Liposomes, Micelles, Membranes

Membrane proteins

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 1 From molecules to polymers Structures assembled through molecular bricks  • Polimers – Polynucleotides  Nucleic Acids (RNA, DNA) – Polipeptides  Proteins

• Micelles, Liposomes, Membranes

• Hybrid structures  Ribosomes, Peptidoglycans

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 2 From molecules to polymers Structures assembled through molecular bricks  • Polimers – Polynucleotides  Nucleic Acids (RNA, DNA) – Polipeptides  Proteins

• Micelles, Liposomes, Membranes

• Hybrid structures  Ribosomes, Peptidoglycans

Amphipathic nature of phospholipids leads to two major architectures in polar (aqueous) solvents:

Amphipathic nature of phospholipids leads to two major architectures in polar (aqueous) solvents: Micelle • Micelles: one layer exposed to solvent

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 5 Architectures of amphipathic lipids Liposome/Vesicle Amphipathic nature of phospholipids leads to two major architectures in polar (aqueous) solvents: • Micelles: one layer exposed to solvent • Membranes (also vesicles/liposomes): two faces – leaflets – exposed to solvent

Bilayer membrane

• Other phases, such as hexagonal (HII), cubic, and more complex also found.

• Other phases,• suchMicelles as hexagonal limited in (H size,II), cubic, less thanand more ~20 complexnm. also found. • Bilayers can be macroscopic, up to ~106 nm. • …a reason for preference of latter in living organisms.

All of these phases are formed by different natural lipids under variable conditions

• Lipid bilayers (as well as micelles) form spontaneously in polar solvents (self-assembly). • Process mainly driven by entropy and by optimization of hydrophobic interactions among lipid tails. • Electrostatic and H-bonds interactions between polar heads and solvents contribute to stabilization. • Membranes are cooperative structures: – Tend to be extensive. – Tend to close on themselves (forming vesicles/compartments) as to avoid hydrophobic edges exposed to solvent. – Are self-sealing (holes thermodynamically unstable).

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 12 Key features of membranes Common features to all membranes • Sheet-like structures 5-10 nm thick (3-4 nm hydrophobic core). • Contain lipids (phospho-, glyco-, sphingo-lipids, sterols), proteins and carbohydrates. • Amphipathic lipids self-assemble in aqueous environment, held together by cooperative non-covalent interactions, and act as a barrier to flux of polar molecules. • Asymmetric: inner and outer leaflet (faces) always differ. • 2D solutions of oriented proteins and lipids: in general can translate into membrane plane, but rotations across membrane infrequent. • Most electrically polarized, with negative potential inside (typically ~ -60 mV).

Different membranes have their peculiarities (e.g. plasma membrane is peculiar with respect to membranes of organelles) and associated proteins can be also highly specific of that membrane.

Asymmetry key feature of biological membranes (e.g. plasma)

Highly variable lipids mixtures, depending on function.

Highly variable protein/lipid mass ratio (from 1:5 to 4:1) depending on role of specific membranes:

• Myelin (membrane insulating certain nervous fibers) has low content of proteins (15-30%) because pure lipids are good insulators. • Plasma membranes contain ~50% of proteins (pumps, channels, receptors, enzymes). • Mitochondrial and chloroplasts internal membranes transduce energy, need proteins (~75% of proteins).

Type of proteins also vary with specific function of membrane.

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 16 Functions of biological membranes Biological membranes define inside vs. outside of any cell and of organelles in eukaryotic cells • Prevent leaking of intracellular material and penetration of unwanted compounds. • Selective permeability through membrane proteins (pumps and channels) floating in lipids sea. • Additional functions associated to other membrane proteins: energy storage, information transduction, receptor functions, enzymatic activity, etc…

• Plasma membranes present in all kinds of cells. • Differ in Gram- and Gram+ bacteria.

• Gram+ and archaea have one membrane surrounded by cell wall. • Gram- two membranes separated by periplasm (contains proteins, peptides, and carbohydrates) lying in between. • Outer membrane quite permeable to small molecules owing to presence of porins.

Differ in prokaryotic and eukaryotic cells • Eukaryotic cells (with exception of plant cells) do not have cell walls, and their cell membranes consist of a single lipid bilayer. In plant cells, cell wall is on outside of plasma membrane.

Fluid mosaic model • Fluid because membranes are 2D solutions of oriented lipids and proteins • Mosaic because they are a composition of different lipids and proteins

• Most processes carried out by/in membranes are mediated by proteins. • Protein classification based on strength of interaction with lipid bilayer, reflecting degree of burial into membrane

Integral membrane proteins (yellow) interact strongly with hydrocarbon chains of lipids • Can be removed by agents competing with hydrophobic interactions, such as detergents or organic solvents (e.g. hexane, toluene). • Most integral proteins span entire lipid bilayer.

Peripheral membrane proteins (azur) bound to hydrophilic heads of lipids by electrostatic interactions and/or H-bonds • Can be dissociated by mild means, such as highly concentrated ionic solvents (e.g. 1 M NaCl) • Some further stabilized by covalent anchor to hydrophobic chains

© Biochemistry, J. Berg et al., 5th ed., 2001 Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 25 Membrane proteins’ topologies • α-helices and β-barrels (β-sheet curled to form a hollow cylinder) preferred structures assumed by integral membrane proteins (embedded in lipid bilayer). • Intra-chain H-bonds in α-helices and β-sheets thermodynamically favored in hydrophobic environment, where no polar competitor molecules are present.

Porin Bacteriorhodopsin

Prostaglandin synthase

© Biochemistry, J. Berg et al., 5th ed., 2001 Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 26 Membrane proteins’ topologies • α-helices usually span entire bilayer perpendicularly to its plane (~20 AA in length). • Most residues non-polar, distribution optimized to enhance stability: – Hydrophobic/apolar AA points towards lipid chains – Polar/charged residues create functional networks

Bacteriorhodopsin

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 27 Membrane proteins’ topologies Propensity of α-helices to insert into hydrophobic bilayers estimated from hydropathy (HP) index, i.e. (per-residue) free energy of transfer of mono-AA α-helices from hydrophobic environment to water: – Empirically, HP ≥ 20 kcal/mol for 20 AA sequence to be found as TM α-helix. – In a HP plot, peak should correspond to TM helix.

• PHE, MET, ILE highest value of transfer free energy  favourable TM helix. • ARG, ASP, LYS, GLU most negative values  unfavourable TM helix. • However… – Peak in HP index does not imply a sequence will give a trans-membrane (TM) helix! – Only valid for α-helices, not applicable to β-barrel!

HP index of a porin (β-barrel)

• β-barrels formed by antiparallel curled β-sheets. • Outside residues mostly nonpolar, inside (water-filled) hydrophilic, realized through alternation of hydrophobic and hydrophilic AA along each strand.

H-bond

• Some proteins attached to bilayer surface and have hydrophobic anchors protruding into the lipid bilayer. • Integral proteins (very stable) although not membrane-spanning.

Prostaglandin synthase

Lipid dynamics include: 1. Chain conformational transitions and defect motions 2. Rotational diffusion around long axes 3. In-plane lateral diffusion (local and jumps) 4. Heads’ motions 5. Out-of-plane vibrations 6. Collective undulations

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 33 Membranes are fluids Lipid and proteins lateral diffusion • Lateral diffusion obeys Einstein rule: s = 4Dt • Diffusion coefficient of various (fluid) membranes ~ 1µm2s-1 (1/100 of water).

• ~ 2 µm in 1s  a lipid can go from one end to other of a bacterium in 1s! • Proteins lateral motilities can vary from very low to lipid-like values: - 10-4 µm2s-1 for fibronectin, a glycoprotein anchoring cells to extracellular matrix (ECM) through linkages with integrin, in turn linked to cytoskeleton (interaction with actin fibers). - 0.4 µm2s-1 for bacteriorhodopsin (fast movement essential for efficient signaling).

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 34 Membranes are fluids Lipid and proteins transverse diffusion (flip-flop) • Flip-flop of lipids occurs very rarely (once in several hours) • Flipping of proteins never been observed Very frequent and fast Very rare

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 35 Membranes are fluids Lipid and proteins transverse diffusion (flip-flop) • Transverse diffusion important mechanism involved in building-up new membranes from existing patches (in eukaryotes plasma membranes built from ER ones). • Flippase enzymes present in ER membrane of eukaryotes and in plasma membrane of prokaryotes transfer some of newly formed phospholipids to opposite monolayer. • Flippases do not bind all phospholipids equally well, thus two membrane leaflets end up having different distributions of phospholipid (asymmetric!)

Membrane building in eukaryotes Flippase action Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 36 Membranes are fluids Fluidity depends on composition and presence of non-fatty-acids lipids • Membranes can exist in different phases: two extreme ones are gel (solid-like) and fluid liquid. • Gel to liquid transition can be caused by conformational changes in packing of phospholipids acyl chains from trans to gauche. • Membrane-mediated processes depends crucially on fluidity!

~~Gel phase Liquid phase~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 37 Membranes are fluids Fluidity depends on composition and presence of non-fatty-acids lipids • Transition from gel-like to fluid state occurs abruptly at melting

~~temperature Tm~~

© Biochemistry, J. Berg et al., 5th ed., 2001 • Additional phases also found (ripple and different fluid-like ones) • Transitions among different phases depend on many factors including temperature, pH, ionic strength, pressure and membrane composition (e.g. saturated/unsaturated lipids ratio and content of molecules such as cholesterol)

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 38 Membranes are fluids Fluidity depends on composition and presence of non-fatty-acids lipids • Some phospholipids (e.g. PC) undergo two steps transition.

• First transition at few degrees below Tm, due to changes in vicinity of polar heads (e.g. increased interaction with solvent). • Two step transition consequence of simultaneous changes in lipid order and membrane curvature  lipids that exhibit a pre-transition temperature display additional lamellar phase (ripple). • Ripple phase partially disordered, displays periodic one dimensional undulations on surface of lipid bilayer (arising from periodic arrangements of linear ordered

and disordered lipid domains). Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 39 Membranes are fluids Fluidity depends on composition and presence of non-fatty-acids lipids

~~Tm depends on length of fatty acyl chains and on their degree of unsaturation:~~

~~• cis double bond induces bending, interfering with ordered packing  Tm is lowered.~~

~~• Long hydrocarbons interact more strongly than short ones. Each additional –CH2– group adds ~0.5 kcal/mol to free energy of interaction of two adjacent chains.~~

© Biochemistry, J. Berg et al., 5th ed., 2001 Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 40 Membranes are fluids Membrane fluidity regulation in bacteria • Bacteria regulate fluidity of their membranes by varying number of double bonds and length of fatty acyl chains. • Ratio of unsaturated to saturated fatty acyl chains in E. coli membrane increases from 0.35 to 1.6 as growth T is lowered from 42°C to 27°C. • Decrease in proportion of saturated residues

~~prevents membrane from becoming too rigid.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 41 Membranes are fluids Fluidity regulation in animal eukaryotic cells • Cholesterol is key regulator of fluidity, allowing bilayers to adopt extra lamellar phase (liquid-ordered), intermediate between gel and fluid. • Opposite effects depending

on T being below or above Tm: - Inserting cholesterol in gel phase disrupts packing, reducing ordering of lipid chains. - In liquid phase rigid hydrophobic moiety of cholesterol intercalates between lipid chains, favoring trans conformation. • In liquid-ordered phase: - Lateral and rotational diffusion similar to liquid-disordered phase.

~~- Conformational order similar to solid-ordered.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 43 Membrane flexibility: a model Flexibility and hetereogenity of membrane “particles” (different kinds of lipids and proteins) reflect on macroscopic shape and rigidity of bilayer

~~• Membrane geometry deformations include stretching, bending, shrinking or expansion, shearing.~~

~~• Free energy cost associated to membrane deformation can be roughly estimated by means of elastic continuum theory.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 44 Membrane flexibility: a model Flexibility and hetereogenity of membrane “particles” (different kinds of lipids and proteins) reflect on macroscopic shape and rigidity of bilayer

• Stretching can be described by simple area function Δa(x1,x2), depending on position on plane (reflects possible inhomogeneity in membrane). • Compression and expansion can be described by simple thickness function w(x1,x2). • Shearing can be describe through angle θ formed by two sides of surface elements.

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 45 Membrane flexibility: a model Flexibility and hetereogenity of membrane “particles” (different kinds of lipids and proteins) reflect on macroscopic shape and rigidity of bilayer

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 46 Membrane flexibility: a model Flexibility and hetereogenity of membrane “particles” (different kinds of lipids and proteins) reflect on macroscopic shape and rigidity of bilayer

• Bending can be described by simple height function h(x1,x2) from a reference plane. • For practical purposes, best plane is 1 2 tangent to point (x 0,x 0) of interest  quadratic expansion of h using Taylor series in local reference frame: 2 h(x1 , x2 ) = ∑κij xi x j i, j=1 • Can be done for every point of even complex surfaces, by sub-dividing surface and introducing many local reference frames.

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 47 Membrane flexibility: a model Flexibility and hetereogenity of membrane “particles” (different kinds of lipids and proteins) reflect on macroscopic shape and rigidity of bilayer

~~• Curvature (bending) of membrane can be calculated from knowledge of h, namely from 2nd order derivatives which account for surface curvature matrix κ:~~

~~! $ 2 κ11 κ12 ∂ h κ = # & κ = # & ij x x " κ 21 κ 22 % ∂ i∂ j~~

~~• Diagonalization of κ corresponds to identify reference frame giving two principal axes of curvature.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 48 Membrane flexibility: a model ΔG of membrane deformation as functional of shape functions Δa, h, w, θ • Area stretching modeled by means of spring network. • Deformation from reference area associated to increase in free energy: " %2 Ka Δa(x1, x2 ) Gstretch = ∫ $ ' da 2 # a0 & 2 Ka Δa • If relative areal strain Δa/a constant: Gstretch = 2 a0 2 • Ka stretch modulus: 55-70 kBT/nm ~ 230-290 mN/m

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 49 Membrane flexibility: a model ΔG of membrane deformation as functional of shape functions Δa, h, w, θ • Bending (deformation from planar surface) modeled by means of spring network. • Free energy as a functional of principal curvatures:

~~K 2 b ! # Gbend = da"κ1 (x1, x2 ) +κ 2 (x1, x2 )$ 2 ∫~~

~~• Kb bending rigidity: 10-20 kBT~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 50 Membrane flexibility: a model ΔG of membrane deformation as functional of shape functions Δa, h, w, θ • Change in thickness modeled by means of elastic network. • Deformation from reference thickness associated to increase in free energy:

~~" %2 Kt w(x1, x2 ) − w0 Gthickness = ∫ da$ ' 2 # a0 &~~

~~2 • Kt stiffness modulus: 60 kBT/nm .~~

~~• Shear deformation also quadratic in θ.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 51 Vesicles Vesicles are closed spherical shells of lipids that can be used as tools to investigate elastic properties of membranes Two main experiments

~~Micropipette aspiration Membrane pulling~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 52 Vesicles Micropipette aspiration • Small pipette (~ 10 µm diameter d) used as a solution probe to grab vesicles. • Pressure difference Δp between micropipette and solution allows suction that deforms vesicle membrane.

~~• Knowledge of Δp and geometric parameters Rv, R1 (~d/2) and l allows determination of surface tension τ and of moduli Ka and Kb. • Laplace-Young relation gives pressures~~

~~Δp needed to maintain spheres of radii RV/R1: 2τ 2τ Δpout = Δpin = Δpin RV R1~~

~~• Since: Δp = Δpin − Δpout Δpout Δp R • We have: τ = 1 2 1−(R1 RV )~~

Δp R1 • For each Δp measure geometric parameters and calculate τ τ =  2 1−(R1 RV ) • From τ calculate moduli Ka and Kb. Δa • E.g. Ka calculated recalling that τ corresponds to ΔG per surface area: τ = Ka a0 • Δa determined from expt. images, or…

~~• Approximated (assuming constant Rv upon suction) by:~~

~~2 2 Δa = 2π R1l + 2π R1 a0 = 4π RV ~~

~~2 Δa R1 (1+ l R1) τ = Ka = Ka 2 a0 2RV~~

~~Slope of τ vs. Δa/a0 gives~~

~~the stretch modulus Ka~~

Typical values for pure phospholipid bilayers ~250 mN/m Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 55 Vesicles Micropipette aspiration

Two main limitations: • Formula linking tension to stretch modulus ignore thermal fluctuations in membrane (entropic effect). • This is valid only at high enough tensions ironing out spontaneous undulations. • Stress-stretch relationship in entropic regime

~~allows determination of bending constant Kb.~~

~~• Values obtained for ideal single-lipid membranes, not accounting lipid heterogeneity, membrane proteins and intra- and extra-cellular connections.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 56 Vesicles Membrane pulling • Closely mimic real world situation, where formation of tubules (e.g. in ER and trans-

~~Golgi network) occurs driven by forces different than those arising from Δp.~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 57 Vesicles Membrane pulling • Closely mimic real world situation, where formation of tubules (e.g. in ER and trans- Golgi network) occurs driven by forces different than those arising from Δp. • Experiments with optical tweezers show that applying a force to a single point of membrane results in tether formation. • Forces are in range 5-20 pN for a variety of different membranes.

~~L G = 8πK + πK + 4πK bend b b r b Vesicle  Tether end Tether body~~

~~2 Ka (a − a0 ) Gstretch = 2 a0~~

~~# 4 3 2 & GpV = −Δp% π R + r π L( $ 3 '~~

~~Gload = − fL~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 59 Vesicles Membrane pulling • Minimizing sum of free energy terms with respect to geometric variables r, L

~~and R gives a relation between applied force and tension and constant Kb~~

~~f = 2π 2Kbτ~~

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course. 60 References • Books and other sources • Physical Biology of the Cell, R. Phillips et al., 2th ed., Chap. 11 • Biochemistry (5th ed.), Berg et al., Chap. 12