Modulation of Asymmetric Flux in Heterotypic Gap Junctions by Pore Shape, Particle Size and Charge

Abstract

Gap junction channels play a vital role in intercellular communication by connecting cytoplasm of adjoined cells through arrays of channel-pores formed at the common membrane junction. Their structure and properties vary depending on the connexin isoform(s) involved in forming the full gap junction channel. Lack of information on the molecular structure of gap junction channels has limited the development of computational tools for single channel studies. Currently, we rely on cumbersome experimental techniques that have limited capabilities. We have earlier reported a simplified Brownian dynamics gap junction pore model and demonstrated that variations in pore shape at the single channel level can explain some of the differences in permeability of heterotypic channels observed in in vitro experiments. Based on this computational model, we designed simulations to study the influence of pore shape, particle size and charge in homotypic and heterotypic pores. We simulated dye diffusion under whole cell voltage clamping. Our simulation studies with pore shape variations revealed a pore shape with maximal flux asymmetry in a heterotypic pore. We identified pore shape profiles that match the in silico flux asymmetry results to the in vitro results of homotypic and heterotypic gap junction formed out of Cx43 and Cx45. Our simulation results indicate that the channel's pore-shape established flux asymmetry and that flux asymmetry is primarily regulated by the sizes of the conical and/or cylindrical mouths at each end of the pore. Within the set range of particle size and charge, flux asymmetry was found to be independent of particle size and directly proportional to charge magnitude. While particle charge was vital to creating flux asymmetry, charge magnitude only scaled the observed flux asymmetry. Our studies identified the key factors that help predict asymmetry. Finally, we suggest the role of such flux asymmetry in creating concentration imbalances of messenger molecules in cardiomyocytes. We also assess the potency of fibroblasts in aggravating such imbalances through Cx43-Cx45 heterotypic channels in fibrotic heart tissue.

Keywords: Brownian dynamics; diffusion simulation; heterotypic gap junctions; intercellular communication; mathematical modeling; permeability.

Figure 1

In vitro and in silico experiment designs with homotypic and heterotypic gap junction pores. (A–D) Basic setup for in vitro dye diffusion experiments under double whole cell voltage clamp with homotypic (A) Cx43 and (B) Cx45 gap junction pores and (C,D) heterotypic Cx43-Cx45 gap junction pores with LY (yellow arrow) injected from (C) Cx43 side and (D) Cx45 side. Voltage pulses of 10 mV/200 ms/1 s were applied and LY dye diffusion was recorded across the gap junction. (E,F) Simulation experiment design for single (E) homotypic and (F) heterotypic gap junction pore. The cell-pore-cell system was divided in 5 sections: (1) cell 1, (2) left mouth, (3) vestibule (4), right mouth, and (5) cell 2.

Figure 2

Properties of heterotypic pores with varying outer mouth size of conical section (R₁-9.2-9.2-9.2). (A) LY fluxes and flux ratios simulated with constant concentration gradient of 2LY + 4Cs in cone to cylinder (blue bars) and cylinder to cone (orange bars) directions. The difference between J_het,₁ and J_het,₂ increased with larger conical mouth size. LY flux asymmetry increased with increasing outer mouth size of the conical section. (B,C) P_dX profiles in simulation (B) cone to cylinder direction and (C) cylinder to cone direction. (D–F) Average force per LY particle in (D) left mouth, (E) vestibule, and (F) right mouth. F_X was in the -x direction in all sections of the pore. (D) F_X magnitudes in the left mouth in either direction were almost equal for different pore mouth sizes. (E) F_X magnitudes in the vestibule rose in the cone to cylinder direction with increase in R₁. (F) The right mouth had high differences in F_X magnitudes between the two directions with F_X magnitude dropping with increasing R₁ in the cylinder to cone direction.

Figure 3

Properties of heterotypic pores with varying inner mouth size of conical section (22.5-R₂-9.2-9.2). (A) LY fluxes rose in both directions with increasing inner mouth size (only R₂). Differences between J_het,₁ and J_het,₂ vary amongst the different cases. LY flux ratio variations appeared to be multimodal with increasing R₂ with maximum flux asymmetry at R₂ = 9.2 Å and 11.2 Å. (B) P_dX in cone to cylinder direction dropped near R₂ and maintained almost a uniform difference amongst the different inner pore mouth sizes. (C) P_dX in the cylinder to cone direction decreased in the left mouth and vestibule with increasing R₂. This tendency flipped by the end of the vestibule with P_dX levels increased with increase in R₂ in the right mouth. (D–F) Average force per LY particle in (D) left mouth, (E) vestibule, and (F) right mouth. (D) Increase in R₂ caused F_X magnitudes (-x direction) in the left mouth to gently decrease in the cone to cylinder direction, and gently rise in the cylinder to cone direction. (E) In the vestibule, F_X increased in the cone to cylinder direction, while decreased in the cylinder to cone direction with increase in R₂. (F) F_X magnitudes in the cone to cylinder direction were negative and varied randomly in the right mouth.

Figure 4

Properties of heterotypic pores with varying cylindrical mouth size (22.5-9.2-R₃-R₃). (A) LY fluxes increased in both directions as the cylinder section was widened. LY flux ratio rose and then dropped with increasing cylinder mouth size with maximal at R₃ = 8.2 Å. (B) P_dX levels remained in the same order up to the mouth of the vestibule in cone to cylinder direction for the different cylinder mouth sizes. Probability profiles almost ran parallel from there on for all cases with probability levels proportional to R₃. (C) P_dX levels dropped at the beginning of the cylindrical mouth (left mouth) and mimicked the pore profile up to the vestibule, after which they gently rose. Profiles for different cylinder sizes ran almost parallel. (D–F) Average force per LY particle in (D) left mouth, (E) vestibule, and (F) right mouth. (E) In the cone to cylinder direction, F_X in the left mouth was marginally affected by increase in the cylinder mouth size. In the cylinder to cone direction though, F_X dropped as the cylindrical mouth was widened. (E) In the vestibule, F_X gently dropped in the cone to cylinder direction while rising in the cylinder to cone direction with widening cylindrical mouth. (F) F_X magnitudes in the right mouth were larger in the cone to cylinder than cylinder to cone direction with magnitude dropping with increasing R₃. F_X was negative for all but R₃ = 6.2 Å.

Figure 5

Properties of heterotypic pores with wide conical mouth and varying cylindrical mouth size (25.9-12.2-R₃-R₃). (A) LY fluxes rose in both directions with increasing cylinder size. Fluxes in cone to cylinder direction were smaller than in cylinder to cone direction for all cylindrical section sizes. LY flux ratios varied nonlinearly with cylinder mouth size with maximal at R₃ = 8.2 Å. (B,C) P_dX profiles in simulations with concentration gradient in (B) cone to cylinder and (C) cylinder to cone direction. P_dX profile variations were similar to those seen in the 22.5-9.2-R₃-R₃ simulations. (D–F) Average force per LY particle in (D) left mouth, (E) vestibule, and (F) right mouth. F_X in the left mouth and vestibule in the cone to cylinder direction simulations remained constant with increasing cylinder size. In the left mouth (D), F_X magnitude in cylinder to cone direction varied nonlinearly with a maximal at R₃ = 7.2 Å. (F) F_X magnitudes in the right mouth were larger in the cone to cylinder than cylinder to cone direction with magnitude dropping with increasing R₃. F_X was negative for all but R₃ = 6.2 Å.

Figure 6

Role of particle size on flux asymmetry in heterotypic pores. Simulation results in heterotypic pore with profile 25.9-12.2-8.2-8.2 with constant concentration gradient, 2 mV transjunctional voltage and q_p = 2e⁻. (A) Particle fluxes dropped nonlinearly as particle radius was increased from 0.8 to 6.6 Å. Flux ratio values (gray bars) ranged from ~0.5 to 0.8. Maximum asymmetry of 0.51 was for particle size of 4.9 Å. (B,C) P_dX levels remain in the same order in cell 1. P_dX profiles were similar to the pore profiles (log 10 scale). (D–H) F_X in the different sections of the cell-pore-cell system. (D) F_X values in cell 1 were marginal compared to other sections. In general, F_X magnitudes dropped in all sections of the pore with increasing particle size. (E) In the left mouth, F_X dropped with increasing particle sizes with F_X in cylinder to cone direction were higher than the cone to cylinder direction for all cases. F_X for r_p = 6 Å in the cylinder to cone direction was unexpectedly high. (F,G) In the vestibule and right mouth, F_X was negative and distinctly higher in the cone to cylinder direction than in the cylinder to cone direction. (H) F_X magnitudes in cell 2 were larger in the cylinder to cone direction in all cases.

Figure 7

Role of particle charge on flux asymmetry in heterotypic pores. Simulation results in heterotypic pore with profile 25.9-12.2-8.2-8.2 with constant concentration gradient, 2 mV transjunctional voltage and r_p = 4.9 Å. (A) Particle fluxes decreased with increasing particle charge. Flux ratio (gray bars) also rose up to q_p = 2e⁻. (B,C) The P_dX profiles were similar in shape but scaled down for high particle charge. (D–H) F_X variation patterns for different q_p were similar in the different sections, but the differences between the 2 directions were magnified with increasing q_p. (D) F_X magnitudes in cell 1 were marginal compared to F_X in other sections. (E) In the left mouth, F_X was negative in cylinder to cone direction and larger in magnitude. (F–G) In the vestibule and right mouth, F_X were larger in the cone to cylinder direction. (H) F_X in cell 2 were small and differences amongst the two directions were marginal.