# Understand how a cell becomes a person – with math

We all start from 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 more than 37,000 billion cells spread over hundreds or thousands of different cell types. .

Although we broadly understand many aspects of this development process, we don’t know many details.

Better understanding how a fertilized egg transforms into trillions of cells to form a human is above all a mathematical challenge. What we need are mathematical models that can predict and show what is happening.

The problem is that we don’t have one – yet.

In engineering, mathematical and computer modeling are now crucial – an aircraft is tested in computer simulations long before the first prototype is even built. But biotechnology still relies heavily on a combination of trial and error — and serendipity — to deliver new treatments and therapies.

Thus, this lack of mathematical models is a major bottleneck for biotechnology. But the emerging discipline of synthetic biology, where a mathematical model would be extremely useful in understanding the potential efficacy of new designs, is crucial, whether for 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 over a hilly landscape. The valleys correspond to cells becoming types – skin, bone, nerve cells – and the hills dividing the valleys correspond to junctions in the developmental process, where a cell’s fate is chosen.

By the time the marble sits at the bottom of the valley, it has become a specialized cell with a defined function.

“Choice” here is a loose term and refers to the myriad of intracellular molecular processes that underlie cellular function and behavior.

In humans, some 22,000 genes and their products could affect cellular dynamics. In comparison, in bacteria the number of genes is much smaller – *Escherichia coli*the most important bacterial model organism, has about 4,500 genes that affect how this cell responds to the environment.

The landscape of hills and valleys described by Waddington attempts to summarize and simplify the concerted action of these thousands of genes, which affect the shape, bumps, number of valleys and hills and other aspects of the landscape.

Now it turns out Waddington’s landscape is more than just a metaphor. It can be linked to mathematical descriptions.

Valley bottoms are identified 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 balanced on a hill, even a slight disturbance will cause it to descend the slope into a particular valley.

The mathematicians of the 1970s took up the concept of the valley and developed a branch of mathematics, with the evocative name of “catastrophe theory”.

This theory considers how highly fertilized mathematical “landscapes” can change, and any qualitative change is called a “catastrophe”, or in less emotive language a “singularity”.

Fifty years later, mathematicians and computer scientists have rediscovered these landscape models in completely new applications.

Because we can now measure gene expression (or activation) in individual cells, we can see that internal molecular processes are like cells traversing a hilly landscape.

So we can now connect the landscape model to the experimental data in a way that Waddington could only dream of.

Linking gene activity to landscape pattern 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 to thousands of fully differentiated cell types in an adult human.

A problem that has received little attention is how the randomness (or noise) of molecular processes inside cells affects the landscape and the dynamics of cells on the landscape.

This is at the heart of our recent research published in *Cellular systems*, where we explore how this molecular noise can profoundly affect dynamics. Our research team, supported by an ARC Australian Laureate Fellowship, aims to develop an approach that integrates chance into a system capable of controlling and shaping the landscape.

In landscape terminology, molecular noise can move valleys and hills – it can even make valleys disappear or form new valleys and hills, changing direction while adding or removing potential destinations from our metaphorical marble.

If we translate this into the language of biology, it means that cell types that might exist in noise-free (or low-noise) systems can disappear once noise affects the system, and vice versa.

Noise matters.

It’s not just an inconvenience or nuisance – noise affects the types of cells that can exist in an organism. The hope is that we can take the growing amount of single-cell molecular data and couple it to mathematical models that account for both the complex dynamics of gene regulation and cellular processes, as well as the effects of noise.

Our ultimate goal is to develop a complete mathematical model of biological cells.

So far we have a mathematical model for only one type of cell (out of about 100 million), the tiny bacterium *Genital mycoplasma*which allows us to study and make verifiable predictions about its behavior.

This is changing thanks to the work of mathematical and computer biologists.

Our research group collaborates with researchers around the world to tackle the complex, but we believe achievable, goal of modeling any type of cell, including the multitude of human cells.

One of the key ideas that gives us this confidence is that biology uses and reuses very similar molecular mechanisms throughout the tree of life.

Our descent from a shared common ancestor is one of the fundamental principles of biology, and we can exploit it to facilitate our work: once we have a model for an organism, the next one will be easier to model, and and so on.

Evolutionary relationships between species mean that we can borrow ideas 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 by filling in gaps in our organism models.

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