Quantitative Model for Ion Transport and Cytoplasm Conductivity of Chinese Hamster Ovary Cells

Abstract

In mammalian cells cytoplasm ion concentrations and hence cytoplasm conductivity is an important indicator of their physiological state. Changes in the cytoplasm conductivity has been associated with physiological changes such as progression of cancer and apoptosis. In this work, a model that predicts the effects of physiological changes in ion transport on the cytoplasm conductivity of Chinese hamster ovary (CHO) cells is demonstrated. We determined CHO-specific model parameters, Na⁺/K⁺ ATPase pumps and ion channels densities, using a flux assay approach. The obtained sodium (P_Na), potassium (P_K) and chloride (P_Cl) permeability and Na⁺/K⁺ ATPase pump density were estimated to be 5.6 × 10^-8 cm/s, 5.6 × 10^-8 cm/s, 3.2 × 10^-7 cm/s and 2.56 × 10^-11 mol/cm², respectively. The model was tested by comparing the model predictions with the experimentally determined temporal changes in the cytoplasm conductivity of Na⁺/K⁺ ATPase pump inhibited CHO cells. Cells' Na⁺/K⁺ ATPase pumps were inhibited using 5 mM Ouabain and the temporal behavior of their cytoplasm conductivity was measured using dielectrophoresis cytometry. The measured results are in close agreement with the model-calculated values. This model will provide insight on the effects of processes such as apoptosis or external media ion concentration on the cytoplasm conductivity of mammalian cells.

Figure 1

The model cell in normal condition. Its membrane contains three types of channels, Cl⁻, K⁺, and Na⁺ which mediate passive movement of these ions and Na⁺/K⁺ ATPase pumps which produce efflux Na⁺ ions and influx K⁺ ions with a 3:2 ratio. [X⁻] are the membrane impermeable anion concentration.

Figure 2

(a) Rubidium uptake by adherent CHO cells in a K⁺-free buffer over a period of two hours. (b) Percentage of Rubidium uptake by adherent CHO cells treated with various concentrations of Ouabain with respect to untreated cells in (a). Ouabain inhibits the Na⁺/K⁺ ATPase pumps. (c) Potassium and Rubidium concentration inside CHO cells in a K⁺-free buffer (0–90 min) and subsequently in a Rb⁺-free buffer (90–180 min). The error bars represent the minimum and maximum values of the ion concentrations for three repeated measurements reported by ICP-OES.

Figure 3

Simulation results of ion concentrations, membrane potential and cell volume for healthy and pump inhibited CHO cells in 1.7 S/m medium. The model is initiated with intracellular ion concentrations close to equilibrium with extracellular fluid except the chloride concentration which is lower due to the intracellular organic anions ([Na⁺]_i = 145 mM, [K⁺]_i = 12 mM, [Cl⁻]_i = 60 mM, [X⁻]_i = 83 mM). V_c is initially defined as 9 × 10⁻¹⁰ cm³. The parameters such as ion permeabilities and Na⁺/K⁺ ATPase pump density are as specified in Table 2. Ion concentrations at steady state are [Na⁺]_i = 11 mM, [K⁺]_i = 145 mM, [Cl⁻]_i = 70 mM and [X⁻]_i = 74 mM. At the point marked with dash line, after 150 minutes, the Na⁺/K⁺ ATPase pump density is reduced to zero, to simulate total Na⁺/K⁺ ATPase pump inhibition. At this time, the model is initiated with variables derived from the results of the first 150 minutes, marked with dash line, and therefore all variables are initially stable. After pump inhibition, there is a gradual depolarization as [K⁺]_i and [Na⁺]_i begin to equilibrate with the extracellular fluid. This depolarization allows [Cl⁻]_i influx and thus volume increases.

Figure 4

Simulated spectrum of the real part of the Claussius-Mossotti factor (Re {K_CM}) for a mammalian cell (Chinese hamster ovary (CHO)), with parameters from. (a) Cytoplasm conductivity varies from 0.35–0.5 S/m and medium conductivity is 0.42 S/m. (b) Cell volume varies from 5 × 10⁻¹⁰–10 × 10⁻¹⁰ cm³ and medium conductivity is 0.42 S/m.

Figure 5

(a) Mean Force Index for 0.17–0.45 S/m medium conductivities. Black stars indicate the obtained results in our previous work, red circles indicate the results obtained in this work. (b) The real part of the K_CM calculated using a double shell model versus the medium conductivity. (c) The real part of the K_CM calculated using a double shell model versus the cytoplasm conductivity. (d)The linear relation between force index and cytoplasm conductivity using (a–c) graphs.

Figure 6

Simulation and experimental results of pump inhibited CHO cells using 5 mM Ouabain. The marked lines show the estimated cytoplasm conductivity using the experimental results of three DEP measurements for 105 min. Each marker represents the average for 5 min intervals (100–150 cells). The solid line represents the simulation results of the pump inhibited CHO cells. To inhibit the pumps, pump density is set to zero.