Mathematical Model Could Unlock Timing of Stem Cell Development

treating cells like masses moving through space
Welch describes the physics-based approach that allows the model to infer cellular change from static snapshots.

At the University of Michigan, computational biologists have found a way to read motion from stillness — inferring how and in what order molecular changes unfold inside transforming stem cells, without ever being able to watch the transformation directly. The tool they built, called MultiVelo, applies the logic of physics to the frozen snapshots that single-cell sequencing produces, estimating the velocity and direction of biological change the way a physicist might reconstruct the arc of a thrown stone. The question it addresses — whether the epigenome or the transcriptome leads when a cell changes identity — is not merely academic; it sits at the foundation of whether stem cell therapies can be designed to work with nature rather than against it. In answering it through mathematics rather than waiting for technology to catch up, the team has turned an existing limitation into a kind of leverage.

  • A core obstacle has paralyzed stem cell research for years: measuring a cell's molecular state requires destroying it, leaving scientists with snapshots but no sense of the journey between them.
  • The stakes are high — without knowing whether epigenetic or transcriptomic changes come first, therapy designers are essentially working in the dark, risking interventions that misalign with the cell's natural sequence.
  • University of Michigan researcher Joshua Welch and his team sidestepped the problem entirely, building a physics-inspired mathematical model that infers the speed and direction of molecular change from data scientists already had.
  • MultiVelo, published in Nature Biotechnology in October 2022, treats cells as masses moving through biological space and calculates their developmental velocity — extracting motion from stillness.
  • The field now has a tool that resolves one of its most stubborn foundational questions, not through a technological leap, but through smarter interpretation of existing evidence — clearing a path that delays in treatment had long blocked.

For years, a deceptively simple problem has slowed stem cell research: scientists cannot watch a cell change in real time because the very act of measuring it destroys it. Single-cell sequencing offers extraordinary precision, but only a frozen moment — the motion between states remains invisible. At the heart of this frustration lies a critical unanswered question: when a stem cell shifts identity, does the epigenome change first, or the transcriptome? The epigenome governs which genes are switched on or off; the transcriptome is the live output of that instruction. Knowing which leads could fundamentally reshape how therapies are designed.

Joshua Welch, an assistant professor at the University of Michigan's Department of Computational Medicine and Bioinformatics, chose not to wait for better technology. Instead, his team built a mathematical model — MultiVelo — that extracts what existing data already contains but cannot easily reveal. Drawing on physics, the model treats cells as objects moving through space and estimates their molecular velocity, much as a physicist reconstructs an object's speed from positional measurements taken at different moments.

Published in Nature Biotechnology in October 2022, MultiVelo doesn't just detect whether a cell is changing — it predicts the direction and pace of that change. For stem cell therapy, this distinction is consequential: interventions designed in alignment with the cell's natural sequence are far more likely to succeed than those working against it. The breakthrough required no new laboratory technology, only a more sophisticated relationship with data already in hand. In a field where foundational gaps translate directly into delayed treatments, clearing even one significant obstacle carries real weight.

At the University of Michigan, a team of computational biologists has cracked open a problem that has slowed stem cell research for years: figuring out which molecular switch flips first when a cell changes its identity. The answer matters enormously for anyone hoping to coax stem cells into becoming the specific tissue types needed for medical treatment. But until now, the timing has remained stubbornly opaque.

The fundamental obstacle is both simple and maddening. When scientists want to measure what a cell is doing at the molecular level—which genes it's expressing, how its DNA is packaged—they have to destroy the cell to read it. It's like trying to understand how a dancer moves by taking a photograph. You get a snapshot, but you lose the motion. Single-cell sequencing technology has made it possible to read individual cells with precision, but that precision comes at the cost of the cell itself. Researchers can see what a cell looks like at one moment, and what it looks like at another moment, but the journey between those two states remains invisible.

This is where the question becomes urgent: does the epigenome change first, or the transcriptome? The epigenome is the layer of molecular instructions that sits atop the DNA itself—chemical tags and structural changes that tell the cell which genes to turn on and off in response to its environment. The transcriptome is the actual output, the genes being expressed right now. Which one leads, and which one follows? The answer could reshape how scientists design stem cell therapies, but without being able to watch cells transform in real time, the field has been stuck.

Joshua Welch, an assistant professor in the Department of Computational Medicine and Bioinformatics at the University of Michigan Medical School, approached the problem sideways. Instead of trying to watch cells change, he and his team built a mathematical model that could infer the direction and speed of molecular change from the snapshots researchers already had. The model, called MultiVelo, borrows its logic from physics. "We treat the cells like they are masses moving through space," Welch explained, "and we're trying to estimate their velocity." Just as a physicist can calculate how fast an object is moving by measuring its position at different times, the model calculates how fast molecular changes are happening by analyzing the state of cells at different stages of development.

The work, published in Nature Biotechnology on October 13, 2022, represents a shift in how researchers might approach the timing problem. Rather than waiting for technology to catch up—to somehow preserve cells while reading them—the team used mathematics to extract information that was already hidden in existing data. The model doesn't just say whether a cell is changing; it predicts the direction of that change and how quickly it's moving. For stem cell therapies, this could be the difference between a treatment that works and one that doesn't. If researchers know which molecular event comes first, they can design interventions that work with the cell's natural sequence rather than against it.

The implications ripple outward. Stem cell therapies have long promised to revolutionize medicine, but progress has been constrained by gaps in basic understanding. Every delay in answering fundamental questions like this one is a delay in treatments reaching patients. With MultiVelo, researchers now have a tool to resolve one of those foundational questions—not through new technology, but through smarter mathematics applied to data they already possess. The model won't answer every question about stem cell development, but it clears away one significant obstacle, and in a field built on incremental breakthroughs, that matters.

The big question in the field is which changes first, the epigenome or the transcriptome
— Joshua Welch, assistant professor at University of Michigan Medical School
We developed an approach based on models in basic physics, treating cells like masses moving through space and estimating their velocity
— Joshua Welch
A Conversa do Hearth Outra perspectiva sobre a história
Inventor

Why has it taken so long to figure out which molecular change happens first in a developing cell?

Model

Because the act of measuring destroys what you're trying to observe. You can sequence a single cell and learn everything about it, but the moment you do, that cell is gone. You can't watch the same cell transform.

Inventor

So researchers have been taking snapshots of different cells at different stages, trying to piece together the story?

Model

Exactly. They see cell A in state one, cell B in state two, cell C in state three. But they're looking at different cells, not the same cell evolving. The timing—which change triggers which—stays hidden.

Inventor

And this new model, MultiVelo, solves that by doing what, exactly?

Model

It uses mathematics borrowed from physics to infer velocity from position. If you know where something was and where it is now, you can calculate how fast it moved. The model does the same thing with molecular states.

Inventor

Does that actually tell you the answer? Which comes first?

Model

It gives you a way to predict it from the data you already have. You're not watching the cell change, but you're inferring the direction and speed of change from the snapshots. That's powerful enough to guide therapy design.

Inventor

What changes if researchers finally know the sequence?

Model

Everything about how you'd design a stem cell treatment. If you know which molecular event triggers the next one, you can intervene at the right moment, in the right way. You're working with the cell's logic instead of against it.

Inventor

Is this the final answer, or just the next question?

Model

It's the next question. But it's a question that couldn't even be asked clearly before. That's how progress works in this field—you clear away one obstacle, and suddenly the path forward becomes visible.

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