The Pump Leak Mechanism Impermeant Molecules and Cell

The Pump Leak Mechanism, Impermeant Molecules and Cell Volume Regulation Alan R. Kay, Dept. Biology, University of Iowa Guertin & Sabatini 2005

• • • Donnan effect & osmotic challenge to cells Ion distribution and the Na+/K+ ATPase (NKA) Modeling ion and water fluxes Toy models – Double-Donnan & Post-Jolly The Pump-Leak Mechanism (PLM) Volume changes & Aquaporin Can impermeant molecules drive ion asymmetries? How do cells determine their size? Paring down models Appeal for new tools

The osmotic challenge to cells • Build a box • Bail water • Pump ions

Ion Distributions in Cells Out In Carl Schmidt 1850 4

The Na+ Pump & Resting Potential -60 m. V Na+/K+ ATPase (NKA)

The Donnan Effect

“There is no mysterious ‘energy-pump’ at work, ‘pumping’ the potassium ions against a concentration gradient. The situation is simply …”

z X • in Skeletal Muscle (m. M): 2 PO 4, 9 Mg. ATP, 34 Phosphorylcreatine, 13 creatine, 24 free amino acids, 18 taurine, 15 anserine & carnosine, 5 urea & 3 lactate Burton RF, 1983

Double Donnan Assume that the membrane is not permeable to Na+ X K Cl 144 125 6 145 150 5 146 187. 5 4 B V (m. V) 25 0 -37. 5 -82. 7 -87. 4 -93. 1 Nao, Ko & Clo = 145, 5 & 150 m. M

Post-Jolly Mechanism s M H 2 O M M H 2 O Post & Jolly 1957

The Pump-Leak Mechanism (PLM) Tosteson DC & Hoffman JF Regulation of Cell Volume by Active Cation Transport in High & Low Potassium Sheep Red Blood Cells. J Gen Physiol, 44: 169 -194, 1960

The Constraint Equation • Membranes can only sustain very small transmembrane pressures • Osmotic Balance: • Ionic Balance: Boyle & Conway, J. Physiol. 1941

The Constraint Equation Kay 2017

The Pump Leak Equations Keener & Sneyd - Mathematical Physiology vol 1

Keener & Sneyd - Mathematical Physiology vol 1

Charge Difference vs Current Sum Methods of Integration Fraser & Huang J Physiol 2004

Kay 2017

Kay 2017

Kay 2017

Linear vs non-linear NKA

Kay 2017

z=0. 5 z=-1 z=-2

Active K+ transport is not essential Kay 2017

Energetics of running the PLM Kay 2017

Kay 2017

Aquaporin

Active Water Transport

PLM can drive transient activity-dependent volume increases

Other Mechanisms for Maintaining Volume Stability Xz H+ H+ Na+ K+ K+ Cl- H 2 O Kay 2017

Neither extracellular nor intracellular impermeants can drive Cl- out of equilibrium

A Cl- binding protein cannot drive Cl- out of equilibrium

Science 2015

How is cell volume controlled? • Unlikely to be through estimation of x • Suggest that cells ‘sense’ membrane area or volume and adjusts x to control size

What Depth of Representation is Needed? Takeuchi A et al. J Gen Physiol 2006; 128: 495 -507

In Out

147 m. M Na+ , 3 m. M K+ 100 m. M Na+ , 50 m. M K+

Acknowledgments • Joseph Raimondo & Kira Düsterwald (UCT) • Yoichiro Mori