Mathematics telling cells what they should be

The cells of the embryos need to get through the "landscape of development" to their fate. New discoveries relate to how they manage to do this so effectively

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

Since then, scientists have been trying to understand how such a drawing is created and how detailed it is. (Drish himself, annoyed that he could not find the answer to this question, threw up his hands in despair and generally stopped working in this area). It is now known that certain 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 randomly - not at all as one might expect from important instructions.

“The embryo is a noisy place,” said Robert Brewster , a systems biologist at the University of Massachusetts Medical School. “But somehow he is going and giving out a reproducible and clear plan for creating the body.”

The same accuracy and reproducibility arise again and again from a sea of ​​noise in various cellular processes. The accumulating facts lead some biologists to a bold assumption: where information is processed, cells can often find not only good solutions to complex life problems, but optimal ones - cells extract as much useful information from their complex environment as theoretically possible. Optimal decoding issues, says Alexandra Volchak , a biophysicist at the Higher Normal School of Paris, “in biology everywhere.”

Traditionally, biologists did not consider the analysis of living systems as optimization tasks, since the complexity of these systems complicates the task of quantifying them, and since it is rather difficult to understand what exactly needs to be optimized. Moreover, although the theory of evolution says that evolving systems can improve over time, there is no guarantee that they will approach the optimal level.

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

Statistics-Understanding Cells

For decades, scientists have studied fruit fly larvae, 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, signaling molecules, morphogens, penetrate the tissues of the embryo, eventually determining the formation of body parts.

Of particular importance are the four gap genes, which are individually expressed in wide, intersecting areas of the body along its axis. The proteins they produce help to regulate the expression of pair-rule genes, which create very precise periodic striped patterns along the embryo. Stripes set the basis for the late division of the body into segments.


Comparison of gene expression of the gap and gene rule pairs

How cells understand these propagation gradients has always been a mystery to scientists. The assumption was widespread that after protein levels direct cells in approximately the desired “direction”, the latter constantly monitor the changing environment and, as they develop, constantly make adjustments, arriving at their destination at a fairly late stage. This model echoes the “developmental landscape” proposed by Conrad Hal Waddington in 1956.. He compared the process of tuning cells to his fate with a ball rolling along a sequence of hollows with an ever-increasing slope and forked 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" - as described by Janet Kondev , a physicist from Brandeis University.

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


Thomas Gregor, a biophysicist at Princeton University

This led a group of researchers from Princeton University led by Thomas Gregor and William Bialek to suspect something else: that the cells can receive all the information necessary for determining their location from the stripes from the expression levels of the gap genes alone, although they do not have periodicity, and therefore are not an obvious source of such instructions.

That is what they discovered.

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

About five years ago, researchers - among them were Mariela Petkova , who began these measurements as a student at Princeton (now she is preparing to defend her doctorate 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 the Bayesian rule that calculates the probability of an event based on basic conditional probabilities). The Bayesian platform allowed them to give out the “best guess” about cell position based only on the expression of the gap gene.

The team found that fluctuations in the four rupture genes 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, the predictions of the decoder turn out to be much less accurate. The versions of the decoder that used less information about all four break genes - for example, those that responded only to the fact that genes were turned on or off - also performed worse on predictions.


William Bialek, Princeton biophysicist

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

And so they did it: even taking into account the limited number of molecules and the noise of the system, varying the concentration of the breakdown genes was enough to separate two adjacent cells on the axis from head to tail - and the rest of the genetic network, apparently, optimally transmitted this information.

“But one question has always remained open: is biology necessary? - said Gregor. “Or is it just something 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 teamed up with biologist Eric Visaus, a Nobel laureate, to test whether cells really use the information that is potentially available to them. They created mutant embryos, changing the morphogen gradients in young fly embryos, which changed the sequence of expression of the rupture genes, and as a result led to the fact that the strips of the pair rule shifted, disappeared, began to duplicate or blur. Researchers found that even in such cases, their decoder could predict changes in mutated expression with surprising accuracy. “They showed that although the mutants have a broken location map, the decoder still predicts it,” Volchak said.


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

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

These discoveries mark a new milestone, according to Condew, who did not participate in the study. They talk about the existence of “physical reality” in the proposed decoder, he said. “During evolution, these cells understood how to implement Bayes' approach using regulatory DNA.”

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

Still, the work provides a new way to talk about early development, gene regulation, and possibly evolution.

More uneven terrain

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

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


Eric Wyaus, Princeton University Biologist, Nobel Laureate

It is possible that the effective work of cells in this case is just a fluke: since the embryos of flies develop very quickly, in this case, evolution may have “found the optimal solution because of the urgent need to do everything very quickly,” said James Briscoe , a biologist from the Francis Crick Institute (London), who did not take part in the work. 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 control of the activity of other genes. Discoveries suggest that an optimal Bayesian decoder is working here, allowing regulatory elements to respond to very small changes in the combined expression of gap genes. “One may ask, what exactly does the decoder code in regulatory DNA? - said Kondev. - And what exactly makes it decode in an optimal way? We could not ask such a question before the appearance of this study. ”

“This research makes the next task in this area precisely this question,” Brisco said. 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 a precursor of the central nervous system - and this requires a completely different mechanism.

In addition, if these regulatory regions require optimal decoding, this can in principle limit their evolution, and therefore the evolution of the whole organism. “So far we have only one example - the life that appeared on this planet as a result of evolution,” said Kondev, so we don’t know the important limitations of what life can be in principle. The discovery of Bayesian behavior in cells may hint that effective information processing may be “a general principle that makes a bunch of atoms gathered together behave in a way that, in our opinion, life should behave”.

But so far this is only a hint. Although it would be something like a “physicist’s dream,” Gregor said, “we are still very far from proof of all this.”

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

The concept of information optimization comes from electrical engineering. At first, the experts wanted to understand what is the best way to encode and decode sound so that people can talk on the phone over transoceanic cables. Later this turned into a more general question of the optimal transmission of information over the channel. The application of this platform to the study of the sensory systems of the brain and how they measure, encode and decode input data was not out of the ordinary.

Now some experts are trying to think about sensor 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 shape. Volchak and colleagues asked what a “good decoding strategy” might look like in an adaptive immune system that should recognize and respond to a huge assortment of intruders.

“I don’t think that optimization will turn out to 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 thinking on this topic is in any case productive.

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

It is because of this that the system that Bialek and colleagues are studying is so attractive. “There are not many examples in biology 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 still unclear,” he said, “is the observation of optimization a curiosity that arises here and there, or is there something fundamental in it.”

If the latter is true, “it will be amazing,” Briscoe said. “The fact that evolution can find 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 the specific chemistry, DNA, and molecules that make up living things - that it’s wider than this,” he said. - And what could be wider? I dont know. Perhaps this work will slightly raise this veil of secrecy. "