Mathematics telling cells how they should be

Embryonic cells need to sneak over the “development landscape” to their fate. New discoveries relate to how they do it so effectively.

In 1891, when German biologist Hans Driesch divided the two-cell sea urchin embryo in half, he discovered that each of the separated cells eventually grew into a full-fledged, albeit smaller, larva. The halves somehow “knew” how to change the development program: apparently, at this stage the complete blueprints of their development were not drawn yet (at least, not in ink).

Since then, scientists have been trying to understand how such a drawing is created and how detailed it is. (Dresh himself, frustrated that he could not find the answer to this question, threw up his hands in despair and stopped working in this area altogether). It is now known that some positional information causes genes to turn on and off throughout the embryo, and assigns certain roles to cells based on their location. However, it seems that the signals carrying this information fluctuate strongly and chaotically - not at all in the way that one would expect from important instructions.

“The embryo is a fairly noisy place,” said Robert Brewster , a systems biologist at the University of Massachusetts Medical School. “But somehow, he is going and giving a reproducible and clear plan for creating a body.”
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The same accuracy and reproducibility arise again and again from a sea of ​​noise in various cellular processes. Accumulating facts lead some biologists to a bold assumption: where information is processed, cells can often find not just good solutions to complex life problems, but optimal ones — cells extract as much useful information from their complex environment as possible in theory. Questions of optimal decoding, as Alexandra Volchak , a biophysicist from the Higher Normal School of Paris, says, “is everywhere in biology”.

Traditionally, biologists have not considered the analysis of living systems as optimization problems, since the complexity of these systems complicates the task of their quantitative description, and since it is rather difficult to understand what needs to be optimized. Moreover, although the theory of evolution says that evolving systems can improve over time, nothing guarantees that they will approach the optimal level.

And yet, when the researchers were able to determine exactly what cells were doing, many of them were amazed at the presence of clear signs of optimization. Hints of this are found in the response of the brain to external stimuli and in the reaction of microbes to chemicals in their environment. And now one of the most convincing facts appeared thanks to a new study of the development of the larvae of flies, as described in the work recently published in the journal Cell.

Cells versed in statistics

For decades, scientists have studied the larvae of fruit flies, looking for clues to the process of their development. Some details were clear from the very beginning: a cascade of genetic signals forms a certain sequence along the axis from head to tail. Then the signaling molecules, morphogens, penetrate the tissues of the embryo, ultimately determining the formation of body parts.

A particularly important role is played by the four “gap genes] genes, which individually express in wide, intersecting areas of the body along its axis. The proteins they produce help regulate the expression of “pair-rule genes] genes, which create very precise, periodic striped patterns along the embryo. The strips define the basis for the late division of the body into segments.


Comparison of the expression of the gene gap and the gene rules pairs

How cells understand these propagation gradients has always been a mystery to scientists. It has been suggested that after the protein levels direct the cells approximately in the right “direction”, the latter constantly monitor the changing environment and as they develop, they constantly make adjustments, arriving at their destination at a rather late stage. This model echoes the “landscape of development” that Conrad Hal Waddington proposed in 1956. He compared the process of setting the cells to their fate with a ball rolling in a sequence of hollows with an ever increasing inclination and splitting paths. Over time, the cell needs to acquire more and more information to clarify its positional data — as if it is aiming at where and in what form it needs to be, playing “20 questions” —that was described by Jeanne Condev , a physicist at Brandeis University.

However, such a system is subject to accidents: some cells will inevitably choose the wrong path and will not be able to return. However, a comparison of the embryo of flies showed that the arrangement of the stripes according to the pair rule occurs with an incredibly small error, only 1% of the length of the embryo - or with an accuracy of up to one cell.


Thomas Gregor, biophysicist from Princeton University

This led a group of researchers from Princeton University, led by Thomas Gregor and William Bialek , to suspect something else: that cells can get all the information they need to determine their location from the expression levels of only the gap genes, although they do not have a periodicity, and therefore , are not the obvious source of this kind of instructions.

That is what they found.

For 13 years, they measured the concentration of proteins of the morphogen and the gene break, in each cell, from one embryo to another, in order to determine exactly how four of the break genes at each of the positions along the axis from head to tail would be expressed. Based on the distribution of these probabilities, they created a “dictionary” or decoder — an exhaustive map capable of producing a probabilistic estimate of the cell's location based on the levels of breakdown gene proteins.

About five years ago, researchers — among them were Mariela Petkova , who started these measurements as a student at Princeton (she is now preparing to defend a doctoral degree in biophysics at Harvard) and Gasper Tkachik , now working at the Austrian Institute of Science and Technology — identified this comparison, assuming that it works as an optimal Bayesian decoder (i.e., a decoder using Bayes' rule that calculates the probability of an event based on basic conditional probabilities). The Bayesian platform allowed them to give the “best guess” about the position of the cell based only on the expression of the gap gene.

The team found that the fluctuations of the four gene breaks can be used to predict the location of cells with an accuracy of one cell. However, this requires no less than the maximum information about all four genes: based on the activity of only two or three genes, decoder predictions turn out to be far less accurate. Versions of the decoder that used less information about all four gap genes — for example, those that responded only to the fact of turning on or off genes — also performed worse on predictions.


William Bialek, biophysicist from Princeton

As Volchak says: “No one has ever measured or shown how well information about the concentrations of these molecular gradients indicates a certain location on the axis.”

And so they did it: even considering the limited number of molecules and the noise of the system, varying the concentrations of the gap genes was enough to separate the two neighboring cells on the axis from the head to the tail — and the rest of the genetic network, apparently, transmitted this information.

“But one question has always remained open: does biology need all this? Said Gregor. “Or is it just something that we measure?” Can regulatory DNA regions that respond to rupture genes actually be designed to be able to decode the location information contained in these genes?

Biophysicists have teamed up with biologist Eric Wishaus, a Nobel laureate, to check whether cells really use the information that is potentially available to them. They created mutant embryos, changing the morphogenic gradients in young fly embryos, which changed the sequence of expression of the rupture genes, and eventually led to the fact that the stripes of the paired rule shifted, disappeared, began to duplicate or erode. The researchers found that even in such cases, their decoder could predict changes in mutated expression with surprising accuracy. “They showed that although the location map of the mutants is broken, the decoder predicts it anyway,” said Volchak.


Encoded body plan drawing
1) At an early stage of development, cells along the body experience different levels of rupture genes.
2) The levels of the gap genes can determine very precisely where the pair rule rule genes should be active.
3) All this leads to the formation of body segments in the later stages.

“One would have thought that if the decoder received information from other sources, the cells could not be deceived in this way,” Brewster added. “The decoder wouldn't work.”

These discoveries signify a new milestone, according to Kondev, who did not participate in the study. They talk about the existence of a “physical reality” at the intended decoder, he said. "In the process of evolution, these cells understood how to implement the Bayesian approach using regulatory DNA."

How exactly the cells do this remains a mystery. So far, "this whole story is wonderful and magical," said John Reinitz , a systems biologist at the University of Chicago.

And yet, the work gives a new way to talk about the early development, regulation of genes, and, perhaps, about evolution.

More uneven terrain

Discoveries provide an opportunity to take a fresh look at the idea of ​​Waddington about the landscape of development. Gregor says that the results of their work testify against the need to play 20 questions or gradually improve knowledge. The landscape is “uneven from the start,” he said. All information is already there.

“Apparently, natural selection rather strongly spurs the system, and it reaches the point where the cells work at the limit of the physically possible,” said Manuel Raso-Mehiyah , an aspirate from the California Institute of Technology.


Eric Wishaus, a biologist from Princeton University, Nobel Prize winner

It is possible that the effective work of the cells in this case is just a fluke: since the embryos of flies are developing very quickly, in this case evolution may have “found the optimal solution because of the hard need to do everything very quickly,” said James Brisco , a biologist. from the Francis Crick Institute (London), who did not participate in the work. In order to definitely establish the presence of a certain general principle, researchers will have to test the decoder in other species, including those that develop more slowly.

However, these results raise new, intriguing questions about regulatory elements, often a mystery. Scientists do not know exactly how regulatory DNA encodes the activity control of other genes. The discoveries suggest that the optimal Bayesian decoder works here, allowing the regulatory elements to respond to very small changes in the combined expression of the gap genes. “You can ask the question, what exactly decoder encodes in regulatory DNA? - said Kondev. - And what exactly makes it decode in the best way? Such a question we could not ask before the advent of this study. "

“This study makes this issue the next task in this area,” said Briscoe. In addition, there may be several ways to implement such a decoder at the molecular level, which means that this idea can be applied to other systems. Hints of this appeared in the development of the neural tube in vertebrates, which is the precursor of the central nervous system — and this requires a completely different mechanism.

In addition, if these regulatory regions require the implementation of optimal decoding, this in principle can limit their evolution, and, therefore, the evolution of the whole organism. “We still have only one example - the life that emerged on this planet as a result of evolution,” said Kondev, therefore we don’t know the important limitations of what kind of life can be in principle. The discovery of the fact that Bayesian behavior in cells may hint that the efficient processing of information can be "a general principle that forces a handful of atoms gathered together to behave in a way that we think life should behave."

But for now this is only a hint. Although it would be something like a "dream of a physicist," Gregor said, "we are still very far from proving all of this."

From wires at the bottom of the ocean to neurons in the brain

The concept of optimizing information comes from electrical engineering. At first, the experts wanted to understand how best to encode and decode sound, so that people could talk on the phone over trans-oceanic cables. Later it became a more general issue of the optimal transmission of information through the channel. The application of this platform to the study of the sensory systems of the brain and how they measure, encode and decode the input data was not out of the ordinary.

Now, some experts are trying to think about sensory systems in this way. For example, Razo-Mehiyya, studied how optimally bacteria sense and process chemicals in the environment, and how this affects their physical form. Volchak and colleagues asked how a “good decoding strategy” might look like in an adaptive immune system, which should recognize and respond to a huge assortment of uninvited guests.

“I do not think that optimization will be an aesthetic or philosophical idea. This is a very specific thing, ”said Bialek. “The principles of optimization often led to the measurement of interesting things.” Whether they turn out to be right or not - he believes that it’s productive to think about this topic anyway.

“Of course, the difficulty is that in many systems the decoded property is not something simple, like a one-dimensional arrangement [of the cell on the embryo's axis],” Volchak said. “This task is harder to define.”

It is because of this that the system that Bialek and his colleagues are studying is so attractive. “In biology, there are not many examples of how a high-level idea, such as information, leads to a mathematical formula,” which can then be tested in experiments on living cells, Kondev said.

It is this union of theory and experiment that Bialek admires. He hopes to see how this approach will further guide the work going on in this context. "What is not yet clear," he said, "is whether the observation of optimization is some kind of wonder that arises here, then there, or there is something fundamental in it."

If the latter turns out to be true, "it will be amazing," said Briscoe. “The fact that evolution is capable of finding extremely effective ways to solve problems will be an amazing discovery.”

Kondev agrees with this. “The physicist hopes that the phenomenon of life is associated not only with a certain chemistry, DNA and molecules that make up living beings - that it is wider than this,” he said. - And what could be wider? I dont know. Perhaps this work will raise this veil of mystery a little. ”