1. Physical Biology 2, 1-7 (2005) Thermodynamic Deductions from the Observed Shape of the Inner Mitochondrial Membrane Peter Salamon San Diego State University Unesco-Roste Workshop CISM 2005

2. Traditional models of inner membrane structure Mitochondria - Organelles inside a cell responsible for ATP production. The ultimate fuel cell?

3. Cristae Membrane Outer Membrane Inner Boundary Membrane Membrane surface rendering of traced mitochondrial tomogram Present focus = tubules

4. The membrane - Inner membrane protein composition: Largely unknown Small mole fraction, over 50% of area. - Inner membrane lipid composition: Phosphatidyl Enthanolamine (PE) - 27.7% Phosphatidyl Choline (PC) – 44.5% Cardiolipin – 17.4% Others – 10.4% Biomembrane -- phospholipid bilayer = oil film to compartmentalize. Inner mitochondrial membrane special -- many embedded proteins.

5. Different lipids have different shapes that depend largely upon the sizes of their polar headgroups.  Different spontaneous curvatures Lodish et al. Molecular Cell Biology 5th Ed., Freeman, 2003 Ding et al. Langmuir 21, 203, 2005 Demixing Spontaneous Curvature

6. Thermodynamic Model -Inner Mitochondrial Membrane Flat regions Lamellar faces Inner boundary membrane Cylindrical regions Tubes Lamellar edges Junctions Reservoir System "A thermodynamic model describing the nature of the crista junction; a structural motif in the mitochondrion.", Christian Renken, Gino Siragusa, Guy Perkins, Lance Washington, Jim Nulton, Peter Salamon, and Terrence G. Frey, Journal of Structural Biology. 138, 137-144 (2002). Cylinder radius = 10 nm. - Inner membrane flat region lipid composition modeled as: Phosphatidyl Ethanolamine (PE) - 39 % Phosphatidyl Choline (PC) – 61 % Study varying the radius and composition

7. The hypothesis Lipids residing in the inner membrane form a thermodynamically stable structure that minimizes free energy.

8. Contributions to free energy while varying tube radius and composition Bending Bending energy due to deviation from sponteneous curvature Different for lipids PE and PC Entropy PE exists in the flat regions at 39% PE and PC composition will be different in the inner and outer faces of the tubular regions Mechanical Work Changing the radius needs work against pressure difference  r = 39% ii oo pp Inner boundary membrane Tubular crista membrane  = % DOPE Intermembrane space Matrix space

9. Entropic Contribution The Elastic energy is least when all of DOPE and DOPC exist in different layers. This costs  G = T *  (  S mix ), where the outer delta is between the layer (inner or outer) and the reservoir (flat region).

10. Elastic energy Change in U (Flat to Cylinder) U = N C *u C + N E *u E u C = 0.5  a 0 (1-a cy /a 0 ) 2 - 0.5  a 0 (1-a ∞ /a 0 ) 2 R0R0 R R∞R∞ Cylinder ( a cy ) Spontaneous( a 0 ) Flat ( a ∞ ) R 0 (DOPE) = 2.05 nm R 0 (DOPC) = 9.05 nm Israelachvili JN, Intermolecular and Surface Forces (SanDiego, CA:Academic,1995).

11. The free energy G = U – TS +  pV U = Elastic energy of membrane due to bending. TS = Compositional entropy of the membrane due to de-mixing of lipid species.  pV = Mechanical energy due to increase in tube radius against pressure difference across membrane. Solve an optimization problem: Given  p  Find min G = f (  i,  o, R)  i = %PE (inner layer)  o = %PE (outer layer) R = Radius tube

12. Results At Pressure difference  p = 0.2 atm., R = 10nm

13. Contributions to free energy  t  p = 0.2 atm,  i  o  = 35%

14. Relevance of lipid composition  p = 0.2 atm, R = 10 nm oo ii

15. Conclusions Predicted pressure difference:  p  = 0.2 atm Predicted lipid redistribution:  i  PE (inner layer tube)     PE (outer layer tube) = 35% Tube radius set by competition between Elastic energy and pressure difference. Pressure difference regulates radius. Radius regulates composition. Reservoir at 39%

16. SDSU Mitomath Group Bio Graduate Students: Christian Renken, Maria Guo, Cori Holman,Vidhya Nagarajan Undergrad Students: Lauren Pittman, Shaun Kiever, Viktoria Nikolova, Melissa Wallace Technician: Lance Washington Faculty: Terry Frey Movies of tomography images can be viewed at http://www.sci.sdsu.edu/TFrey/TFrey.html http://www.sci.sdsu.edu/TFrey/TFrey.html Math Graduate Students: Gino Siragusa Jack Rose Undergrad Students: John Manor, Annalinda Arroyo Associates: Jim Nulton Faculty: Peter Salamon Joe Mahaffy Physics Graduate Students: Arun Ponnuswamy, Denny Williams Undergrad Students: Eric Vazquez Faculty: Arlette Baljon

17. Simulation…

18. Permeability Transition Membrane Remodeling Future: Mitochondrial role in Apoptosis (Programmed Cell Death) ● Release of Cytochrome c and Smac Ca 2+

20. Measurements of Mitochondrial Membrane Structures Reveals Common Structural Motifs Outer-Inner Membrane 22 ± 4nm Crista Junction 28 ± 6nm Crista Diameter 31 ±  7nm TGF 3/03