EFFICIENCY & EQUILIBRIUM Lecture 1 : Geometry – Nature’s Poetry
Lecture 3: Mechanical and Chemical Equilibrium In the...
Transcript of Lecture 3: Mechanical and Chemical Equilibrium In the...
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PHYS 461 & 561, Fall 2011-2012 109/29/2011
Lecture 3: Mechanical and Chemical Equilibrium
In the Living CellLecturer:Brigita Urbanc Office: 12909(Email: [email protected])
Course website: www.physics.drexel.edu/~brigita/COURSES/BIOPHYS_20112012/
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PHYS 461 & 561, Fall 2011-2012 209/29/2011
The Central DogmaOf Molecular Biology
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PHYS 461 & 561, Fall 2011-2012 309/29/2011
The Bacterial Standard Ruler: E. coli
➔ prokaryotic cell (no compartments)
➔ minimal requirements for life:DNA based genomeDNA → RNA transcriptionribosomes (convert RNA into protein sequences)
A) AMF imageB) electron micrographC) schematic picture
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PHYS 461 & 561, Fall 2011-2012 409/29/2011
What is the E. coli's intracellular environment like?crowded with many macromolecules
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PHYS 461 & 561, Fall 2011-2012 509/29/2011
Molecular census on E. coli (has 4 lipid layers):
➔ volume: 1 fL = 1015 L; mass: 1pg = 1012 g; density: 1g/mL (H2O)
➔ dry weight of the cell: ~30%of its total (0.30pg); half of dry weight is protein (0.15 pg)
➔ half of dry mass comes from the carbon content of E. coli, so there is ~1010 carbon atoms in a cell
➔ number of proteins: assume each protein ~300 amino acids and each amino acid 100 Da (30 kDa; 1 Da = 1.6 x 1024 g), thus: 3 x 106 proteins (1/3 of these within the membrane, 2/3 inside)
➔ number of ribosomes: the mass of each ribosome 2.5 Mda; each ribosome is consists 1/3 of protein and 2/3 of RNA; 20% of all proteins in the cell resides in ribosomes: 20,000 ribosomes (Total ribosomal protein mass/protein mass inside on ribosome)
➔ the diameter of ribosome is 20 nm: 10% cell volume
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PHYS 461 & 561, Fall 2011-2012 609/29/2011
An E. coli cell: Macromolecular census
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PHYS 461 & 561, Fall 2011-2012 709/29/2011
(A) the protistGiardia lamblia(B) a plant cell(C) yeast cell
(with a bud)(D) red blood cell(E) a fibroblast
cell(F) a nerve cell(G) retinal rod cell
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PHYS 461 & 561, Fall 2011-2012 809/29/2011
Molecular census on a yeast cell:
➔ E. coli volume: VE. Coli
= 1.0 m3 (1 x 2 m)➔ Yeast: a sphere of diameter 5 m: V
yeast = 65 m3 ~ 60 V
E. Coli ;
surface area Ayeast
~ 80 m2 ; yeast nucleus a sphere of diameter
2 m and volume ~ 4 m3 with 1.2 x 107 base pairs (bp) of yeast genome (16 chromosomes)
➔ DNA packed into nucleosomes (histoneDNA complexes): 150 bp wrapped around a cylindrical core, histone octamer (radius 3.5 nm, height 6 nm, volume 230 nm3), with 50 bp spacers:
Nnucleosomes
~ 60,000 (Exp. 80,000 nucleosomes with a mean spacing of ~170 bp)
➔ volume of one bp ~ 1 nm3 & volume of all histones: 14 x 106 nm3 ➔ the genomic DNA packing fraction
pack ~ 3 x 103
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PHYS 461 & 561, Fall 2011-2012 909/29/2011
Chemical, mechanical, electromagnetic, thermal energyversus length scale
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PHYS 461 & 561, Fall 2011-2012 1009/29/2011
Thermal energy at room temperature T = 300 K:
kBT = 1.38 x 1023 J/K x 300 K = 4.1 pN nm
= 25 meV = 2.5 kJ/mol = 0.6 kcal/mol(Avogadro's number: N
A = 6.022 x 1023)
Brownian (thermal) motion: important for nm to m length scales. For macromolecules (DNA, proteins, lipids, and carbohydrates) ~ nmScale: thermal energy ~ energy needed for intramolecular rearrangement!
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PHYS 461 & 561, Fall 2011-2012 1109/29/2011
Discussion: Where does the energy to sustain life come from?
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PHYS 461 & 561, Fall 2011-2012 1209/29/2011
➔ food intake (animals eat plants and other animals, how about plants?)
CO2 + H
2O + energy ↔ sugar + O
2
➔ plants requires input energy (through photosynthesis store some input EM energy (sunlight) into the chemical bonds of sugar)
How is then sugar converted into the energy the cells need to beable to form the needed macromolecules? How do the cells store
the energy?
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PHYS 461 & 561, Fall 2011-2012 1309/29/2011
Metabolic breakdown of glucose in a glycolysis pathway
metabolism … cellulartransformation of onemolecule into another
needs input energy (ATP)
produces more energy(ATP, NADH)
end product: two molecules of pyruvate
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PHYS 461 & 561, Fall 2011-2012 1409/29/2011
1. ATP (conversion to ADP releases ~ 20 kBT energy;
unit of energy in cell processes)
hydrolysis(take away PO
42)
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PHYS 461 & 561, Fall 2011-2012 1509/29/2011
2. Transferable electrons on NADH and NADPH:NADPH gives up its hydrate ion and liberates energy
OXYDATION:electrons removed(spontaneous)
REDUCTION:electrons added(requires energy)
hydrateion
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PHYS 461 & 561, Fall 2011-2012 1609/29/2011
3. Create H+ gradients across the membrane(can be converted to ATP or NADH energy)
energy releaseenergy storage
H+ ions
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PHYS 461 & 561, Fall 2011-2012 1709/29/2011
Synthesis of Biological Molecules
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PHYS 461 & 561, Fall 2011-2012 1809/29/2011
Biosynthesis of proteins➔ glucose as a sole carbon source: 1010 Catoms in E.coli cell (6 Catoms per glucose, need 2 x 109 glucose molecules just to construct a cell)
➔ metabolic pathways for synthesis of 20 amino acids known but complex; connected to glycolytic pathway: (alanine from pyruvate in a single step by a single enzyme)
➔ an average energetic cost to synthesize an amino acid is:1.2 ATP equivalents aerobically4.7 ATP equivalents anaerobically
➔ Build a protein from amino acids: 4 ATP equivalents form peptide bondsattach amino acids to tRNA (carries one codon, 7393 nucleotides)power the movement of ribosome
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PHYS 461 & 561, Fall 2011-2012 1909/29/2011
In total, to build a protein: 5.2 ATP equivalents per amino acid:
For the entire E.coli cell: 5.2 ATP x 300 x 3 x 106 = 4.5 x 109 ATP
How about DNA/RNA building? to synthesize one nucleotide: 1020 ATP cost of assembling nucleotides into polymers is small (10%)
How much energy can one glucose generate? under ideal growing conditions: 30 ATP (CO
2 waste product)
Total cost of E.coli cell building: 1010 ATP or 6 x 108 glucose molecules (1/3 of the material required under ideal conditions and up to 10fold in less efficient growth conditions)
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PHYS 461 & 561, Fall 2011-2012 2009/29/2011
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PHYS 461 & 561, Fall 2011-2012 2109/29/2011
Seven major classes of macromolecular components
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PHYS 461 & 561, Fall 2011-2012 2209/29/2011
Biological Systems as Minimizers
➔ mechanical and chemical equilibrium: minimization problems
➔ mechanical / chemical equilibrium: short time scalesExample:
if k+ and k >> r (faster reactions), then A and B can be treated asif in chemical equilibrium
A B Ck+
k
r
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PHYS 461 & 561, Fall 2011-2012 2309/29/2011
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PHYS 461 & 561, Fall 2011-2012 2409/29/2011
Protein folding: Free energy minimization principle
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PHYS 461 & 561, Fall 2011-2012 2509/29/2011
Mechanical Equilibrium: Potential Energy Minimization
U(x) = k (xx0)2/2 – mg (x x
0)
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PHYS 461 & 561, Fall 2011-2012 2609/29/2011
Optical trap as a massspring system➔ bead in an optical trap with DNA tether exerting a force:
U(x) = ktrap
x2/2 Fx