Osmosis, Osmolarity, Edema Molecules move between blood plasma, cells,

and interstitial fluid

Three main compartments

Images: https://courses.lumenlearning.com/nemcc-ap/chapter/body-fluids-and-fluid-compartments/

Classification of Membranes

Permeable impermeable semi-permeable

Cellular plasma membrane is semi-permeable

Osmosis• The biological membranes and cellular barriers

are not permeable for all types molecules

Osmosis• Differentially permeable membrane, same

solvent. Solvent follows solutes, if solutes are not evenly distributed, until extra pressure Posm is created

• Osmotic pressure is the hydrostatic pressure produced by a solution in a space divided by a partially permeable membrane due to a differential in the concentrations of water

• Rule: Water follows solute until either – solute concentrations become equal, or – additional pressure is created in a compartment with

higher combined solute concentration

Osmotic Pressure depends on solute concentrations difference between compartments

• Colligative property. Osmotic pressure depends on the final number of solute molecules, not on their chemical identity

• Water flows to the area where there are more non-water molecules

• Osmotic pressure looks like the gas law formula, where n is the total number of moles of the solute particles

• For V = 1L , Dn/V becomes DM• DM includes all dissociated forms of each

solute

• Posm = DP = Phigher-Plower

PosmV = ΔnsoluteRTPosm = ΔMsoluteRT

Higher pressure : lower pressure

P1V = n1,soluteRTminusP2V = n2,soluteRT

Deriving equation for Osmotic PressureCorrection for solute dissociation (i)

• Propensity of water to follow higher solute concentration is countered by extra work PosmV. V=1L = 10-3 m3

at T=36oC • M is molarity (molar concentration), not mass! • The total M needs to be corrected via van’t

Hoff’s factors, i, i.e. M →i�M if solute dissociates partially

GP =GP0+VΔP

PosmV = −nwRT ln xw= −nwRT ln(1− xstuff ) ≈ nwRTxstuff

Posm = (nstuff /V )RT = ΔMRTPosm[bar]= ΔMRT ≈ 25.7ΔM[bar]

Van’t Hoff factor, i• The number of moles of particles per mole of solute

is the van't Hoff factor, i. If solute does not dissociate (or associate), i = 1

• The original solute molecules may further dissociate• The factor counts the ALL DERIVATIVE FORMS of the

dissolved ingredient, x : molar fraction

• E.g. NaCl results in Na+ and Cl-, x1=0, x2=1 i=2• Example with partial dissolution to three fractions:– 50% monomers, 30% in 2 particles, 20% in 3 particles: i =

0.5 + 2!0.3 + 3!0.2 = 1.7; €

i = x1 + 2x2 + 3x3 + ..

Posm=iDM RT

Examples• The observed lower van’t Hoff factors

illustrate the differences between activities and concentrations. Ions are not fully independent on each other.

Tonicity of extracellular fluids

Isotonic Hypotonic Hypertonic Normal Turgid Plasmolysis

Molarity vs Molality

• Molarity Mi ≡ ni,moles / liter of solution• Mole fraction xi ≡ ni,moles / Sni

• Molality mi ≡ ni,moles / kg of solvent

1 molal solution: 1 mole of solute per 1kg of solvent

xsolute = nsolute/nwater = Msolute /55.5

One liter of pure water contains 55.5 Moles of water molecules (1000g/18g mol-1=55mol)

What Osmolarity is Normal?• Osmolarity of plasma is 285-295 milli-

osmoles/L• I.V.: any fluid > 550 mOsm/L should not be infused

rapidly• The higher the tonicity, the lower should be the rate

of infusion.• Calculated osmolarity in mM units =

2[Na+] + (2[K+]) +[Glucose]+[Urea]+ [Ethanol] ( all [C] in mmol/L)

(glucose mol. mass = 180g/mol: 3.5 – 6.5 mmol/L)– normal range for blood sodium is between 135 and 145

mM/L (different units: 3.10 mg/ml to 3.34 mg/ml)

Seawater osmolarity: ~ 1000 mOsm, do not drink it

Tonicity of intravenous fluids• Osmolality: total solute concentration in a fluid

compartment.• Tonicity: the combined ability of solutes to

produce an osmotic driving force that causeswater to move from one compartment toanother.– Solutes that are capable of moving water are

called “effective osmoles”.– These are solutes that are unable to cross from

the extracellular to the intracellularcompartment: sodium, glucose, mannitol,sorbitol.

– The control of tonicity will determine the normalstate of cellular hydration and cell size. This is ofparticular concern in the case of brain cells.

• Pharmaceutical labeling regulations may require a statement on tonicity.

Non-polar molecules cross membranes:oxygen, carbon dioxide, ethanol

Water, urea use some assistance

Fasting glucose: 4.4 to 6.1 mmol/L(79.2 to 110 mg/dL)

Urea: ~ 3 to 7 mmol/L

Osmolarities of therapeutic solutions or

infusions : examples

• Osmolalities of some intravenous fluids you will encounter during your clinical rotations

• High tonicity of enteralfeeding of premature infants has been implicated in necrotisingenterocolitis (NEC)

https://www.openanesthesia.org/iv-solutions-osmolality/

Normal saline

Lactated Ringers

How to measure osmolarities using boiling or freezing?

• Osmolarities of IV or oral medications can be measured by freezing point depression

• Why?

Boiling and Freezing Points

• Adding solute makes the liquid state more desirable for water because of the entropy increases and the chemical potential becomes lower. If xw is equal to 1 in pure water:

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Δµwater = RT ln(1− xsolutes) ≈ −RTxsolutesΔSwater _ in _ solution = Rxsolutes

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µw = µwpure + RT ln xw

Boiling point elevation of a solution

• A solution of solvent (concentration = xsolute ) exhibits a higher boiling temperature than that of pure solvent. Units of xs need to match the units of Kb

DTboiling = Kb xs

Pure solvent: xw = 1, boiling temperature T*

0=D-D * STH vapvap

Solute added: xw < 1, boiling temperature T

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Δ vapH −T(Δ vapS + Rxsolute ) = 0

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ΔT⋅ Δ vapS = ΔT⋅ Δ vapH /T = TRxsolute

ΔT = T −T∗ ≈ xsoluteRT∗2

Δ vapH

'

( ) )

*

+ , ,

Pure solvent: xw = 1, freezing temperature T*

Solute added: xw < 1, freezing temperature T

Freezing point depression of a solution

• A solution exhibits a lower freezing temperature than that of pure solvent

DTfreezing = Kf x

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ΔT = T −T∗ ≈ xsoluteRT∗2

Δ fusH

&

' ( (

)

* + + €

Δ fusH −T∗Δ fusS = 0

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Δ fusH −T(Δ fusS + Rxsolute )

Osmotic Pumps for Slow Drug Delivery

Semi-permeable

OROS (Osmotic [Controlled] Release Oral [Delivery]

System) is a controlled release oral drug delivery system in the form of a tablet. The tablet has a rigid water-permeable jacket with one or more laser drilled small holes. Water entering the tablet pushes the active drug through the opening in the tablet.

Name (Generic name)Acutrim (phenylpropanolamine)Adalat OROS (nifedipine)Alpress LP (prazosin)Cardura XL (doxazosin)Concerta (methylphenidate)Covera HS (verapamil)Ditropan XL/Lyrinel XL (oxybutynin)Dynacirc CR (isradipine)Efidac 24 (pseudoephedrine, ..)Glucotrol XL (glipizide)Invega (paliperidone)Minipress XL (prazosin)Procardia XL (nifedipine)Sudafed 24 (pseudoephedrine)Tegretol XR (carbamazepine)Volmax (salbutamol)

Some Problems:§ Pressure may be too

high: P ~ 25.7 atm • DM

§ Subject to dose dumping if membrane breaks

counseling patients about not chewing or splitting tablets may be important

§ Slightly more expensive to formulate than coating tablets

§ Possible hole plugging

XL/XR : extended releaseCR : controlled release

Two main liquid body compartments

• Two Main Compartments– Intracellular =

Cytoplasmic (inside cells), ICF : 2/3

– Extracellular (outside cells), ECF : 1/3

• ECF can be further partitioned into blood plasma and interstitium

Total Body Water = WEIGHT x 0.5 (women) or0.6 (men)

Homeostasis

• Definition: Processes by which bodily equilibrium is maintained constant.

• Examples of Bodily homeostasis:• temperature• blood pressure• heart rate• blood glucose level• body fluid composition• Osmolarity• Extra cellular fluid (ECF) volume • Acid-Base balance

Two main interfaces:• tonicity of ICF vs ECF • inside ICF: blood

plasma vs the remaining ECF

Distribution of Solutes in three fluids

K+ in cells

Cells

No albumin in lympth

Na+ in fluids

Plasma vs Lymph: Edema• Edema is defined as soft tissue swelling

due to expansion of the interstitialvolume. Edema can be localized or generalized.

• Some extracellular fluid compartments, a.k.a. trans-cellular fluids (cerebrospinal fluid, intraocular fluid and joint fluid) do not communicate freely with the rest of the body.

Water flow

Albumin+ blood proteins

Less Protein

Cells

Mechanisms maintaining interstitial fluid volume

• Plasma vs Lympth, the role of albumin: 70% of Ponc is due to albumin. Albumin size: ~ 10 nM (100Å)

• Oncotic pressure is a form of osmotic pressure created by plasma protein molecules that are impermeable across the capillary membrane.

• Starling's Law: Hydrostatic Pressure - Oncotic pressure = net fluid movement out of capillary into interstitium.

• P = 120mmHg systolic pressure (+Patm). The smallest pressure in capillaries ~ 20mmHg

60-80 nm• endocrine glands• intestines• pancreas• glomeruli of kidney

30-40 μmAllow cells to pass• Bone marrow• Lymph nodes• Adrenal glands

• < 10 nM• Regular capillaries• CNS (tighter)

Drugs in plasma: protein bindingBlood protein Normal level % Function

Serum Albumins 3.5-5.0 g/dl 55%

create and maintain osmotic pressure; transport insoluble molecules

Globulins 2.0-2.5 g/dl 38% participate in immune system

Fibrinogen 0.2-0.45 g/dl 7% Blood coagulation

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Fibrinogen gets converted to insoluble fibrin during blood clottingEnzymes, Pro-enzymes, hormones, .. < 1%

• Protein binding limits drug concentration, may be used as an “extended-release” mechanism

Human Serum Albumin & Drugs• HSA maintains osmotic/oncotic pressure • C=35 - 50 g/L =3.5 - 5.0 g/dL=0.5-0.75mM • Transports many drugs• Transports thyroid hormones, T3 (Tri-iodo-

thyronine) and T4 (Thyroxine) • Transports other hormones, particularly

fat-soluble ones • Transports fatty acids ("free" fatty acids)

to the liver • Transports unconjugated bilirubin (heme

catabolism, yellow bruises and brown feces)• Competitively binds calcium ions (Ca2+) • Buffers pH

Renal toxin CMPF in drug site 1Stephen Curry

Albumin carries Bilirubin from destroyed heme molecules in the spleen to liver

15-20% of T3and T4 -> HSA(majority by TBG)[ ]

HSA with myristic acid and ketoprofen

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PDB code: 7jwn

Many cavities, looks like a sponge

Albumin and other drug binding proteins

• HSA MW 67 kDa, 609 amino acids• Half life 20 days (drug half life

extension)• Likes to bind drugs with carboxyls

and/or hydrophobic areas • Other proteins binding drugs

– Lipoprotein– Glycoprotein– α, ß‚ and γ globulins.

• The bound portion may act as a reservoir or depot from which the drug is slowly released in free form.

Hypoalbuminemia• Liver disease (eg cirrhosis)• Excess excretion by the kidneys• Excess loss in bowel (e.g., Ménétrier's

disease)• Wounds and Burns (plasma loss)• Increased vascular permeability• Acute disease states (‘negative prot.’)• Mutations causing analbuminemia• Malnutrition (starvation)

HSA loaded with multiple ligands

Review• Chemical potential of the same molecule in

different phases or compartments (osmosis) must be equal

• Chemical potential of water is lower (better) in solution If xsolutes is small:

• Osmotic pressure: Posm=DMRT, where DM is molarity difference corrected by dissociation, i, osmolarity vs molarity: DM=iDM0

• Osmosis: semi permeable membranes.• Osmolarity and Tonicity: counting solutes that

can not cross the membrane and taking dissociation into account ( i, van’t Hoff’s factor).

• Boiling point elevation• Freezing point depression (Kf does not depend

on solutes!). Kf = 1.858 K kg/mol• Water pressure reduction: Raoult’s law• Gas dissolution in water: Henry’s law• The effects are entropic and to the first

approximation do not depend on the nature of solutes (colligative properties)

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µw _ in _ solution = µw _ pure + RT ln(xw )Δµw = RT ln(1− xsolutes) ≈ −RTxsolutesΔSw ≈ Rxsolutes

Posm =ΔnsolV

RT = iΔMRT

ΔTboiling = KbxsolutesΔTfreezing = K f xsolutesPw_ vap_ solution = Pw_ vap_ purexwaterPsolute_ in_ gas = KHenry

solutexsolute_ in_water