Relative Activity and Inter-System Extrapolation Factors

Why recombinant activity needs a bridge to liver systems

A recombinant enzyme assay can identify and quantify the turnover supported by a particular enzyme, but the assay system is not human liver tissue. The amount of enzyme, its catalytic activity per unit enzyme, and the surrounding system can differ. A numerical result per picomole of recombinant enzyme therefore cannot be read directly as a result per milligram of human liver microsomal protein.

Relative activity factors (RAFs) and inter-system extrapolation factors (ISEFs) provide related ways to bridge that gap. A RAF maps recombinant turnover directly to a liver-microsome basis using the activity of a marker reaction. An ISEF separates the correction for relative activity per enzyme amount from the measured abundance of that enzyme in liver microsomes. Either method can support an estimate of an enzyme's contribution, provided its assumptions are plausible and its units are handled consistently.

Definition: A relative activity factor (RAF) is the human liver microsomal activity of an enzyme-selective marker reaction per milligram of microsomal protein, divided by that same marker activity per picomole of the corresponding recombinant enzyme. With these normalizations, RAF has units of pmol enzyme-equivalent/mg microsomal protein. An inter-system extrapolation factor (ISEF) is the ratio of marker-reaction activity per picomole of enzyme in human liver microsomes to marker-reaction activity per picomole of enzyme in the recombinant system. ISEF is dimensionless.

Definitions and the link between RAF and ISEF

For a specified enzyme and marker reaction, let \(v_{\mathrm{HLM}}\) be the marker rate per milligram of human liver microsomal protein, and let \(v_{\mathrm{rec}}\) be the marker rate per picomole of recombinant enzyme. Let \(A_{\mathrm{HLM}}\) be the abundance of that enzyme in human liver microsomes, in pmol/mg. The rates must refer to the same marker reaction and be measured under conditions suitable for comparing activity.

The direct activity ratio is the RAF. To define ISEF, first express the HLM marker rate per picomole of enzyme: \(v_{\mathrm{HLM}}/A_{\mathrm{HLM}}\). Then compare that rate with \(v_{\mathrm{rec}}\). These definitions give the following identity:

\mathrm{RAF}=\frac{v_{\mathrm{HLM}}}{v_{\mathrm{rec}}} =\frac{v_{\mathrm{HLM}}/A_{\mathrm{HLM}}}{v_{\mathrm{rec}}}\,A_{\mathrm{HLM}} =\mathrm{ISEF}\times A_{\mathrm{HLM}}.

The identity is useful because the two approaches expose different components of the scaling. RAF is an empirical, direct mapping to the HLM protein basis. ISEF estimates the relative catalytic activity per enzyme amount and then uses the measured enzyme abundance to express that activity on the same HLM protein basis. The algebra does not establish that either factor transfers perfectly from a marker reaction to a drug substrate; that is a scientific assumption to assess.

Key result: If recombinant intrinsic clearance for a drug substrate is \(CL_{\mathrm{int,rec}}\) in µL/min/pmol enzyme, then its estimated HLM intrinsic clearance by the RAF approach is \(CL_{\mathrm{int,rec}}\times\mathrm{RAF}\), in µL/min/mg HLM protein. The ISEF form is \(CL_{\mathrm{int,rec}}\times\mathrm{ISEF}\times A_{\mathrm{HLM}}\), with the same resulting units.

This scaling assumes that the marker reaction is sufficiently selective for the enzyme of interest, that rates are measured in a comparable and appropriate range, and that the marker-based difference between systems is informative for the drug substrate. The ISEF calculation additionally requires a credible enzyme-abundance measurement. If more than one recombinant enzyme contributes to a drug pathway, estimate the contribution attributable to each enzyme separately before calculating any total or share.

Worked Example: Calculating a RAF and HLM Intrinsic Clearance

All values in this example are hypothetical. Suppose an enzyme-selective marker reaction has an HLM rate of 0.240 nmol/min/mg HLM protein. In a recombinant preparation, the rate is 0.600 pmol/min/pmol enzyme. The drug's recombinant intrinsic clearance is 0.0150 µL/min/pmol enzyme. Estimate RAF and the drug's HLM intrinsic clearance, assuming the marker scaling applies to the drug.

Step 1: Put the marker rates in compatible units. Since 1 nmol equals 1,000 pmol, the HLM marker rate is \(0.240\times1{,}000=240\) pmol/min/mg HLM protein.

Step 2: Calculate RAF.

\mathrm{RAF} =\frac{240\ \mathrm{pmol/min/mg}}{0.600\ \mathrm{pmol/min/pmol}} =400\ \mathrm{pmol/mg}.

The activity units cancel, leaving an enzyme-equivalent amount per milligram of HLM protein. This is not necessarily a direct measurement of enzyme abundance; it is an activity-based factor.

Step 3: Scale the drug's recombinant intrinsic clearance.

CL_{\mathrm{int,HLM}} =0.0150\ \frac{\mathrm{\mu L}}{\mathrm{min\cdot pmol}} \times400\ \frac{\mathrm{pmol}}{\mathrm{mg}} =6.00\ \frac{\mathrm{\mu L}}{\mathrm{min\cdot mg}}.

Under the stated transfer assumption, the estimated contribution is 6.00 µL/min/mg HLM protein. It is an in vitro system estimate, not a whole-liver clearance or a clinical clearance.

Using ISEF to separate activity from enzyme abundance

The ISEF approach can be informative when a measured enzyme abundance is available and the question is whether the recombinant system and HLM differ in activity per unit enzyme. The marker activities must be normalized to the amount of the relevant enzyme in each system before taking their ratio. Comparing unnormalized rates would mix differences in enzyme amount with differences in activity per enzyme molecule.

Worked Example: Calculating an ISEF-Based Estimate

All values are hypothetical. Suppose the enzyme abundance in HLM is 80.0 pmol/mg. A marker rate normalized to enzyme amount is 1.20 pmol product/min/pmol enzyme in HLM and 1.50 pmol product/min/pmol enzyme in the recombinant system. The recombinant drug intrinsic clearance is 0.0200 µL/min/pmol enzyme. Calculate ISEF and estimate the HLM contribution.

Step 1: Calculate ISEF.

\mathrm{ISEF} =\frac{1.20\ \mathrm{pmol/min/pmol}}{1.50\ \mathrm{pmol/min/pmol}} =0.800.

The marker activity per enzyme amount in HLM is 80.0% of that in the recombinant system under the assay conditions.

Step 2: Apply ISEF and abundance to the recombinant drug clearance.

CL_{\mathrm{int,HLM}} =0.0200\ \frac{\mathrm{\mu L}}{\mathrm{min\cdot pmol}} \times0.800 \times80.0\ \frac{\mathrm{pmol}}{\mathrm{mg}} =1.28\ \frac{\mathrm{\mu L}}{\mathrm{min\cdot mg}}.

The estimate is 1.28 µL/min/mg HLM protein. The equivalent RAF is \(0.800\times80.0=64.0\) pmol/mg. Thus, direct scaling gives \(0.0200\times64.0=1.28\) µL/min/mg, as required by the relationship between RAF and ISEF.

Define the target basis.
Specify whether the desired estimate is per milligram of HLM protein or on a further scaled basis. Do not mix units from different bases.

Choose the factor form.
Use RAF for a direct marker-based mapping, or calculate ISEF and multiply by enzyme abundance when the components are available and useful to distinguish.

Scale each enzyme estimate.
Multiply recombinant drug intrinsic clearance by RAF, or by ISEF and enzyme abundance. Check that the final units are µL/min/mg HLM protein.

Interpret and quality-check.
Compare enzyme-specific estimates only after checking assay comparability, marker selectivity, enzyme abundance, and the assumptions that permit transfer to the drug substrate.

Scaled contributions and pathway shares

When recombinant data are available for multiple enzymes, scaling each estimate to the same HLM protein basis makes their contributions comparable. For a specified pathway, the contribution assigned to each enzyme is its scaled intrinsic clearance. If the estimates describe distinct, additive routes under the assay conditions, their sum is the estimated total for those routes; the share assigned to one enzyme is its contribution divided by that sum. This calculation describes the estimates supplied to it and does not by itself prove that all relevant routes have been measured.

Worked Example: Comparing Scaled Enzyme Contributions

All data are hypothetical. Suppose three enzymes are assigned to a drug's metabolism, with the following recombinant intrinsic clearances and RAFs: enzyme A, 0.0250 µL/min/pmol and 60.0 pmol/mg; enzyme B, 0.0120 µL/min/pmol and 150 pmol/mg; enzyme C, 0.00400 µL/min/pmol and 50.0 pmol/mg. Assume the RAF for each enzyme is appropriate for this drug's turnover through that enzyme, and the three estimates represent distinct additive routes.

Step 1: Scale each estimate.

\begin{aligned} CL_{\mathrm{int,A}} &= 0.0250\times60.0=1.50\ \mathrm{\mu L/min/mg},\\ CL_{\mathrm{int,B}} &= 0.0120\times150=1.80\ \mathrm{\mu L/min/mg},\\ CL_{\mathrm{int,C}} &= 0.00400\times50.0=0.200\ \mathrm{\mu L/min/mg}. \end{aligned}

Step 2: Sum the estimated contributions. The total for these three specified routes is \(1.50+1.80+0.200=3.50\) µL/min/mg HLM protein.

Step 3: Calculate each route's share. For enzyme A, \(1.50/3.50=0.429\), or 42.9%. For enzyme B, \(1.80/3.50=0.514\), or 51.4%. For enzyme C, \(0.200/3.50=0.0571\), or 5.71%. The rounded shares sum to approximately 100.0%.

These are conditional shares of the estimated total for the three specified routes. If the factors are biased, an enzyme is omitted, or routes are not represented as assumed, the shares may not represent the true biological distribution of metabolism.

Assumptions, diagnostics, and alternatives

The main diagnostic question is whether the factor captures a difference between systems that is relevant to the drug substrate. Review how the marker was selected and whether it is selective for the enzyme being scaled. Check that marker rates are reproducible and comparable in the two systems, that enzyme abundance refers to the relevant HLM preparation, and that the resulting factor and scaled clearance have coherent units. Implausibly large or small factors warrant investigation rather than automatic acceptance.

Nonselective marker activity: if multiple enzymes materially produce the marker product, the rate ratio may not isolate the enzyme of interest. A different marker or a more specific experimental design may be needed.
Unmatched assay conditions: differences in incubation conditions, enzyme preparation, or rate normalization can be mistaken for inter-system activity differences. Comparisons require documented, suitable conditions.
Questionable transfer to the drug: a marker and a drug substrate can respond differently to the system. A factor is not a universal property of an enzyme that guarantees accurate scaling for every substrate.
Inconsistent normalization: using a rate per milligram in one system and a rate per enzyme amount in the other produces a ratio with the wrong meaning. Recheck both the denominator basis and the final units.
Overinterpreting a pathway share: shares are conditional on the included scaled contributions and their assumptions. They are not direct observations of in vivo fractions unless further evidence supports that interpretation.

RAF and ISEF are not competing physical mechanisms: under the definitions used here, ISEF multiplied by enzyme abundance equals RAF. They differ in how the mapping is represented. RAF is convenient when a direct, marker-based conversion is the goal. ISEF is useful when the activity-per-enzyme correction and enzyme abundance need separate examination. Direct abundance scaling without an inter-system activity correction is another possible approach, but it effectively assumes comparable activity per enzyme amount between recombinant and liver systems. That assumption should not be made silently.

A scaled HLM estimate may be carried to a whole-liver basis using appropriate preparation-scaling factors, such as microsomal protein per gram of liver and liver mass, as established in earlier material on IVIVE scaling. That additional conversion changes the units and scope of the estimate; it does not repair an unsuitable marker, an invalid ISEF, or a failed transfer assumption. Likewise, a whole-liver estimate is not by itself a prediction of systemic clearance, which depends on further physiological considerations.

Common pitfall: “The ISEF is 0.8, so the HLM estimate is 80% of recombinant clearance.” This omits enzyme abundance and leaves the estimate on a per-enzyme basis. The correct conversion is \(CL_{\mathrm{int,rec}}\times\mathrm{ISEF}\times A_{\mathrm{HLM}}\), yielding clearance per milligram of HLM protein.

Check Your Understanding

Use the definitions and units in this tutorial. Solutions follow the questions.

A marker rate is 90.0 pmol/min/mg HLM and 0.300 pmol/min/pmol recombinant enzyme. What is RAF, with units?
An ISEF is 1.25 and enzyme abundance is 40.0 pmol/mg HLM. What RAF follows from the defined relationship?
Using your RAF from question 1, calculate the HLM estimate for a recombinant intrinsic clearance of 0.0100 µL/min/pmol enzyme.
Two scaled enzyme contributions are 2.00 and 3.00 µL/min/mg HLM. What is the share of the first contribution in their two-route total?
Why is it not valid to interpret an ISEF of 0.70 alone as an HLM intrinsic clearance estimate?

Solutions. (1) RAF \(=90.0/0.300=300\) pmol/mg HLM. (2) RAF \(=\mathrm{ISEF}\times A_{\mathrm{HLM}}=1.25\times40.0=50.0\) pmol/mg HLM. (3) \(0.0100\times300=3.00\) µL/min/mg HLM. (4) The two-route total is \(2.00+3.00=5.00\) µL/min/mg, so the first share is \(2.00/5.00=0.400\), or 40.0%. (5) ISEF is dimensionless and represents relative marker activity per enzyme amount. Estimating clearance per milligram also requires recombinant drug intrinsic clearance and HLM enzyme abundance.