Signaling pathways as linear transmitters

One challenge in biology is to make sense of the complexity of biological networks. A good system to approach this is signaling pathways, whose well-characterized molecular details allow us to relate the internal processes of each pathway to their input-output behavior. In this study, we analyzed mathematical models of three metazoan signaling pathways: the canonical Wnt, MAPK/ERK, and Tgfβ pathways. We find an unexpected convergence: the three pathways behave in some physiological contexts as linear signal transmitters. Testing the results experimentally, we present direct measurements of linear input-output behavior in the Wnt and ERK pathways. Analytics from each model further reveal that linearity arises through different means in each pathway, which we tested experimentally in the Wnt and ERK pathways. Linearity is a desired property in engineering where it facilitates fidelity and superposition in signal transmission. Our findings illustrate how cells tune different complex networks to converge on the same behavior

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

Cross-hierarchy systems principles

One driving motivation of systems biology is the search for general principles that govern the design of biological systems. But questions often arise as to what kind of general principles biology could have. Concepts from engineering such as robustness and modularity are indeed becoming a regular way of describing biological systems. Another source of potential general principles is the emerging similarities found in processes across biological hierarchies. In this piece, I describe several emerging cross-hierarchy similarities. Identification of more cross-hierarchy principles, and understanding the implications these convergence have on the construction of biological systems, I believe, present exciting challenges for systems biology in the decades to come

Symmetrization in jellyfish: reorganization to regain function, and not lost parts

We recently reported a previously unidentified strategy of self-repair in the moon jellyfish Aurelia aurita. Rather than regenerating lost parts, juvenile Aurelia reorganize remaining parts to regain essential body symmetry. This process that we called symmetrization is rapid and frequent, and is not driven by cell proliferation or cell death. Instead, the swimming machinery generates mechanical forces that drive symmetrization. We found evidence for symmetrization across three other species of jellyfish (Chrysaora pacifica, Mastigias sp., and Cotylorhiza tuberculata). We propose reorganization to regain function without recovery of initial morphology as a potentially broad class of self-repair strategy beyond radially symmetrical animals, and discuss the implications of this finding on the evolution of self-repair strategies in animals

Evidence that fold-change, and not absolute level, of β-catenin dictates Wnt signaling

In response to Wnt stimulation, β-catenin accumulates and activates target genes. Using modeling and experimental analysis, we found that the level of β-catenin is sensitive to perturbations in the pathway, such that cellular variation would be expected to alter the signaling outcome. One unusual parameter was robust: the fold-change in β-catenin level (post-Wnt/pre-Wnt). In Xenopus, dorsal-anterior development and target gene expression are robust to perturbations that alter the final level but leave the fold-change intact. These suggest, first, that despite cellular noise, the cell responds reliably to Wnt stimulation by maintaining a robust fold-change in β-catenin. Second, the transcriptional machinery downstream of the Wnt pathway does not simply read the β-catenin level after Wnt stimulation but computes fold-changes in β-catenin. Analogous to Weber's Law in sensory physiology, some gene transcription networks must respond to fold-changes in signals, rather than absolute levels, which may buffer stochastic, genetic, and environmental variation

Sensing relative signal in the Tgf-β/Smad pathway

How signaling pathways function reliably despite cellular variation remains a question in many systems. In the transforming growth factor-β (Tgf-β) pathway, exposure to ligand stimulates nuclear localization of Smad proteins, which then regulate target gene expression. Examining Smad3 dynamics in live reporter cells, we found evidence for fold-change detection. Although the level of nuclear Smad3 varied across cells, the fold change in the level of nuclear Smad3 was a more precise outcome of ligand stimulation. The precision of the fold-change response was observed throughout the signaling duration and across Tgf-β doses, and significantly increased the information transduction capacity of the pathway. Using single-molecule FISH, we further observed that expression of Smad3 target genes (ctgf, snai1, and wnt9a) correlated more strongly with the fold change, rather than the level, of nuclear Smad3. These findings suggest that some target genes sense Smad3 level relative to background, as a strategy for coping with cellular noise

Fold-change detection and scalar symmetry of sensory input fields

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold change. We ask what the benefit of FCD is and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input field by a scalar. Thus, the FCD search pattern depends only on the spatial profile of the input and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. Furthermore, we show that FCD entails two features found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feed-forward loops. We find that bacterial chemotaxis displays feedback within the present class and hence, is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study, thus, suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields

The incoherent feedforward loop can provide fold-change detection in gene regulation

Many sensory systems (e.g., vision and hearing) show a response that is proportional to the fold-change in the stimulus relative to the background, a feature related to Weber's Law. Recent experiments suggest such a fold-change detection feature in signaling systems in cells: a response that depends on the fold-change in the input signal, and not on its absolute level. It is therefore of interest to find molecular mechanisms of gene regulation that can provide such fold-change detection. Here, we demonstrate theoretically that fold-change detection can be generated by one of the most common network motifs in transcription networks, the incoherent feedforward loop (I1-FFL), in which an activator regulates both a gene and a repressor of the gene. The fold-change detection feature of the I1-FFL applies to the entire shape of the response, including its amplitude and duration, and is valid for a wide range of biochemical parameters

Quantifying the Gurken morphogen gradient in Drosophila oogenesis

Quantitative information about the distribution of morphogens is crucial for understanding their effects on cell-fate determination, yet it is difficult to obtain through direct measurements. We have developed a parameter estimation approach for quantifying the spatial distribution of Gurken, a TGFα-like EGFR ligand that acts as a morphogen in Drosophila oogenesis. Modeling of Gurken/EGFR system shows that the shape of the Gurken gradient is controlled by a single dimensionless parameter, the Thiele modulus, which reflects the relative importance of ligand diffusion and degradation. By combining the model with genetic alterations of EGFR levels, we have estimated the value of the Thiele modulus in the wild-type egg chamber. This provides a direct characterization of the shape of the Gurken gradient and demonstrates how parameter estimation techniques can be used to quantify morphogen gradients in development