We all start with a single cell, the fertilized egg. From this cell, through a process involving cell division, cell differentiation and cell death, a human being takes shape, ultimately consisting of over 37 trillion cells in hundreds or thousands of different cell types.
While we have a broad understanding of many aspects of this development process, we do not know many of the details.
A better understanding of how a fertilized egg transforms into trillions of cells to form a human is primarily a mathematical challenge. What we need are mathematical models that can predict and show what happens.
The problem is, we don’t have one yet.
In engineering, mathematical and computer modeling are now crucial: an airplane is tested in computer simulations long before the first prototype is built. But biotechnology still largely relies on a combination of trial and error and luck to find new treatments and therapies.
Hence, this lack of mathematical models is a major bottleneck for biotechnology. But the nascent discipline of synthetic biology, in which a mathematical model would be extremely useful for understanding the potential effectiveness of new designs, is crucial, whether it be drugs, devices or synthetic fabrics.
This is why mathematical models of cells, especially whole cells, are widely regarded as one of the great scientific challenges of this century.
But are we making progress? The short answer is yes, but sometimes we have to look back to move forward.
In the 1950s, British biologist and mathematician Conrad Hal Waddington described cell development as a marble rolling down a hilly landscape. Valleys correspond to cells that become types – skin, bone, nerve cells – and the hills that divide valleys correspond to junctions in the development process, where a cell’s fate is chosen.
By the time the marble settles in the valley floor, it has become a specialized cell with a defined function.
“Choice” is a vague term here and refers to the multitude of intracellular molecular processes that underlie cellular function and behavior.
In humans, about 22,000 genes and their products could influence cell dynamics. In comparison, the number of genes in bacteria is much smaller: Escherichia coli, the most important bacterial model organism, has around 4,500 genes that influence how this cell responds to the environment.
The landscape of hills and valleys described by Waddington tries to summarize and simplify the concerted action of these thousands of geniuses, which influence the shape, the irregularities, the number of valleys and hills and other aspects of the landscape.
Now it turns out that the Waddington landscape is more than just a metaphor. It can be linked to mathematical descriptions.
We identify the valley floors with stable states: left to itself, the marble (or undifferentiated) cell located at the bottom of the valley will remain there forever. But if the marble is hovering on top of a hill, even a slight disturbance will cause it to run down the slope in a particular valley.
Mathematicians in the 1970s took the valley concept and developed a branch of mathematics, with the evocative name “catastrophe theory”.
This theory considers how highly fertile mathematical “landscapes” can change and any qualitative change is called a “catastrophe” or, in less emotional language, a “singularity”.
Fifty years later, mathematicians and computational scientists have rediscovered these landscape models in entirely new applications.
Since we can now measure gene expression (or activation) in individual cells, we can see that the internal molecular processes are like cells traversing a hilly landscape.
So, we can now connect the landscape model with experimental data in a way that Waddington could only dream of.
Linking gene activity to the landscape model has become an active and exciting area of research. We hope to use it to understand how cells move through this landscape, from a single fertilized egg cell to thousands of fully differentiated cell types in an adult human.
One problem that has received little attention is how the randomness (or noise) of molecular processes within cells affects the landscape and the dynamics of cells in the landscape.
This is at the heart of our recent research published in Cell systems, where we explore how this molecular noise can profoundly affect dynamics. Our research team, supported by an ARC Australian Graduate Scholarship, aims to develop an approach that incorporates randomness into a system that can control and shape the landscape.
In landscape terminology, molecular noise can displace valleys and hills, it can even make valleys disappear or form new valleys and hills, changing direction by adding or removing potential destinations of our metaphorical marble.
If we translate this into the language of biology, this means that the types of cells that might exist in quiet (or low-noise) systems can disappear once the noise hits the system and vice versa.
It’s not just an inconvenience or annoyance – noise affects the types of cells that may exist in an organism. The hope is that we can use the growing amount of single-celled molecular data and couple them with mathematical models that consider both the complex dynamics of gene regulation and cellular processes, as well as the effects of noise.
Our ultimate goal is to develop a comprehensive mathematical model of biological cells.
So far, we have a mathematical model for just one cell type (out of about 100 million), the tiny bacterium Mycoplasma genitalium, which allows us to study and make verifiable predictions about its behavior.
This is changing thanks to the work of mathematical and computational biologists.
Our research group is collaborating with researchers around the world to address the complex, but we believe achievable, goal of modeling any cell type, including the multitude of human cells.
One of the key insights that give us this confidence is that biology uses and reuses very similar molecular mechanisms throughout the entire tree of life.
Our ancestry from a shared common ancestor is one of the fundamental principles of biology and we can use it to simplify our work: once we have a model for one organism, it will be easier to model the next and so on.
Evolutionary relationships between species mean that we can borrow insights from other species. And in a multicellular organism, where all cells are derived from a single fertilized egg, we can borrow information from other cell types as we fill in the gaps in our organism models.
Mathematical methods for the analysis of single-cell transcriptomic data
Megan A. Coomer et al, Noise distorts the epigenetic landscape and shapes cell fate decisions, Cell systems (2021). DOI: 10.116 / j.cels.2021.09.002
Provided by the University of Melbourne
Citation: Understanding how a cell becomes a person, with mathematics (2022, September 15) recovered on September 22, 2022 from https://phys.org/news/2022-09-cell-person-math.html
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