# Step-by-Step Solution We are to find the **maximal enhancement (facilitation)** for diffusive transport of CO₂ via binding with myoglobin, using the provided parameters. Then, compare it to O₂ transport under similar conditions. ## Step 1: Write the Facilitation Expression The *facilitation factor* (maximal enhancement) for gas transport due to reversible binding is (according to classic diffusion-reaction theory): \[ \text{Facilitation factor} = 1 + \frac{D_s [Mb] k_+}{D k_-} \] where - \( D \): Diffusion coefficient of free CO₂ - \( D_s \): Diffusion coefficient of myoglobin-CO₂ complex - \( [Mb] \): Myoglobin concentration - \( k_+ \): Association (binding) rate constant - \( k_- \): Dissociation (unbinding) rate constant ## Step 2: List the Given Values From your question, we interpret: - \( [Mb] = 1.2 \times 10^{-5} \) M (assuming typo, not "1.2x10"; units must match) - \( D_s = 2.1 \times 10^{-6} \) cm²/s (assuming "2.1 x 10-5" is a typo, as typical protein diffusion is ~10⁻⁶ cm²/s) - \( D = 1.7 \times 10^{-5} \) cm²/s (assumed for free CO₂, consistent with small molecule diffusion) - \( k_+ = 3 \times 10^8 \) M⁻¹s⁻¹ - \( k_- = 1.7 \) s⁻¹ ## Step 3: Plug in the Values First, calculate \( D_s [Mb] k_+ \): \[ D_s [Mb] k_+ = (2.1 \times 10^{-6}) \times (1.2 \times 10^{-5}) \times (3 \times 10^{8}) \] \[ = 2.1 \times 1.2 \times 3 \times 10^{-6 -5 + 8} \] \[ = 7.56 \times 10^{-3} \] Now, calculate \( D k_- \): \[ D k_- = (1.7 \times 10^{-5}) \times 1.7 = 2.89 \times 10^{-5} \] So, \[ \frac{D_s [Mb] k_+}{D k_-} = \frac{7.56 \times 10^{-3}}{2.89 \times 10^{-5}} \approx 261.6 \] Add 1 for the facilitation factor: \[ \text{Facilitation factor} = 1 + 261.6 = 262.6 \] ## Step 4: Final Answer for CO₂ The **maximal enhancement** for diffusive transport of CO₂ via binding with myoglobin, under the given conditions, is **about 263-fold**. ## Step 5: Comparison with Oxygen Oxygen (O₂) transport is usually facilitated by myoglobin to a similar or often higher degree, but the rate constants and binding affinities differ. For O₂, the association and dissociation rates are typically higher, and myoglobin binds O₂ more strongly than CO₂. However, at similar myoglobin concentrations and under optimal physiological conditions, the maximal facilitation for O₂ is often in the range of 200–400 fold. Thus, under **similar concentration levels** and using typical values, **CO₂ and O₂ both experience significant transport facilitation** (hundreds-fold) by myoglobin, with O₂ potentially having a slightly higher maximal facilitation due to its more favorable binding kinetics. --- **Summary:** The maximal enhancement for CO₂ transport via myoglobin, given the parameters, is about **263-fold**. This is comparable to oxygen facilitation at similar conditions, which may be slightly higher depending on the exact kinetic rates.