Enzyme clustering accelerates processing of intermediates through metabolic channeling

Abstract

We present a quantitative model to demonstrate that coclustering multiple enzymes into compact agglomerates accelerates the processing of intermediates, yielding the same efficiency benefits as direct channeling, a well-known mechanism in which enzymes are funneled between enzyme active sites through a physical tunnel. The model predicts the separation and size of coclusters that maximize metabolic efficiency, and this prediction is in agreement with previously reported spacings between coclusters in mammalian cells. For direct validation, we study a metabolic branch point in Escherichia coli and experimentally confirm the model prediction that enzyme agglomerates can accelerate the processing of a shared intermediate by one branch, and thus regulate steady-state flux division. Our studies establish a quantitative framework to understand coclustering-mediated metabolic channeling and its application to both efficiency improvement and metabolic regulation.

Figure 1

Different types of intermediate channeling in a two-step metabolic pathway, where a substrate is processed by enzyme E₁ and turned into intermediate, which is then processed by enzyme E₂ and turned into product. (a) Direct channeling. The intermediate is funneled from enzyme E₁ to enzyme E₂ by means of a protein tunnel that connects the active sites of E₁ and E₂, thus preventing the intermediate from diffusing away. (b) Proximity channeling. Top: E₁ and E₂ are positioned near enough to each other such that the intermediate produced by E₁ is processed by E₂ before it can escape by diffusion, even in the absence of an actual channel. Bottom: if E₁ and E₂ are not near enough to each other, an intermediate molecule produced by E₁ escapes by diffusion, and it cannot be processed by E₂. (c) Enzyme clustering. Once E₁ produces an intermediate molecule, even though the probability of the intermediate being processed by any individual E₂ enzyme is low, the probability that the intermediate will be processed by one of the many E₂ enzymes in the agglomerate can be high.

Figure 2

Two-step metabolic pathway with an unstable intermediate. (a) The two-step metabolic pathway. Substrate S₀ is processed by enzyme E₁ and turned into intermediate S₁, which is then processed by enzyme E₂ and turned into product P. (b) Enzyme configurations in the two-step metabolic pathway. Left: the cell cytoplasm is divided into multiple identical basins, each basin is represented by a dashed circle. Within each basin, enzymes are clustered into a central spherical agglomerate (shown in green). Right: blow-up showing the dynamics of the metabolic pathway within an agglomerate with radius r^*. Substrate S₀, which is produced throughout the cytoplasm, is processed by E₁ and turned into S₁, which is then processed by E₂. Both S₀ and S₁ may escape from the agglomerate by diffusion. (c) Metabolic pathway efficiency ε and efficiencies of the first and second step ε₁, ε₂ as functions of basin radius R. For each R, efficiency is optimized over enzyme densities n₁(r),n₂(r), which are assumed to be spherically symmetric. Local enzyme density is constrained by n₁(r) + n₂(r)≤n_max, and the total catalytic activity is fixed to κ_cat. The efficiencies of the first and second step ε₁, ε₂ are a decreasing and an increasing function of R respectively. Hence, the optimal efficiency is obtained as a tradeoff between ε₁ and ε₂, and is equal to ε_opt = 0.53 at R_opt = 6.5 μm. Except where noted, k₁ = k₂ and parameter values are the same for all figures. The optimal efficiency ε_opt = 0.53 is about 5.9 times larger than the efficiency ε_delocalized = 0.09 of a delocalized configuration where enzymes are uniformly distributed in space. (d) Optimal distributions of enzymes E₁,E₂ and corresponding concentrations of substrate S₀ and intermediate S₁ as functions of r/R, where the optimal basin radius (i.e., half the optimal spacing between clusters) is R = R_opt = 6.5 μm from b. The local enzyme density n₁(r) + n₂(r) and its maximal value n_max are also shown. The optimal enzyme distribution is a compact cluster with radius r^* ≈ 0.26 μm composed of a shell of E₁ and E₂ surrounded by a halo of E₂. Inset: concentrations of substrate S₀ and intermediate S₁ as functions of r/R in the entire basin.

Figure 3

Two-step metabolic pathway with an unstable intermediate for uniform enzyme spheres with equal density. (a) Metabolic pathway efficiency for uniform enzyme spheres of enzymes E₁ and E₂ with N₁ = N₂ compared to the optimal case from Figure 2c, and efficiencies of the first and second step of the pathway for uniform enzyme spheres as functions of basin radius R. For each R, efficiency is optimized over enzyme densities n₁(r),n₂(r), which are assumed to be spherically symmetric. Local enzyme density is constrained by n₁(r) + n₂(r)≤n_max, and the total catalytic activity is fixed to κ_cat. The optimal efficiency and radius for uniform enzyme spheres are ${\epsilon }_{\text{opt}}^{\text{spheres}}=0.50$ and $R_{\text{opt}}^{\text{spheres}}=6.15\mathrm{\mu }\mathrm{m}$, close to the values ε_opt = 0.53 and R_opt = 6.5 μm obtained for the fully optimized case. (b) Optimal distributions of enzymes E₁,E₂ and corresponding concentrations of substrate S₀ and intermediate S₁ for uniform enzyme spheres of enzymes E₁ and E₂ as functions of r/R, where the basin radius is $R=R_{\text{opt}}^{\text{spheres}}=6.15\mathrm{\mu }\mathrm{m}$ from a. The local enzyme density n₁(r) + n₂(r) and its maximal value n_max are also shown. The optimal enzyme distribution is a compact cluster with radius r^* ≈ 0.25 μm composed of a sphere uniformly filled with enzymes E₁ and E₂. Inset: concentrations of substrate S₀ and intermediate S₁ as functions of r/R in the entire basin region.

Figure 4

Metabolic pathway with a branch point, in E. coli. (a) The arginine/pyrimidine branch point in E. coli. CarB (with CarA, not shown) synthesizes carbamoyl phosphate, which can be committed towards arginine biosynthesis by ArgI or towards pyrimidine (e.g., uracil, UMP) synthesis by PyrB. For our experiments we fused CarB to PyrB (CarB-PyrB). Ornithine and aspartate are, respectively, arginine-specific and pyrimidine-specific biosynthetic reactants upstream of the branch point. (b) (left) Expression of CarB-PyrB at the low level characteristic of the endogenous carB gene does not produce phase-bright foci and (right) does not generate arginine pseudoauxotrophy. Cell density is plotted versus time in minimal conditions, in the presence of additional arginine, additional uracil, and both additional arginine and additional uracil (scale bar, 5 μm). Optical densities plotted are the mean ± s.e.m. (N_replicates = 6). (c) (left) High-level expression of CarB-PyrB induces the formation of phase-bright foci, indicated by arrows, and (right) causes arginine pseudoauxotrophy. The same quantities as in b are plotted (scale bar, 5 μm, N_replicates = 12). (d) The arginine pseudoauxotrophy results from metabolite shunting. Metabolomic analysis reveals that high-level CarB-PyrB expression causes the pyrimidine pathway pools to increase whereas the arginine pathway pools decrease downstream of ArgI but increase upstream of ArgI. Relative metabolite levels are the mean ± s.e.m. (e) Two-step metabolic pathway with a branch point. Substrate S₀ is processed by enzyme E₁ and turned into substrate S₁. Substrate S₁ is then processed by either enzyme E_A or E_B and turned into product P_A or P_B, respectively. (f) Schematics of the spatial distributions of enzymes E₁,E_A,E_B in the colocalized case. E₁ and E_B are uniformly distributed in a compact sphere of radius r₁ = r_B ≡ r* ≤ r_A, whereas E_A is uniformly distributed in a larger sphere with the typical radius of an E. coli cell r_A = R = 0.79 μm, we set N₁ = N_B, and the combined density of E₁ and E_B is set at the dense-packing limit n_max = 25 mM. (g) Efficiency fractions x_A = ε_A/(ε_A + ε_B),x_B = ε_B/(ε_A + ε_B) of the two branches of the pathway as functions of the fraction N_B/(N_A + N_B) of enzyme E_B, for the colocalized case in f and for the delocalized case where E₁,E_A and E_B are uniformly distributed in a sphere of radius r_A = R = 0.79 μm. In both cases the number of E_A molecules is fixed to N_A = 2,000 enzymes, and the catalytic constants for E₁,E_A,E_B, that is, the values of k_cat/K_M for CarB, ArgI and PyrB, respectively, are k₁ =5.3 ×10⁴ liter/s/mol (ref. 35), k_A = 4.3 ×10⁷ liter/s/mol (ref. 36), k_B = 4.8 × 10⁷ liter/s/mol (refs. 30,37). Other parameters are as given in Online Methods: Model parameters.

Figure 5

Phase-bright clusters and arginine pseudoauxotrophy increase with increasing CarB-PyrB overexpression. (a) Cell density with inducible CarB-PyrB expression as a function of time for different levels of anhydrotetracyline (aTc) inducer concentration and in different media: in minimal conditions, in the presence of additional arginine, additional uracil and both additional arginine, and additional uracil. Mean of N_replicates = 4 plotted. (b,c) Phase images (b) (scale bars, 5 μm) and quantification (c) of phase-bright foci as functions of aTc inducer concentration. Number of phase-bright spots per cell followed an exponential distribution. Mean and 95% confidence intervals are shown as the s.e.m. (N_{0 nM} = 760, N_{0.5 nM} = 632, N_{5 nM} = 317).

Figure 6

Ratio between the efficiency ε_A in the colocalized case and the efficiency ε_A in the delocalized case as a function of the fraction N_B/(N_A +N_B ) of enzyme E_B for the two-step metabolic pathway with a branch point for the same geometry and parameters as in Figure 4.