A predictive model reveals the role of network motifs in a MAPK signaling pathway

The work that I focused on for most of my time as a graduate student at the University of North Carolina at Chapel Hill was published today in Science Signaling. I am so excited to share this work with the world! It has been a tremendous team effort with extensive efforts from all of my co-authors, particularly the co-first author, Dr. Matt Peña, who collected the majority of the experimental data, and my primary advisors for this work, Drs. Tim Elston and Beverly Errede.

Below, I've taken the opportunity to break down the abstract sentence by sentence to share my work with a broader audience, not just experts in MAPK signaling and mathematical modeling.

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The Abstract

An abstract is a brief description of a research article that includes an introduction, methods, and key results. If you have a strong background of knowledge in the subject area, these abstracts can be quick and informative to read, but if you have a limited background in the field of research, they can be very complicated or confusing. I'm going to break our abstract down so it can be more interpretable to non-experts in the field.

Cells use signaling pathways to receive and process information about their environment.

In case you don't know about signaling pathways, signaling pathways are (as described here) the way cells get and respond to information about their environment. This is true for all cells, from the different types of cells that make up your body to organisms that are only a single cell. In your body signaling pathways are what let your cells respond to hormones, neurotransmitters, and nutrients. Signaling pathways are really important, and incorrect functioning of these pathways can lead to many diseases including cancer.

These nonlinear systems rely on feedback and feedforward regulation to respond appropriately to changing environmental conditions.

Signaling pathways are not linear. They do not simply go from A to B to C like is shown on the left. There are lots of other more complicated things that make them nonlinear, like feedback and feedforward loops. A feedback loop occurs when something further down in the pathway (like C in our example) affects something above it in the pathway (like B in our example). The downstream component (C) can affect the upstream component (B) in a positive way, such as making more of it or activating it, which we call positive feedback. The downstream component can also affect the upstream component in a negative way, such as degrading it or deactivating it, which we call negative feedback. A feedforward loop occurs when something further up in the pathway (like A in our example) directly affects multiple things below it in the pathway (like B and C in our example). These loops help cells change their response appropriately and dynamically when something outside of the cell changes.

Mathematical models describing signaling pathways often lack predictive power because they are not trained on data that encompass the diverse time scales on which these regulatory mechanisms operate.

We, and by we I mean a community of scientists, including myself, who use math to understand signaling pathways, make mathematical models that help us better understand these pathways. Put simply, we write mathematical equations that describe the way components in the system (like A, B, and C in the example above) relate and interact with each other. We then use those equations, which we call a model, to better quantify and understand the pathway. These models can often explain how a pathway behaves, but they can rarely predict what the pathway will do if something is changed. A key hypothesis of my research was that we will be able to make models that do a better job predicting the response to new changes, if we build the model to explain a defined set of changes.

Now, we've explained what we're studying - mathematical models of signaling pathways - and what we're specifically trying to do - build models that can better predict new responses which will help us better understand the pathway.

We addressed this limitation by measuring transcriptional changes induced by the mating response in Saccharomyces cerevisiae exposed to different dynamic patterns of pheromone.

This sentence tells you what we did. First, we tell you what signaling pathway we studied - the mating response pathway in Saccharomyces cerevisiae, which is the fancy scientific name for baker's yeast (yes, the same yeast you may have used to make bread). This is a mitogen-activated protein kinase (MAPK) pathway. That's important because humans have many MAPK signaling pathways too, and when they don't work correctly, they can cause cancer. So you can understand why we really want to better understand how MAPK pathways work. But back to yeast, when yeast sense a mating pheromone, they activate this pathway to prepare to mate. We designed special yeast that makes a protein that fluoresces green when the pathway is active. In the video below you can see the yeast get more green when they respond to mating pheromone and less green as they stop responding when the mating pheromone is removed. This video also highlights another important part of what we did; we exposed the yeast to different dynamic patterns of pheromone. Here the yeast are getting a pulsing pattern of pheromone, where they are exposed to pheromone for 90 minutes and then the pheromone is removed for 90 minutes.

We found that pheromone-induced transcription persisted after pheromone removal and showed long-term adaptation upon sustained pheromone exposure.

This sentence tells you about some of our results, specifically the results of the experiments we did with the yeast. First, we found that the "pheromone-induced transcription," or "response," continued after pheromone removal. This is shown by arrow (A) in the picture below. This means that the cells are "remembering" that the stimulus (pheromone) was present and continue to respond to it even after the stimulus is not there anymore. Next, we found that if cells are exposed to pheromone for a very long time, they eventually stop responding to it, which we call long-term adaptation. This is shown by arrow (B) in the picture below. Last, we found that the amplitude, or size, of the response depends on how long the cells were exposed to pheromone, which can be seen by comparing the two (C) arrows below. These three findings are what we call the response features.

We developed a model of the regulatory network that captured both characteristics of the mating response. We fit this model to experimental data with an evolutionary algorithm and used the parameterized model to predict scenarios for which it was not trained, including different temporal stimulus profiles and genetic perturbations to pathway components.

In this sentence, we tell you about the mathematical model we built. I'll admit that we don't say much about the specifics of the model in the abstract, but there are some key takeaways. Our model was built to capture the response features we described above. It included things about the yeast mating response pathway that we know from decades of research on how the pathway worked. To find the right numbers, or parameters, for our model we used a special type of machine learning called an evolutionary algorithm. Most importantly, we used our model to predict new scenarios, like different pheromone stimulus patterns and changes to the pathway itself.

Our model allowed us to establish the role of four architectural elements of the network in regulating gene expression. These network motifs are incoherent feedforward, positive feedback, negative feedback, and repressor binding. Experimental and computational perturbations to these network motifs established a specific role for each in coordinating the mating response to persistent and dynamic stimulation.

This last section is the most exciting. We talk about what we learned from our model that we wouldn't have been able to learn without doing all the math. We learned that specific motifs, like feedforward and feedback, each have a unique job in regulating the pathway response. This result is explained most clearly in the figure above. We have our three key signaling motifs: feedforward, positive feedback, and transcriptional derepression, which we also called repressor binding. Each of these motifs is responsible for one of the response features. Feedforward causes long-term adaptation, positive feedback regulates the amplitude or size of response, and transcriptional derepression, activation by "derepressing" the repressor, causes persistent signaling after the pheromone is removed.

The Conclusion

Understanding the roles of these motifs can help us understand how these motifs may be affecting pathways that are involved in diseases. The experimental and mathematical portions of this research work together to make discoveries that would not have been otherwise possible. Mathematical modeling is an important tool in biological and biomedical research and can help push the fields forward to understanding things that are too complex and intertwined to be understood with just experimentation.