Imagine a ball being thrown into the air. It curves upwards, then downwards, and traces an arc to land at a distant point. A simple mathematical equation can describe the path of the ball and you can predict where it will land. Although biological systems are more difficult to predict, Jonathan Weissman (MIT professor of biology), Xiaojie Qiu (Postdoc) and their collaborators at University of Pittsburgh School of Medicine are trying to make the path taken cells by the ball as predictable as possible. Instead of focusing on how cells move in space, they examine how cells change with the passage of time.

Qiu, Weissman and Jianhua Xing (Professor of Computational and Systems Biology at the University of Pittsburgh School of Medicine) have created a machine-learning framework that can describe the mathematical equations that describe a cell’s progression from one stage to the next. This includes its transformation from a stem cell to a different type of mature cell. This framework, is also used by the researchers to determine the underlying mechanisms that drive changes in cells. These insights could be used by researchers to influence cells to follow a particular path, which is a common goal for biomedical research as well as regenerative medicine.

In a paper, the researchers discuss dynamo . This paper was published in the Cell on February 1. The framework’s many analytical capabilities are explained and used to help understand the mechanisms of human blood cells production. For example, why does one type of blood cell form first (appares more quickly than others).

Qiu states that the goal is to develop single-cell biology in a quantitative way. “We want to map the changes in a cell’s interplay with regulatory genes as precisely as an astronomer can. Then we want to be able understand those changes and be able control them.”

How to map out a cell’s future travel

Dynamo uses data from many cells to create its equations. It needs to know how different genes are expressed in cells from one moment to the next. Because RNA is a measure of gene expression, researchers can estimate this by looking at the changes in RNA levels over time. Researchers use the levels of RNAs to predict the trajectory of cells. This is similar to knowing the velocity and starting position of a ball to determine its trajectory. It is difficult to calculate changes in RNA levels from single cell sequencing data because it only measures RNA one time. To determine how RNA levels are changing, researchers must use clues such as RNA-being made at the time sequencing was performed and equations for RNA turnover.

To get accurate measurements that allow dynamos to work, Qiu and his colleagues had to improve upon their previous methods. They used an experimental method to tag new RNA and distinguish it from older RNA. This was combined with advanced mathematical modeling to overcome the limitations of previous estimation methods.

Next, the researchers had to shift from looking at cells at discrete times in time to taking a continuous view of how cells change. This is similar to switching from a map with only landmarks to one that shows the continuous landscape. It makes it possible to trace the paths between landmarks. The group was led by Qiu, Zhang and used machine learning to uncover continuous functions that defined these spaces.

“There have been great advances in methods to broadly profile transcriptomes and other -omic’ information at single-cell resolution. However, the analytical tools for exploring these data have not been predictive but descriptive,” Weissman says. He is also a Whitehead Institute member, a member at the Koch Institute for Integrative Cancer Research and an investigator at the Howard Hughes Medical Institute. You can do things with continuous functions that aren’t possible using cells from different states. You can ask, “If I change one transcription factor, how will it affect the expression of other genes?”

These functions can be visualized using Dynamo , which turns them into maps based on math. Each map’s terrain is determined by factors such as the relative expression of key genes. The current gene expression dynamics determines the starting point of a cell on a map. You can trace the path starting at that location to determine where the cell ends up.

By testing dynamo against cloned cell lines, the researchers confirmed its predictions about dynamos’s fate. These cells share the same genetics as dynamo and have the same ancestry. One of the two clones that were almost identical would be sequenced, while the other would go on to differentiate. Dynamo’s predictions of what would happen to each sequenced cell were similar to what happened to its parent clone.

From math to biology and non-trivial prediction

Dynamo can gain insight into the biological mechanisms by determining the continuous function of a cell’s movement over time. The ability to calculate derivatives of the function can provide a wealth information. Researchers can determine functional relationships between genes, such as how they interact with each other. Calculating acceleration is a way to determine if a gene’s expression changes rapidly, even if it is at a low level. It can also be used to identify which genes are key in determining a cell’s fate early in its trajectory.

Researchers tested their tools on blood cell differentiation, which is a complex and multi-branched tree. They worked with Vijay Sankaran, a blood cell expert from Boston Children’s Hospital and Harvard Medical School. Eric Lander of Broad Institute as well as the MIT Department of Biology confirmed a recent discovery that megakaryocytes form earlier than other types of blood cells. Dynamo also discovered the mechanism for this early differentiation. The gene that drives megakaryocyte formation, FLI1 can self-activate and is found in high amounts early in progenitor cell cells. This allows progenitors to become megakaryocytes early.

Researchers hope that dynamo will help them understand how cells change from one state to the next and also assist researchers in controlling it. Dynamo includes tools that simulate how cells change depending on various manipulations and a method for finding the best path to get from one state to another. Researchers can use these tools to help them predict how to best reprogram any type of cell. This is a critical challenge in stem cell biology, regenerative medicine and stem cell biology. There are many possible uses for these tools.

“If we create a set equations that describe how genes in a cell interact, we can computationally predict how to transform terminally differentiated cell into stem cells or how a cancerous cell might respond to different combinations of drugs that would not be possible to test experimentally,” Xing said.

Dynamo goes beyond statistical and descriptive analyses of single-cell sequencing data to develop a predictive theory about cell fate transitions. The dynamo tool suite can give deep insight into how cells change over the course of time. Researchers will be able to predict cell fates as well as their arcs, which is as predictable as a baseball’s arc.