Mathematical Modelling of Morphogenesis and Regeneration (on the basis of cell memory)

1. Moscow, 2017 Mathematical Modelling of Morphogenesis and Regeneration(on the basis of cell memory) V. Volpert (CNRS, Univ. Lyon 1)

2. Introduction to the mathematical theory of morphogenesis Growth and forms (D’Arcy Thompson) Turing structures Morphogenetic gradients (Lewis Wolpert, Peter Lawrence. Christiane Nusslein-Volhard, …) Phyllotaxis

3. Regeneration is related to morphogenesis • Hydra and planarians – champions of regeneration • Liver, fingertips, … in humans • Deer antlers • …

4. Regeneration of zebra fish

5. Regeneration of zebra fish: skin

6. Regeneration of zebra fish: scales

7. Regeneration of zebra fish: scales

8. Some conclusion • Local regeneration is determined by local regulation (cell-cell contact, cytokines, cell differentiation and proliferation). • What happens in case of large (global) regeneration: hydra, planarian, … ?

9. Mike Levin’s slide (Tuffs Univ)

10. Cell memory, tissue (body) memory, target morphology and other science fiction

11. Cell memory: well known • Neurons: axons, synapses, neurotransmitters • Other cell types: lymphocytes (memory cells), pancreatic cells … (receptors, ion channels, calcium level …)

12. Cell memory: … and beyond • Neurons: axons, synapses, neurotransmitters • Other cell types: lymphocytes (memory cells), pancreatic cells … (receptors, ion channels, calcium level …) • Amoeba memory and learning

13. Cell memory: … till quite strange • Neurons: axons, synapses, neurotransmitters • Other cell types: lymphocytes (memory cells), pancreatic cells … (receptors, ion channels, calcium level …) • Amoeba learning • Learning by eating

14. Cell memory: … till quite strange • Neurons: axons, synapses, neurotransmitters • Other cell types: lymphocytes (memory cells), pancreatic cells … (receptors, ion channels, calcium level …) • Amoeba learning • Learning by eating

15. Next conclusions Thus, there are cells (besides neurons) that can keep memory. If a tissue consists of such cells, will it be a tissue with memory?

16. Tissue (body) memory: wikipedia Body memory is a hypothesis that the body itself is capable of storing memories, as opposed to only the brain. The idea could be pseudoscientific as there are no known means by which tissues other than the brain are capable of storing memories.[1][2] Body memory is used to explain having memories for events where the brain was not in a position to store memories and is sometimes a catalyst for repressed memory recovery. These memories are often characterised with phantom pain in a part or parts of the body – the body appearing to remember the past trauma. The idea of body memory is a belief frequently associated with the idea of repressed memories, in which memories of incest or sexual abuse can be retained and recovered through physical sensations.[1] An example of body memory is based on decapitated animals that upon regrowing their head seem to recall past memories and training. This may suggest evidence that such means may be available to simpler forms of life.[3][4]

17. Tissue (body) memory: wikipedia Body memory is a hypothesis that the body itself is capable of storing memories, as opposed to only the brain. The idea could be pseudoscientific as there are no known means by which tissues other than the brain are capable of storing memories.[1][2] Body memory is used to explain having memories for events where the brain was not in a position to store memories and is sometimes a catalyst for repressed memory recovery. These memories are often characterised with phantom pain in a part or parts of the body – the body appearing to remember the past trauma. The idea of body memory is a belief frequently associated with the idea of repressed memories, in which memories of incest or sexual abuse can be retained and recovered through physical sensations.[1] An example of body memory is based on decapitated animals that upon regrowing their head seem to recall past memories and training. This may suggest evidence that such means may be available to simpler forms of life.[3][4]

18. Body memory: wikipedia Studies done by biologists at Tufts University have been able to train worms despite the loss of the brain and head. This may confirm memory is stored in other parts of the body, at least in some animals. A worm reduced to 1/279th of the original worm can be regrown within a few weeks and show signs of training, by heading towards light and open space in order to search for food, an unnatural and dangerous behavior, that can be trained in a few weeks. With each head removed, the speed of which the individual remembers seems to increase, reducing training times. This may be a proof of body memory or muscle memory, or may just be a sign of epigenetics showing the appearance of memory. [Anthony, Sebastian. "Decapitated worms can regenerate their brains, and the memories stored inside".]

19. Body memory: wikipedia In the 1950s and 1960s James McConnell conducted experiments on flatworms to measure how long it took them to learn a maze. McConnell trained a group of flatworms to move around a maze and then chopped them into small pieces and fed them to an untrained group of worms. The untrained group learned to complete the maze faster compared to other worms that had not been fed the trained worms. McConnell believed the experiment indicated a form of cellular memory.[6] It was later shown that the training involved stressing the worms with electric shocks to avoid mistakes in the maze. This kind of stress releases hormones that stay in the body, thus there was no evidence for memory transfer. Similar experiments with mice being trained in a maze and being fed to untrained mice also showed improved learning. It was not a memory that was transferred but a hormonally enriched heart or liver.[6]

20. Tissue memory: facts • Antlers • Planarian regeneration • Limb regeneration from tail

21. Now we ready for modeling:1. tissue memory and regeneration

22. Cell memory: signaling 1. Each cell produces a signal and receives signal from other cells u = f(d) d Signal decays in space

23. Signal distribution

24. Signal distribution: amputation A part of the tissue is removed Old signal New signal

25. Regeneration: algorithm 1. Remaining cells produce a new signal proportional to the difference of u* (target signal) and u(t) current signal 2. Cells at the blastema (cut) can proliferate 3. The cell receiving the largest proliferating signal divides first

26. Regeneration: results Original form

27. Regeneration: results Original form Amputation

28. Regeneration: results Original form Amputation Regeneration depends on the signal

29. Cell memory and tissue regeneration

30. Cell memory and tissue regeneration

31. Cell memory and tissue regeneration

32. Regeneration: results

33. Regeneration: results

34. 2. organism regeneration/growth (morphogenesis)

35. Cell memory: signaling 1. Each cell produces a signal and receives signal from other cells u = f(d) d Signal decays in space

36. Cell memory: signaling 1. Each cell produces a signal and receives signal from other cells 2. New signal 3. Cell motion

37. Three cells

38. Many cells

39. Stem cells and differentiated cells Stem cells Differentiated cells Differentiated cells die by apoptosis if the survival signal produced by the stem is less than a critical value.

40. Growth and form

41. Conclusions • There are some evidences of the existence of tissue memory though the biological mechanisms are not known • Models based on cell memory allow the description of some aspects of morphogenesis and regeneration • There are interesting mathematical questions behind

42. Genotype vs phenotypein morphogenesis Returns to the genetic form after some time

43. Morphogenesis and evolution