by the intrinsic copy number, turnover, and binding kinetics of temperature-sensitive proteins. Developing a model based on the canonical TlpA protein, we find that a cell can estimate temperature to within 2%. We compare this prediction with in vivo data on temperature sensing in bacteria.

Spiral Wave Propagation in Communities with Spatially Correlated Heterogeneity.

Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still unclear. Here, we use a minimal FitzHugh-Nagumo-type model to investigate excitable wave propagation in a two-dimensional heterogeneous community. The model shows three dynamic regimes in which waves either propagate directionally, die out, or spiral indefinitely, and we characterize how these regimes depend on the heterogeneity parameters. We find that in some parameter regimes, spatial correlations in the heterogeneity enhance directional propagation and suppress spiraling. However, in other regimes, spatial correlations promote spiraling, a surprising feature that we explain by demonstrating that these spirals form by a second, distinct mechanism. Finally, we characterize the dynamics using techniques from percolation theory. Despite the fact that percolation theory does not completely describe the dynamics quantitatively because it neglects the details of the excitable propagation, we find that it accounts for the transitions between the dynamic regimes and the general dependency of the spiral period on the heterogeneity and thus provides important insights. Our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.

Cell-to-Cell Information at a Feedback-Induced Bifurcation Point.

A ubiquitous way that cells share information is by exchanging molecules. Yet, the fundamental ways that this information exchange is influenced by intracellular dynamics remain unclear. Here we use information theory to investigate a simple model of two interacting cells with internal feedback. We show that cell-to-cell molecule exchange induces a collective two-cell critical point and that the mutual information between the cells peaks at this critical point. Information can remain large far from the critical point on a manifold of cellular states but scales logarithmically with the correlation time of the system, resulting in an information-correlation time trade-off. This trade-off is strictly imposed, suggesting the correlation time as a proxy for the mutual information.

Precision of Flow Sensing by Self-Communicating Cells.

Metastatic cancer cells detect the direction of lymphatic flow by self-communication: they secrete and detect a chemical which, due to the flow, returns to the cell surface anisotropically. The secretion rate is low, meaning detection noise may play an important role, but the sensory precision of this mechanism has not been explored. Here we derive the precision of flow sensing for two ubiquitous detection methods: absorption vs reversible binding to surface receptors. We find that binding is more precise due to the fact that absorption distorts the signal that the cell aims to detect. Comparing to experiments, our results suggest that the cancer cells operate remarkably close to the physical detection limit. Our prediction that cells should bind the chemical reversibly, not absorb it, is supported by endocytosis data for this ligand-receptor pair.

Physical constraints on accuracy and persistence during breast cancer cell chemotaxis.

Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of cell motion, but whether any of these quantities is physically constrained by the others is poorly understood. Using a combination of theory, simulations, and 3D chemotaxis assays on single metastatic breast cancer cells, we investigate the links among these different aspects of chemotactic performance. In particular, we observe in both experiments and simulations that the chemotactic accuracy, but not the persistence or speed, increases with the gradient strength. We use a random walk model to explain this result and to propose that cells' chemotactic accuracy and persistence are mutually constrained. Our results suggest that key aspects of chemotactic performance are inherently limited regardless of how favorable the environmental conditions are.

Statistics of correlated percolation in a bacterial community.

Signal propagation over long distances is a ubiquitous feature of multicellular communities, but cell-to-cell variability can cause propagation to be highly heterogeneous. Simple models of signal propagation in heterogenous media, such as percolation theory, can potentially provide a quantitative understanding of these processes, but it is unclear whether these simple models properly capture the complexities of multicellular systems. We recently discovered that in biofilms of the bacterium Bacillus subtilis, the propagation of an electrical signal is statistically consistent with percolation theory, and yet it is reasonable to suspect that key features of this system go beyond the simple assumptions of basic percolation theory. Indeed, we find here that the probability for a cell to signal is not independent from other cells as assumed in percolation theory, but instead is correlated with its nearby neighbors. We develop a mechanistic model, in which correlated signaling emerges from cell division, phenotypic inheritance, and cell displacement, that reproduces the experimentally observed correlations. We find that the correlations do not significantly affect the spatial statistics, which we rationalize using a renormalization argument. Moreover, the fraction of signaling cells is not constant in space, as assumed in percolation theory, but instead varies within and across biofilms. We find that this feature lowers the fraction of signaling cells at which one observes the characteristic power-law statistics of cluster sizes, consistent with our experimental results. We validate the model using a mutant biofilm whose signaling probability decays along the propagation direction. Our results reveal key statistical features of a correlated signaling process in a multicellular community. More broadly, our results identify extensions to percolation theory that do or do not alter its predictions and may be more appropriate for biological systems.

Highly Polyvalent DNA Motors Generate 100+ pN of Force via Autochemophoresis.

Motor proteins such as myosin, kinesin, and dynein are essential to eukaryotic life and power countless processes including muscle contraction, wound closure, cargo transport, and cell division. The design of synthetic nanomachines that can reproduce the functions of these motors is a longstanding goal in the field of nanotechnology. DNA walkers, which are programmed to "walk" along defined tracks via the burnt bridge Brownian ratchet mechanism, are among the most promising synthetic mimics of these motor proteins. While these DNA-based motors can perform useful tasks such as cargo transport, they have not been shown to be capable of cooperating to generate large collective forces for tasks akin to muscle contraction. In this work, we demonstrate that highly polyvalent DNA motors (HPDMs), which can be viewed as cooperative teams of thousands of DNA walkers attached to a microsphere, can generate and sustain substantial forces in the 100+ pN regime. Specifically, we show that HPDMs can generate forces that can unzip and shear DNA duplexes (∼12 and ∼50 pN, respectively) and rupture biotin-streptavidin bonds (∼100-150 pN). To help explain these results, we present a variant of the burnt-bridge Brownian ratchet mechanism that we term autochemophoresis, wherein many individual force generating units generate a self-propagating chemomechanical gradient that produces large collective forces. In addition, we demonstrate the potential of this work to impact future engineering applications by harnessing HPDM autochemophoresis to deposit "molecular ink" via mechanical bond rupture. This work expands the capabilities of synthetic DNA motors to mimic the force-generating functions of biological motors. Our work also builds upon previous observations of autochemophoresis in bacterial transport processes, indicating that autochemophoresis may be a fundamental mechanism of pN-scale force generation in living systems.

Temporal precision of regulated gene expression.

Important cellular processes such as migration, differentiation, and development often rely on precise timing. Yet, the molecular machinery that regulates timing is inherently noisy. How do cells achieve precise timing with noisy components? We investigate this question using a first-passage-time approach, for an event triggered by a molecule that crosses an abundance threshold and that is regulated by either an accumulating activator or a diminishing repressor. We find that either activation or repression outperforms an unregulated strategy. The optimal regulation corresponds to a nonlinear increase in the amount of the target molecule over time, arises from a tradeoff between minimizing the timing noise of the regulator and that of the target molecule itself, and is robust to additional effects such as bursts and cell division. Our results are in quantitative agreement with the nonlinear increase and low noise of mig-1 gene expression in migrating neuroblast cells during Caenorhabditis elegans development. These findings suggest that dynamic regulation may be a simple and powerful strategy for precise cellular timing.

Limits to the precision of gradient sensing with spatial communication and temporal integration.

Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. Although much is known about the limits of measurement precision by cells, the limits placed by the communication are not understood. Motivated by recent experiments, we derive the fundamental limits to the precision of gradient sensing in a multicellular system, accounting for communication and temporal integration. The gradient is estimated by comparing a "local" and a "global" molecular reporter of the external concentration, where the global reporter is exchanged between neighboring cells. Using the fluctuation-dissipation framework, we find, in contrast to the case when communication is ignored, that precision saturates with the number of cells independently of the measurement time duration, because communication establishes a maximum length scale over which sensory information can be reliably conveyed. Surprisingly, we also find that precision is improved if the local reporter is exchanged between cells as well, albeit more slowly than the global reporter. The reason is that whereas exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation-global inhibition." Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account.

Communication shapes sensory response in multicellular networks.

Collective sensing by interacting cells is observed in a variety of biological systems, and yet, a quantitative understanding of how sensory information is collectively encoded is lacking. Here, we investigate the ATP-induced calcium dynamics of monolayers of fibroblast cells that communicate via gap junctions. Combining experiments and stochastic modeling, we find that increasing the ATP stimulus increases the propensity for calcium oscillations, despite large cell-to-cell variability. The model further predicts that the oscillation propensity increases with not only the stimulus, but also the cell density due to increased communication. Experiments confirm this prediction, showing that cell density modulates the collective sensory response. We further implicate cell-cell communication by coculturing the fibroblasts with cancer cells, which we show act as "defects" in the communication network, thereby reducing the oscillation propensity. These results suggest that multicellular networks sit at a point in parameter space where cell-cell communication has a significant effect on the sensory response, allowing cells to simultaneously respond to a sensory input and the presence of neighbors.

Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis.

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and little is known about how multicellular signal processing modulates single-cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored whether cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow epidermal growth factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.

Modeling of cytometry data in logarithmic space: When is a bimodal distribution not bimodal?

Recent efforts in systems immunology lead researchers to build quantitative models of cell activation and differentiation. One goal is to account for the distributions of proteins from single-cell measurements by flow cytometry or mass cytometry as readout of biological regulation. In that context, large cell-to-cell variability is often observed in biological quantities. We show here that these readouts, viewed in logarithmic scale may result in two easily-distinguishable modes, while the underlying distribution (in linear scale) is unimodal. We introduce a simple mathematical test to highlight this mismatch. We then dissect the flow of influence of cell-to-cell variability proposing a graphical model which motivates higher-dimensional analysis of the data. Finally we show how acquiring additional biological information can be used to reduce uncertainty introduced by cell-to-cell variability, helping to clarify whether the data is uni- or bimodal. This communication has cautionary implications for manual and automatic gating strategies, as well as clustering and modeling of single-cell measurements. © 2018 International Society for Advancement of Cytometry.

Growth of bacteria in 3-d colonies.

The dynamics of growth of bacterial populations has been extensively studied for planktonic cells in well-agitated liquid culture, in which all cells have equal access to nutrients. In the real world, bacteria are more likely to live in physically structured habitats as colonies, within which individual cells vary in their access to nutrients. The dynamics of bacterial growth in such conditions is poorly understood, and, unlike that for liquid culture, there is not a standard broadly used mathematical model for bacterial populations growing in colonies in three dimensions (3-d). By extending the classic Monod model of resource-limited population growth to allow for spatial heterogeneity in the bacterial access to nutrients, we develop a 3-d model of colonies, in which bacteria consume diffusing nutrients in their vicinity. By following the changes in density of E. coli in liquid and embedded in glucose-limited soft agar, we evaluate the fit of this model to experimental data. The model accounts for the experimentally observed presence of a sub-exponential, diffusion-limited growth regime in colonies, which is absent in liquid cultures. The model predicts and our experiments confirm that, as a consequence of inter-colony competition for the diffusing nutrients and of cell death, there is a non-monotonic relationship between total number of colonies within the habitat and the total number of individual cells in all of these colonies. This combined theoretical-experimental study reveals that, within 3-d colonies, E. coli cells are loosely packed, and colonies produce about 2.5 times as many cells as the liquid culture from the same amount of nutrients. We verify that this is because cells in liquid culture are larger than in colonies. Our model provides a baseline description of bacterial growth in 3-d, deviations from which can be used to identify phenotypic heterogeneities and inter-cellular interactions that further contribute to the structure of bacterial communities.

Dynamic Sampling and Information Encoding in Biochemical Networks.

Cells use biochemical networks to translate environmental information into intracellular responses. These responses can be highly dynamic, but how the information is encoded in these dynamics remains poorly understood. Here, we investigate the dynamic encoding of information in the ATP-induced calcium responses of fibroblast cells, using a vectorial, or multi-time-point, measure from information theory. We find that the amount of extracted information depends on physiological constraints such as the sampling rate and memory capacity of the downstream network, and it is affected differentially by intrinsic versus extrinsic noise. By comparing to a minimal physical model, we find, surprisingly, that the information is often insensitive to the detailed structure of the underlying dynamics, and instead the decoding mechanism acts as a simple low-pass filter. These results demonstrate the mechanisms and limitations of dynamic information storage in cells.

Fundamental Limits to Collective Concentration Sensing in Cell Populations.

The precision of concentration sensing is improved when cells communicate. Here we derive the physical limits to concentration sensing for cells that communicate over short distances by directly exchanging small molecules (juxtacrine signaling), or over longer distances by secreting and sensing a diffusive messenger molecule (autocrine signaling). In the latter case, we find that the optimal cell spacing can be large, due to a trade-off between maintaining communication strength and reducing signal cross-correlations. This leads to the surprising result that sparsely packed communicating cells sense concentrations more precisely than densely packed communicating cells. We compare our results to data from a wide variety of communicating cell types.