Lecture, Reading & PSets - MIT OpenCourseWare...Source: Li, Leon D. et al. "Spatial configuration and composition of charge modulates transport into a mucin hydrogel barrier." Biophysical

Lecture, Reading & PSets:Chap 2: E-fields -- sources, "kinetics"• What are E and H fields .......in BioSystems….• Concepts: (1) QuasiStatics; (2) Charge Relaxation• Some important & useful applications

Chap 3: Transport & Electrochemical InteractionsEffects of Molecular Charge on:

• Donnan Partitioning into tissues, gels, cells, ECM• Electrostatics ↔ Binding (to ECM / ICM, receptors)• Osmotic Pressure in tissues/gels• Diffusion (Deff): effects of electrostatic interactions

(Come back to this at end: “Integrative Case Studies)

Term Paper

1

Biophysical J 2013

ABSTRACT: The mucus barrier is a glycoprotein gel that coats all wet surfaces in the human body, including the respiratory, gastrointestinal, and urogenital tracts.• Criteria that govern transport through

mucus barrier are unknown.• Charge distribution of solutes is a

critical parameter to modulatetransport through mucin-basedbarriers: implications for drugdelivery

• Ionic strength within the mucinbarrier strongly influences transportspecificity

COO−SO3−

lots of...

Gastric mucin glycoprotein (MUC5AC 641 kDa)

© Royal Society of Chemistry. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.Source: Li, Leon et al. "A microfluidic in vitro system for the quantitative study of the stomach mucus barrier function." Lab on a Chip 12, no. 20 (2012): 4071-4079.

© source unknown. All rights reserved. This content is excluded from our Creative Commons license. For moreinformation, see http://ocw.mit.edu/help/faq-fair-use/.

2

http://ocw.mit.edu/help/faq-fair-use/http://dx.doi.org/10.1039/C2LC40161Dhttp://dx.doi.org/10.1039/C2LC40161Dhttp://ocw.mit.edu/help/faq-fair-use/

Fig. 1 Microfluidic device enables mucin barrier formation on-chip. (a) A mucin sample initially filling

both the flow and mucin channels (step 1, top-down view) is shaped into a layer of fixed width between a buffer flow and a microfluidic valve inside the mucin channel (step 2). Fluorescent peptides flushed into the device arrive at the mucin barrier surface and transport into the mucin barrier over time. (step 3)

(b) Formation and stability of the mucin barrier on-chip is assessed using fluorescently labeled mucins, showing that the mucin barrier surface interface is stable over time.

(c) Mucins are gradually lost from the mucin barrier over time, likely due to surface fluid shearing. We limit the duration of permeability measurements to 10 min to ensure that a majority of the initial mucin quantity remains inside the mucin barrier during the experiment. n = 3 devices.

Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.Source: Li, Leon D. et al. "Spatial configuration and composition of charge modulates transport into a mucin hydrogel barrier." Biophysical Journal 105, no. 6 (2013): 1357-1365.

3

http://www.sciencedirect.comhttp://dx.doi.org/10.1016/j.bpj.2013.07.050http://dx.doi.org/10.1016/j.bpj.2013.07.050

fixed charge in molecular

matrix

mobile charges e.g., ions

(1)

(2)

(3)

(4)

(5)

(6)

TOT

“Complete Description of Electrochemical Coupling & Transport”

4

EKG: L >> (1/κ) ⇒ elec. migration dominates diffusion

++ ++

__ _ __

∇2Φ = 0+

(air)σ = 0, εo

τheart ~ 1 sec


matrix


(1)

(2)

(3)

(4)

(5)

(6)

TOT


~0

6

(air) σ = 0, εo

σ,ε++ +++

__ _ __

Jin = σEin

Jout = 0

σ,εnano-sec’s

later

n • Ein = 0

t = 0+ (after heart beats)

Ein = dipole + uniform field to match BC at r=R

7

EKG: L >> (1/κ) ⇒ elec. migration dominates diffusion

++ ++

__ _ __

∇2Φ = 0+

(air)σ = 0, εo

τheart ~ 1 sec

Equilibrium Upteake of Pfizer Mystery Drug: 760 Da; pI ~11 (peptide; basic)

? ? ? ? ?

Can drug charge increase penetration and retention of drug into desired tissue (tumor…)

Courtesy of Alan Grodzinsky. Used with permission.

9

http://web.mit.edu/continuum/www/Research.html


matrix


(1)

(2)

(3)

(4)

(5)

(6)

TOT


Equilibrium

0

=0

=0

10

(1)

(2)

(4)

(5)(6)

“Donnan Equilibrium”

= 0

(3) = 0

Boltzmann:

(for all species)

TOT

Electro-neutrality

−∇Φ

11

CNa CH Cdrug CCl COHCNa CH Cdrug CCl COH

bath bath bath

bath bath

= = = =

1zi

bathCiCi

1zi= const =

(1) Boltzmann (for all species)

ρm + F(CNa - CCl) = 0

(3) Electroneutrality (with approximations):

drug

12

Can You Use Donnan to Find: Charge of the Drug ??

measured

(bath conc. given)BoltzmannNa+, Cl ̶ partitioning

m mElectroneutrality

ρm

_Tissue fixed charge density

bath

measuredbath

Calculated (Donnan)

Find drug valence Z

Giventissue

13

Pfizer Mystery Drug: “Pf-Pep”760 Da; pI ~ 11 (5 amino acids; basic)

RU = Kpart 1+ n

Kd + cFMeasure Equil Uptake of 125I-Pf-pep @ pH 7:

14

• small (760 Da)• basic (pI ~ 11)

Is “Pf-pep” = Arg-Tyr-Lys-Arg-Thr

Donnan partitioning experiment

1/Z

?Different tissue samples having varying ρ

m

_tissue

Calculate from Donnan

Measure Pf-pep partitioning

© source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.

15

http://ocw.mit.edu/help/faq-fair-use/

12

+ ++

pH →

net c

harg

e →

Is “Pf-pep” = Arg-Tyr-Lys-Arg-Thr16

Equilibrium Binding of H+ to COO- and NH2

groups

Gives Kd

Gives n “reversible, bimolecular,

1st order” reactions


17


CHARMM (Chemistry at HARvardMacromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. The CHARMM Development Project involves a network of developers throughout the world working with Martin Karplus and his group at Harvard to develop and maintain the CHARMM program.

Nobel Prize in Chemistry, Oct 9, 2013......... for the development of multiscale models for complex chemical systems.... The computer simulations combine classical physics, which is able to track a multitude of atoms, and quantum mechanics..... including electrostatic interactions....

Photographs of scientists removed due to copyright restrictions.

18

http://en.wikipedia.org/wiki/Macromolecularhttp://en.wikipedia.org/wiki/Force_field_(chemistry)http://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Software_package_(installation)http://en.wikipedia.org/wiki/Martin_Karplushttp://en.wikipedia.org/wiki/Harvard

Example of Equilibrium

Binding Isotherm

Gives Kd

Gives n

Does Pfizer “Pf-pep” bind to charge groups inside cartilage (tumor ECM, etc?)


19


cBtiss + cFtiss

cbathRU =

cBtiss ncFtiss Kd + cF

=

nM

cFtisscbath

Kpart =

125cF125cbath

Kpart =

RU = Kpart 1+ n

Kd + cF

Kpart = 1.4

Kd ~ 5nM

Kpart 1+ nKd

(n~ 50 nM)

Equilibrium Binding


20


RU = Kpart 1+ n

Kd + cF

Labeled + Unlabeled Pf-Pep

Uptake of Pf-pep Measured at pH 7

0

21

Non-Equil Transport into and across tissue of “125I-Pf-pep” = (Arg-Tyr-Lys-Arg-Thr)

No Lag due to Binding!


22


(Byun+, 2010)

• small (760 Da)• basic (pI ~ 11)

“Pf-pep” = Arg-Tyr-Lys-Arg-Thr

Donnan partitioning experiment

1/Z

Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.Source: Byun, Sangwon et al. "Transport and equilibrium uptake of a peptide inhibitor of PACE4 into articular cartilage is dominated by electrostatic interactions." Archives of Biochemistry and Biophysics 499, no. 1 (2010): 32-39.

23

http://www.sciencedirect.comhttp://dx.doi.org/10.1016/j.abb.2010.04.019http://dx.doi.org/10.1016/j.abb.2010.04.019

Annals Rheumatic Diseases, 2012

PACE4 = a “pro-protein convertase”….activates matrix metalloproteases and ADAMTS-family proteases

24


matrix


(1)

(2)

(3)

(4)

(5)

(6)

TOT


Non-Equilibrium

=0

25

Biophysical J 2013

ABSTRACT: The mucus barrier is a glycoprotein gel that coats all wet surfaces in the human body, including the respiratory, gastrointestinal, and urogenital tracts.• Criteria that govern transport through

mucus barrier are unknown.• Charge distribution of solutes is a

critical parameter to modulatetransport through mucin-basedbarriers: implications for drugdelivery

• Ionic strength within the mucinbarrier strongly influences transportspecificity

COO−SO3−

lots of...

Gastric mucin glycoprotein (MUC5AC 641 kDa)

© Royal Society of Chemistry. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.Source: Li, Leon et al. "A microfluidic in vitro system for the quantitative study of the stomach mucus barrier function." Lab on a Chip 12, no. 20 (2012): 4071-4079.

© source unknown. All rights reserved. This content is excluded from our Creative Commons license. For moreinformation, see http://ocw.mit.edu/help/faq-fair-use/.

26

http://ocw.mit.edu/help/faq-fair-use/http://dx.doi.org/10.1039/C2LC40161Dhttp://dx.doi.org/10.1039/C2LC40161Dhttp://ocw.mit.edu/help/faq-fair-use/

Fig. 1 Microfluidic device enables mucin barrier formation on-chip. (a) A mucin sample initially filling

both the flow and mucin channels (step 1, top-down view) is shaped into a layer of fixed width between a buffer flow and a microfluidic valve inside the mucin channel (step 2). Fluorescent peptides flushed into the device arrive at the mucin barrier surface and transport into the mucin barrier over time. (step 3)

(b) Formation and stability of the mucin barrier on-chip is assessed using fluorescently labeled mucins, showing that the mucin barrier surface interface is stable over time.

(c) Mucins are gradually lost from the mucin barrier over time, likely due to surface fluid shearing. We limit the duration of permeability measurements to 10 min to ensure that a majority of the initial mucin quantity remains inside the mucin barrier during the experiment. n = 3 devices.


27

http://dx.doi.org/10.1016/j.bpj.2013.07.050http://dx.doi.org/10.1016/j.bpj.2013.07.050http://www.sciencedirect.com

Peptide Solutes containing 20 amino acids:• K = lysine (10, +)• E = glutamic acid (10, -)• A = alanine (10, neutral)

Fluorescein tag net charge = -1

̶̶

̶̶

̶̶

̶̶

28

+ ̶with with

no no

0.5% mucin in 20 mM NaCl / 20mM HEPES; peptides at 4 µM

t=0

1 min

2 min

2 min

no mucin

(no mucin controls)Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.Source: Li, Leon D. et al. "Spatial configuration and composition of charge modulates transport into a mucin hydrogel barrier." Biophysical Journal 105, no. 6 (2013): 1357-1365.

29


With mucin (20 mM ionic strength)

Mucin-free buffer (20 mM ionic strength)

t = 10 min

(mucin-free)

(with mucin)


30

http://dx.doi.org/10.1016/j.bpj.2013.07.050http://dx.doi.org/10.1016/j.bpj.2013.07.050http://www.sciencedirect.com

The ionic strength of the mucin barrier can regulate its selective properties. • Increasing ionic strength within

the mucin barrier significantly increases penetration and transport of the cationic (9-fold increase in accumulation from 5 to 200 mM ionic strength), but only marginally increases transport of the anionic peptide

5 mM 20 mM 200 mM

+ pep

- pep

Effects of Ionic Strength: shields

electrostatic binding interactions

t = 10 min


31


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Documents

Lecture, Reading & PSets - MIT OpenCourseWare...Source: Li, Leon D. et al. "Spatial configuration and composition of charge modulates transport into a mucin hydrogel barrier." Biophysical