1. 1st Paris Workshop on SMA in Biology at meso or macroscopic scales
Welcome at LPNHE on behalf of the organizing comittee
Few changes :
Dr Tisseau and Dr Dittrich are sick
We have an opportunity to publish contributions in a special issue of "The Journal of Biological Physics and Chemistry" (JBPC)

2. Program

3. SMA to understand Emergence ?
B. Laforge
Université Pierre et Marie Curie-Paris6
Impact of some knowledges in Physics to built a theory of Emergence and its consequences for building a theory of biology and some comments on SMA based approach

4. Elementary ‘‘particles’’ today

5. Interaction Mediators
Figure from:

6. But still many open questions
SM can only handle 3 interactions (gravitation ?)
SM has a large number of free parameters 25
SM structure including 3 families is ad hoc
Mass generation mecanism is unknown
dynamic mecanism (spontaneous symetry breaking)
1 prototype mecanism : Higgs mecanism
Predict at least one scalar field : Higgs boson
Why do we handle fundamental energy scales so different (EW, GUT, Plank)
Why is there more matter than antimatter in the universe (CP)
5% of the mass of the universe is built from the matter we know (if General Relativity holds)… What is Dark matter ? What is Dark energy …

7. From a microscopic theory of matter and interactions to a theory of complex systems structuration
Hydrogen atom and quantum mecanics
Emergence and statistical physics : « gaz parfaits »
Building a reductionnist theory of Emergence
Consequences for biology and the SMA approach

8. Schrödinger’s Equation describes local variations
Hydrogen Atom
Schrödinger’s Equation describes local variations
of wave function
V is potential energy due to e-p interaction
y(r,t) is the electron wave function
P(r) = | y(r,t)|² = probability to have electron in position r at time t
Equation solution is :

9. Bound and Diffusion statesEp r
In a boud state, wace function is localized in the potential well and decrease exponentially to 0 outside. In a diffusion state, wave function do not goes to 0 at infinity but has assymptotically a plane wave behaviour describing a free particle.

10. A remark on 1st quantification
Equilibrium state (F=-dV/dr=0)
In a potential well, Energy is quantified (The wave length of quantified states are given by the width of the potential width…)
quantification ↔ limit conditions

11. H spectrum

12. Chimical links
We have even been able to predict links with 5 electrons ! (2005)

13. Quantum chemistry : ab initio computation
Allows also to predict macromolecules properties (proteins)
Do we speak there about emergence ?

14. Thermodynamics of a « gaz parfait »

15. Thermodynamics of a « gaz parfait »

16. Thermodynamics of a « gaz parfait »

17. Thermodynamics of a « gaz parfait » and Emergence
The law PV = N k T is a emergent law of the system (This relation is known from classical thermodynamics of diluted gaz)
Nevertheless, This law is reducible using a microscopic theory of a gaz and given a « connection » which relates T and the average squared velocity of particles.
What is the origin of this emergence ?
If no constraint apply on gaz molecules (i.e. V is well defined) then the relation cannot hold… External contrainst are part of the origin of this law !

18. Phase Transitions
Statistical physics allows also tounderstand some other non trivial phenomena based on local dynamics and constant conditions
Ferromagnetic magnetizagion (phase transition)

19. Building a model of Emergence
Let’s get interested by a system composed of N constituants in interaction
1st case : isolated system
Internal Energy U of the system is minimized
Time to explore system phase space is linked to internal dynamics of constituents and is given by a characteristic time t1
The system final state is the minimum of U
 no emergence
2nd case : The system has outer interactions giving rise to a fixed potential
The system minimises U + Ep
Caracteristic time is still t1
System final state can be understtod in terms of unlying constituants poperties where outer of the system act has a constraint (exemple of gaz parfait)
 no emergence (?)

20. Building a model of Emergence
3rd case : system in interaction with a potentiel that changes with time
system minimises U + Ep
Caracteristic time to explore phase space is t1
Caracteristic time of a change of Ep is t2
Si t2 >> t1 , back to case 2
Si t1 >> t2 system evolution is dominated by changes of Ep(t). System can never explore its phase space i.e. the potential U + Ep.
Final state will depend on histoiry of Ep changes
the system has emergent properties
the system is still reductible to its componants, their
interactions AND History of contraints that it has experienced.

21. Building a model of Emergence
4th case : system in interaction with a potentiel that changes with time and exchange matter with outer world
U is not well defined anymore  total energy is minimized
Caracteristic time to explore phase space is t1
Caracteristic time of a change of Etot is t2
Si t2 >> t1 , back to case 2
Si t1 >> t2 system evolution is dominated by changes of Etot(t). System can never explore its phase space before Etot changes.
Final state will depend on histoiry of Etot changes
the system has emergent properties
the system is still reductible to its componants, their
interactions AND History of contraints that it has experienced.

22. illustration U Ep
Etot X

23. Exemple

24. Impact for biology
In biology, for almost any system during its organisation, local environnement local is changing rapidly and a lot of quantities are exchanged : case 4 !
Is this idea of emergence still reductionnist allows to address biological problems in a new way… ?

25. Model biology as a word under contraints
a local stochastic dynamics, and dynamics of constraints (multi-scales)
DNA and cell and body structures are the contraints :
In that framework, ‘‘gene’’ is a strong local contrainst

26. SMA based approach In biology, we have to deal with :
- various time and space scales (multiscale)
- constraints that have their own dynamics and are
local properties of the environment
Simulation is the only tool to address these problems. SMA is a very nice tool as it is the actual implementation of the idea of local interactions with local environment
But results have to be looked at the light of 2 dynamics (local interactions + conditions) if we want to explain and not only reproduce emergent properties