Relationship between Mathematics and Genetics

Question

I was wondering how can we mathematically define the biological nature around us. How can we mathematically define a real plant or a tree, growing from being a 1 cell to a full grown plant with many cells, and having the unique shape it has (For example palm tree vs bush tree).

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From what I know, the DNA encodes all of the information required to define a plant (or other forms of living like animals/humans).
If I want for example to genetically engineer a plant, for example, I want to create a blue rose, I can take a red rose and a yellow rose, decode their DNA sequence, check where the two sequences differ, they will probably differ at the place that defines the color of the rose, Now I will change the code at this place to something else and I will probably get some rose colored with a color that is neither red nor yellow, I will experiment more with this place (in the DNA sequence) till I will get a color that is close to blue.

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I mean: can't we define a real living plant (with its DNA) mathematically.

We can very well mathematically define what are the angles and shapes of the leafs, the thickness of the branches, the color of the flowers and their general shape, and many many more features. Now the real problem is how can we encode all of these abstract mathematical information into the DNA (which is structured like a bit sequence) in a mathematically abstract process.

Can't we find mathematical rules or axioms that define how a cell divides into two or more cells (while taking the DNA into account) to create a full grown creature with the clear features visible as stated above.

Maybe we can develop some mathematical model that can simulate the growth process of the cells (maybe by some recursive sequence or algorithm) that will compose the whole creature so that we can determine the general shape of the creature by its DNA sequence and vice versa.

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It seems that math can attack physical, chemical, machine, computer (discrete case) and abstract mathematical stuff very well, but unfortunately it seems that mathematics cannot attack biological and genetic stuff very well.

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Thanks for any information/share of knowledge.

Answer 1

There are two big problems with this:

1. The present model is unlikely to be complete.
2. Even if you could write your model down, it would be very large and you would need enormous computing resources to answer even simple questions

Re 1.: It would interesting to know, what the present state of the art is of creating something living just from some DNA sequencer, DNA, water and heat. If Synthetic Life is current, it is not possible to synthesize a living cell de novo yet.

Answer 2

Well, the question is way too vast and naive (and probably out of topic). First, DNA is not at all what you think, and our knownledge and possibilities either. DNA is not that clear. Parts here and there encode proteines, or indeed early pieces that will be progressively assembled and modified after. Gene translation is controled by more or less specific positive and negative modulators (which keys make crucial bits of information outside of genes), but also by the geometry of how parts of the DNA are rolled or unrolled, here again under some complex control and extra bits (cf "epigenetics"). The proteic active network is incredibly complex, reactive to environment (interior to the cell, to the body, or from the outside).

Besides, shapes and patterns are almost never encoded in DNA, not even the detail of brain connections (there wouldn't be enough bits in DNA for this, anyway), not even the detailled connection of retina to first visual areas through the optical nerve (connection is self-organised too). Morphogenesis result from complex mechanical and biological retroactions of the current stage of developpement vs new triggers telling to grow more this or this part. I.e. largely self-organisation, with some indirect trigering.

Cellules divisions and intercommunication is probably simpler, but yet far from totally known and way more complicated than you think. They are many kind of cells, stage of cells, here also there is a complex communication network. BTW the very notion of tissues show the self-organisation of several "auto-environments" of cells.

A few links to start learning:

• https://en.wikipedia.org/wiki/Morphogenesis
• https://en.wikipedia.org/wiki/Human_embryogenesis
• https://en.wikipedia.org/wiki/Embryogenesis
• ( morphogenesis of given organs, like the brain, are also fascinating)
• https://en.wikipedia.org/wiki/Cellular_automaton
• https://en.wikipedia.org/wiki/Reaction–diffusion_sys https://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogenesis
• https://en.wikipedia.org/wiki/Transcriptome
• https://en.wikipedia.org/wiki/Epigenetics
• https://en.wikipedia.org/wiki/DNA

Answer 3

Moreover, maths are not as magic as you think to solve everything.

For instance even if the Schrödinger equation gives the fondamental rules of particles and atoms, nobody is able to calculate atomes more complex than hydrogen or maybe helium, not too speak of molecules. (That's why you will always need multiphysics, describing each scale independantly, and "theory of everything" will always be of very limited interest and explaination power).

Turbulence is all implicitely defined by the Navier-Stokes equations, but we are very far to understand all its details and behaviors.

There exist many other example, but maybe just reminding there exist deterministic chaos should calm down the idea that maths can allow to control and predict everything.

Answer 4

There are many ways to model depending on what features you might want to capture. As an arbitrary example consider http://www.sciencedirect.com/science/article/pii/S002251931000531X?via%3Dihub