Biophysical regulation of lipid biosynthesis in the plasma membrane

Abstract

We present a cellular model of lipid biosynthesis in the plasma membrane that couples biochemical and biophysical features of the enzymatic network of the cell-wall-less Mycoplasma Acholeplasma laidlawii. In particular, we formulate how the stored elastic energy of the lipid bilayer can modify the activity of curvature-sensitive enzymes through the binding of amphipathic alpha-helices. As the binding depends on lipid composition, this results in a biophysical feedback mechanism for the regulation of the stored elastic energy. The model shows that the presence of feedback increases the robustness of the steady state of the system, in the sense that biologically inviable nonbilayer states are less likely. We also show that the biophysical and biochemical features of the network have implications as to which enzymes are most efficient at implementing the regulation. The network imposes restrictions on the steady-state balance between bilayer and nonbilayer lipids and on the concentrations of particular lipids. Finally, we consider the influence of the length of the amphipathic alpha-helix on the efficacy of the feedback and propose experimental measurements and extensions of the modeling framework.

FIGURE 1

Forces that act between lipids at different depths include electrostatic and hydrogen bond interactions at the headgroup, interfacial tension at the hydrophilic-hydrophobic interface, and the packing of the hydrocarbon chains. The lateral pressure profile π(z) depends crucially on the chemical nature of the lipid head group and the length and saturation of the lipid hydrocarbon chains. The lateral pressure profile determines the spontaneous curvature J_s of a lipid monolayer (14).

FIGURE 2

A. laidlawii lipid biosynthetic network. (A) The biochemical network. The main lipids in the plasma membrane of A. laidlawii A-EF22 are (6): phosphatidylglycerol (PG), diacylglycerol (DAG), monoglucosyl-DAG (MGlcDAG), diglucosyl-DAG (DGlcDAG), and glycerophosphoryl-DGlcDAG (GPDGlcDAG). Phosphatidic acid (PA), the liponuleotide CDP-DAG, and PG-phosphate (PGP) are lipid intermediates. The top branch is the PG pathway and the bottom branch is the glucolipid pathway. The abbreviated soluble reactants are glucose (Glc) and UDP-Glc, glycerol-3-phosphate (G3P), the inorganic phosphate ions P_i and PP_i, and the nucleotide CTP. R indicates an acyl chain. Six of the seven enzymes have irreversible rate equations. A. laidlawii also synthesizes three monoacyl derivatives of the glucolipids: monoacyl-MGlcDAG (MAMGlcDAG), monoacyl-DGlcDAG (MADGlcDAG), and monoacyl-bisglycerophosphoryl-DGlcDAG (MABGPDGlcDAG) (6). However, these lipids have been excluded from the model as they are not always synthesized (5) and their biosynthetic pathways have been postulated, but are not known (59). (B) A biophysical picture of the network. Lipids are color coded according to their J_s, which is linked to their molecular shape as shown. The same color code is used to show that the activity of MGS and DGS increases when the plasma membrane has a large negative It can be seen, for instance, that in the case of the lower pathway the effect of MGS and DGS is to increase the effective size of the headgroup of the lipid upon which they are acting and therefore systematically increase the value of J_s among DAG, MGlcDAG, and DGlcDAG. By controlling the rate of the steps between DAG/MGlcDAG and MGlcDAG/DGlcDAG, the system is capable of regulating A. laidlawii also synthesizes three monoacyl-derivatives of the glucolipids: monoacyl-MGlcDAG (MAMGlcDAG), monoacyl-DGlcDAG (MADGlcDAG), and monoacyl-bisglycerophosphoryl-DGlcDAG (MABGPDGlcDAG) (6). However, these lipids have been excluded from the model as they are not always synthesized (5) and their biosynthetic pathways have been postulated, but are not known (59).

FIGURE 3

(A) Geometric argument used to calculate c_bound, the curvature of a lipid monolayer consisting entirely of lipids that lie alongside an amphipathic α-helix. (B) Association constant K_a as a function of for a 19-residue α-helix (dark solid line) and, for a 58-residue α-helix, such as that of CCT, plotted for comparison (dark dashed line). The dashed vertical line is J_s = −1/6 nm⁻¹ and the solid vertical lines give the measured range of of lipid extracts (5). (Inset) Helical-wheel projection of residues 67–85 of MGS. The bar gives the Eisenberg consensus normalized hydrophobicity scale (76).

FIGURE 4

(A) Histogram of the distribution P_MGS() of the steady-state for a sampling of 10⁶ random parameter sets, where V_cell,MGS is fixed and the other six V_cell,Enzyme values are varied. k is defined in Eq. 10 and measures the logarithmic variation of the parameter set. The individual V_cell,Enzyme distribution used (solid, top inset) ensures that the logarithmic variation k is sampled uniformly (solid, bottom inset). If uniform individual V_cell,Enzyme distributions were used (dashed, top inset), then k would approach a Gaussian distribution (dashed, bottom inset). (B) Marginal probability distributions P_Enzyme() of all seven enzymes, where one V_cell,Enzyme is fixed, whereas the other six V_cell,Enzyme are varied. The dashed vertical line indicates the critical value below which bilayers do not form. (C) Cumulative probability that the steady state will be viable () against the logarithmic variation k of the state.

FIGURE 5

(A) Effect of the biophysical feedback on the control of the steady-state The four marginal distributions P(), obtained from 10⁶ random parameter sets in which all seven enzyme rates V_cell,Enzyme are varied, show a reduction of the probability of inviable states with < −1/6 nm⁻¹. In the absence of feedback, we fix K_a,MGS at the reference value of K_a,MGS () shown in Fig. 3 B (×). MGS is modeled to have a 19-residue α-helix (□), DGS is modeled with a 19-residue α-helix (○), both MGS and DGS are modeled with 19-residue α-helices (▵). (B) The cumulative probability that the steady state forms a bilayer () as a function of the logarithmic variation k.

FIGURE 6

Histogram of the distribution of steady-states L*, showing the probability distribution of and the distance of L* to the experimental concentration L_exp. The data are obtained by sampling 10⁶ random parameter sets as in Fig. 5. (A) Distribution in the absence of feedback. The vertical dashed line at separates the nonbilayer and bilayer fractions. The dashed lines correspond to the steady-state that results from adding a particular lipid to L_exp until one reaches a monocomponent state, marked by crosses. (B) Distribution when both MGS and DGS exert biophysical feedback through a 19-residue amphipathic α-helix.

FIGURE 7

Effect of amphipathic α-helix length on steady-state Shown are three marginal distributions P() of the steady-state under uncertain parameters where both MGS and DGS are curvature sensitive with amphipathic α-helices of different lengths: 19-residue (blue, same as Fig. 5 A), 57-residue (green), and 114-residue (red). Vertical dashed line at indicates the nonbilayer region. (Inset) Probability that the steady state does not form a bilayer against α-helix length, when MGS has an α-helix (×); DGS has an α-helix (+); and MGS and DGS both have α-helices (□). Colored squares correspond to the three plotted P() in the main figure.