1 Flashcards
What is a cell
Basic unit of life Smallest unit able to
reproduce
Eukaryotic cells
Everything except bacteria
Prokaryotic cells
bacteria cells
What is a tissue
Group of cells plus matrix that have a specific
function
Four main types of tissue
epithelial
connective
muscle
nervous
what is the Extracellular matrix
3D matrix surrounding the cell :
• provides support and structure for cells
• regulates cell function
Van’t Hoff equation -osmotic pressure
tells us that osmotic pressure is proportional to concentration : Π=𝑐𝑅𝑇
Polyelectrolyte
polymer with groups that
dissociate in solvent leaving
charged regions
Proteoglycan function in ecm and how its achieved
Proteoglycans attract and retain water in the ECM
Important for
• filling space
• allowing transport of solutes
• mechanical properties
achieve this by exerting an osmotic pressure
what is a Proteoglycan
core protein chain with GAG “hairs” bonded to it 2 types decorin and aggrecan
Glycosaminoglycans (GAGs)
Polysaccharide chains • Four main groups • Hyaluronan • Chondroitin sulphate & dermatan sulphate • Heparan sulphate • Keratan sulphate
Decorin
A few GAG chains
• Chondroitin and dermatan sulphate
• Role in developing collagen fibres
“decorates” collagen fibers
Aggrecan
100s of GAG chains
Chondroitin and keratan sulphate
Role in providing structure to extracellular matrix
issues with the Van’t Hoff equation
bad for high concentrations and doesnt account for charged molecules
Donnan model - cocentration
semi permeable membrane in a in a jar of solution so some molecules cant make it through impacting the concentration of ions / final distribution of solutes
cell model - concentration
tba
What do aggrecan molecules attach to when they form an aggrecan aggregate
Hyaluronan
which distribution can be used to model the charge density in the rod-in-cell model
Boltzmann
What is the term that describes the contents of a cell (fluid plus organelles)?
Cytoplasm
Why are glycosaminoglycans good at attracting and retaining water in the extracellular matrix?
They have a negative charge
They are fixed in the matrix
Poisson’s equation for electrostatics
𝛻^2𝜓( 𝑟) =−𝜌 (𝑟)/𝜀 𝜌 (𝑟) =𝑧𝑒𝑐 (𝑟) 𝜓 𝑟 Mean electric potential at r 𝜌 𝑟 Mean charge density at r 𝜀 Permittivity of the solution c(r) Ion concentration at r
Diffusivity definition
A measure of how easily a solute diffuses through a medium - diffusion coefficient
Diffusivity equation
⟨ 𝑥^2⟩ =2𝑑𝐷t
𝑑 Number of dimensions
𝐷 Diffusivity
𝑡 Time
Stokes-Einstein equation -diffusivity
𝐷 = 𝑘𝑇/6𝜋𝜇𝑅 𝐷 Diffusivity 𝑘 Boltzmann’s constant 𝑇 Temperature 𝜇 Fluid viscosity 𝑅 Radius of sphere
what scenario does the Stokes-Einstein equation consider
Stokes-Einstein equation
considers a spherical particle with
a no-slip boundary condition
Hydrodynamic radius /Stokes radius
the radius of the molecule as the radius of a
sphere with the same diffusivity
Factors affecting
diffusivity
- Steric exclusion
- Hydrodynamic drag
- Tortuosity
Steric exclusion
when a solute molecule in water has a relatively larger hydrodynamic radius than water leading to a deficiency of the solute molecule in the vicinity of a second solute molecule
Hydrodynamic drag
Fluid drag opposes solute movement
More drag as solute radius increases
Tortuosity equation
𝜏 =𝑙′/𝑙
𝜏 Tortuosity
𝑙 Linear distance
𝑙′ Path length
Reptation
large molecules wiggle through holes
Fick’s first law - diffusion
𝐽 =−𝐷(𝑑𝑐/𝑑𝑥)
J Diffusion flux (amount per unit area
per unit time)
𝐷 Diffusivity
𝑑𝑐/𝑑𝑥 Concentration gradient
Steric partition coefficient
Steric partition coefficient reduces diffusivity and also concentration
𝐶 =𝐾𝐶_0
Fick’s second law - diffuision
𝜕𝑐/𝜕𝑡 =𝐷𝜕^2𝑐/𝜕𝑥^2 c Concentration 𝑡 Time 𝑥 Distance 𝐷 Diffusivity
what does Fick’s first law describe
there is an area of high and an area of low concentration these do not change the flux of solute is constant - calculates the flux
what does Fick’s second law describe
Solute spreads out from source
Concentration changes as a function of time and distance
What causes fluid flow
mechanical or osmotic pressure
Darcy’s law - volume flow ratw
𝑄 =−𝐴𝜅/𝜇 𝑑𝑃/𝑑𝑥 𝑞 =−𝜅/𝜇 𝑑𝑃/𝑑𝑥 𝑄 Volume flow rate 𝑞 Volume flow rate per unit area 𝐴 Cross-sectional area 𝜿 Intrinsic hydraulic conductivity 𝜇 Fluid viscosity 𝑑𝑃/𝑑𝑥 Pressure gradient
what does Darcy’s law describe
describes the flow of a fluid through a porous medium
what is Hydraulic conductivity
Describes how easily water can flow through a porous medium
what affects Hydraulic conductivity
- size of pores
- spatial distribution
- connectivity
Poiseuille equation - Flow along pipe of circular cross section
Flow along pipe of circular cross section 𝑄 =−𝜋𝑟^4/8𝜇 𝑑𝑃/𝑑𝑥 𝑄 Volume flow rate 𝒓 Pipe radius 𝜇 Fluid viscosity 𝑑𝑃/𝑑𝑥 Pressure gradient
Carman-Kozeny equation - hydraulic conductivity
𝜅 =𝜀𝑟^2/𝐺 𝜅 Hydraulic conductivity 𝜺 Fractional void volume 𝑟 Mean hydraulic radius of tubes 𝐺 Kozeny factor
what does the Kozeny factor depend on
depends on channel shape and tortuosity • straight tubes, G = 2 • random orientation, G = 3 – 5 • but also depends on ε • G → 100 as ε→ 1
Poroelasticity
Theory that describes the behaviour of a poroelastic material
• porous elastic solid
• filled with viscous fluid
• interaction between fluid flow and solid deformation
Terzaghi’s theory of effective stress
Load shared between solid and fluid 𝜎 =𝜎∗ +𝑝 𝜎∗ Effective stress 𝑝 Pore pressure 𝜎 Total stress
what happens in terms of the Terzaghi equation at a sealed boundary
all components are constant
what happens in tersm of the Terzaghi equation at a free draining boundary
total stress constant
effective stress increases
pore pressure decreases
what happens to hydraulic concutivity with increaed strain
it decreases
Viscoelasticity
A viscoelastic material has both an elastic and a viscous component to its response
Elastic behaviour
• Apply a force • Material deforms • Remove force • Material reforms to original shape • Energy stored in material and then returned
Viscous behaviour
• Apply a force • Material flows • Remove force • Material remains ‘deformed’ • Energy dissipated and not returned
Hysteresis
• Strain increased then decreased • Stress differs between loading and unloading • Energy lost
Creep
- Constant stress applied
* Strain increases over time
Stress relaxation
- Constant strain applied
* Stress reduces over time
Spring equation
𝜎 =𝐸𝜖
Dashpot equation
𝜎 =𝜂 𝑑𝜖/𝑑𝑡
𝜂 - viscosity
Maxwell model - overview
Spring and dashpot in series
Stress equal in both components
Total strain equals sum of components
Elastic behaviour for sinusoidally varying stress
Elastic behaviour
• Strain in phase with applied stress
• Peak stress at peak strain
Viscoelastic behaviour for sinusoidally varying stress
- Strain lags stress by p/2
* Peak stress at peak strain rate
Storage modulus
elastic behaviour (energy stored) 𝐸′ =𝐸∗cos𝛿
Loss modulus
viscous behaviour (energy dissipated) 𝐸′′ =𝐸∗sin𝛿
what does the loss factor depend on
temperature
hydration
frequency
The stress experienced by the solid part of the material in Terzaghi’s theory
Effective stress
collagen types and uses
Collagen I – tendon, skin, blood vessels, bone
• Collagen II – cartilage
• Collagen III – co-distributed with type I
• Collagen IV – basement membranes
Organisation of collagen
Microfibrils- • Collagen molecules • Tropocollagen • Three polypeptide chain Fibrils- cross-linked in staggered arrangement
Collagen IV in basal lamina
Basal lamina is part of the basement membrane which is alayer of ECM that separates and anchors epithelium to connective tissue the Collagen IV forms sheets
what is Elastin
Elastin
• Elastic fibres
• elastin core (90 % of the fibre)
• sheath of microfibrils (fibrillin)
Formation and assembly of elastin
made in endoplasmic reticulum sent to golgi body transported to membrane sent to ecm hydophobic so clumps together
what does a polymer tend towads in terms of entropy
tends to high entropy state to minimise distance between end (relaxed polymer)
