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)

Program

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

Elementary ‘‘particles’’ today

Interaction Mediators Figure from: http://www.particleadventure.org

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 …

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

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 :

Bound and Diffusion states Ep 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.

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

H spectrum

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

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

Thermodynamics of a « gaz parfait »

Thermodynamics of a « gaz parfait »

Thermodynamics of a « gaz parfait »

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 !

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

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 (?)

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.

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.

illustration U Ep Etot X

Exemple

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… ?

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

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