1. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze The Florence EMBIO group: people and scientific activity Lapo Casetti Dipartimento di Fisica and CSDC, Università di Firenze

2. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze CSDC Center for the Study of Complex Dynamics The CSDC is our “home” It is an inter-departmental structure of our University which hosts also researchers from the CNR (National Research Council) and from other research structures Graduate school on Nonlinear dynamics and complex systems: one graduate student funded by EMBIO starting January, 2006 All EMBIO researchers in Florence are part of CSDC

3. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze People experiment Physics Department Dr. Francesca Sbrana EMBIO graduate student EMBIO postdoc ISC - CNR Dr. Bruno Tiribilli Dr. Massimo Vassalli theory Physics Department Dr. Lorenzo Bongini Dr. Lapo Casetti Dr. Carlo Guardiani Prof. Roberto Livi Lorenzo Mazzoni EMBIO researcher Energetics Department Dr. Franco Bagnoli ISC - CNR Dr. Antonio Politi Dr. Alessandro Torcini INAF Dr. Marco Pettini

4. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Call for applications! The call for applications for the EMBIO research position in the Florence group is being opened: look at www.unifi.it/bu The position is a research-only, fixed-term one (2 ½ years) starting April 1, 2006. Net salary is around 1500-1600 euros per month We are looking for a young but experienced researcher able to contribute with original ideas and to take a leading role in the theoretical side of the project We welcome applications from EMBIO partners The deadline is tight (August 20 or so) due to Italian rules, so hurry up!

5. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Outline experiment Atomic Force Microscopy How it works Pulling proteins Modeling Simple statistical models Reconstructing the (free) energy landscape theory Simple models of proteins BPN models Dynamical simulations Energy landscape Geometric and topological properties Dynamics on the “connectivity graph” Dr. Lorenzo Bongini

6. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze An Atomic Force Microscope acts on the sample as a dynamometer able to probe the local interactions between tip and sample. If no specific interaction occurs between tip and sample, the system senses the geometry of the potential barrier defining the sample: the topography. The probe is a micrometric cantilever, made by photo- litographic methods, with a sharp tip on the bottom. In the interaction potential with the sample, the cantilever behaves like an elastic spring with k ranging from 0.01 to 100 N/m Atomic Force Microscopy By performing a scanning, the system spans the XY plane and the information collected can be imaged as a 2D map of the interaction. With standard cantilevers one obtains a topographic map of the surface (Microscopy) wherever using functionalised tips is possible to obtain specific maps such as magnetic, electric or affinity ones (Spectroscopy)

7. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Protein stretching

8. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Typical AFM stretching patterns Displacement Z Force

9. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Experimental protocol Cys I 27 I 28 I 29 I 30 Au T4 or T8 fragment Adsorption link Cys-Cys amino acids create a polar link with the gold substrate The system studied behaves like a series of three springs. We have to choose the spring elastic constants accordingly to what we are interested in

10. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Sawtooth pattern Oberhauser et al., PNAS 98, p.468-472 (2001)

11. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Modeling sawtooth patterns Displacement Z Force The unfolding pattern is modeled like a polymer extension between two successive rupture events. The speed typically used allows to trait this region as in equilibrium. No information about folding is found by this approach; only mechanical parameters can be computed

12. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Polymer extension Worm-like chain WLC FJC Freely-jointed chain ERT Exponential rising of Tension

13. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze WLC model Worm Like Chain Model L p persistence length, L C contour length Z displacement, T temperature Li et al., Nature 418, p.998 (2002)

14. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze A unified approach Our aim is to find a simple model allowing a complete statistical description of the stretching experiment (not only polymer extension) Franco Bagnoli, Carlo Guardiani

15. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze The model: schematic view

16. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze The model: basic features

17. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Energy: harmonic term

18. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Energy: interaction term

19. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze A typical plot

20. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Beyond our toy model Development of a more realistic protein model: Three-dimensional model Modelling of interactions between monomers Study of the role of the mass of the cantilever and protein

21. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Free energy reconstruction Reaction coordinate z’z0 r i f N

22. EMBIO kick-off meeting – Cambridge CSDC - Università di Firenze Free energy reconstruction: Jarzinski equality JE allows to reconstruct the free energy landscape by averaging over a set of non- equilibrium measurements