State Representations for Cell and Gene Therapy Products

Why State Definitions Matter

A cell or gene therapy dose can contain several biologically different quantities. A cell product may include viable cells, nonviable cells, and viable cells that differ in whether they carry or express the engineered construct. A vector preparation may contain physical particles, genome-containing particles, and particles with measurable transducing activity. After administration, vector genomes, transduced cells, and transgene product are further distinct quantities. Treating them as one undifferentiated “dose” can make a model impossible to interpret.

A state is a quantity in the model whose value, together with the model inputs and rules, is sufficient to determine the modeled system’s future behavior. A state is not automatically the same thing as a dose, an assay result, or a functional effect. State definitions should specify what is counted, where it is counted, and what biological property qualifies an item for inclusion.

A dose can be used to set an initial condition or enter the model as an input, but it is not necessarily a state that persists unchanged after administration. For example, a stated cell dose may be a product-level count, whereas the model may need separate quantities for viable and nonviable cells. Similarly, a vector dose reported as physical particles does not by itself specify how many genomes are present, how many cells will be transduced, or how much transgene product will appear.

A State Vocabulary for Cell and Gene Therapies

The following quantities are useful starting points. Their precise meanings must be stated for each application, because assays and product specifications may use different operational definitions.

• Infused cells: cells administered as a cell product. This is an administered quantity; it may include viable and nonviable cells unless the reported dose explicitly excludes one of these groups.
• Viable cells: cells meeting a defined viability criterion at the time and in the compartment of interest. Viability does not, on its own, establish that a cell is engineered, expressing the intended construct, or capable of the desired function.
• Vector particles: physical vector particles, defined by the relevant particle or capsid measurement. Physical particles need not all contain a vector genome or have measurable transducing activity.
• Vector genomes: copies of the vector genome, with the measurement specifying whether the copies are inside particles, free, or associated with cells or tissue. Genome copies are not cells and are not necessarily equivalent to infectious or functional units.
• Transduced cells: cells that meet a stated criterion for vector entry or vector-genome presence. The criterion might be based on a detectable genome, but genome detection alone does not necessarily establish transgene expression or biological function.
• Expressing cells and transgene product: expressing cells meet a defined expression criterion; the transgene product is the resulting molecule measured as an amount or concentration. Product concentration is not a cell count, and a cell’s expression level can vary.

These quantities can be related without being interchangeable. Under an explicitly chosen definition, expressing cells may be a subset of transduced cells, and viable engineered cells may be a subset of viable cells. But the relationships are not universal: a genome assay may detect material that is not in a viable cell, and vector genomes can persist without detectable expression. The model should encode only the subset relationships justified by the biological definitions and measurements.

Units help make the distinctions visible. Cell states may be counts or counts per volume; vector-particle states may be particle counts; vector-genome states may be copies; and transgene product may be mass per volume or amount per volume. A model should not add quantities with different units or silently treat a ratio of two quantities as a third state.

State Definitions and Model Closure

A useful test of a proposed state representation is whether the state variables contain enough information to determine the modeled changes. If two biologically different situations have the same proposed state value but can evolve differently, that value alone does not provide a closed representation. The following simple derivation shows why total cell count may be inadequate when viable and nonviable cells behave differently.

Let \(N_v\) be viable cells and \(N_d\) be nonviable cells in one compartment, both measured in cells. Let \(M=N_v+N_d\) be the total cell count. For illustration only, suppose viable and nonviable cells disappear at constant first-order rates \(k_v\) and \(k_d\), respectively, with units of inverse time. Then:

If \(k_v\ne k_d\), knowing \(M\) alone does not determine \(dM/dt\): the same total can consist of different proportions of viable and nonviable cells. For example, if \(M=100\) cells, one system could contain \(80\) viable and \(20\) nonviable cells, while another contains \(20\) viable and \(80\) nonviable cells. Their rates of total-cell change differ whenever the two disappearance rates differ. Thus, separate states are needed if those categories have different modeled behavior and their proportions cannot be treated as fixed. This argument concerns state sufficiency; it does not prescribe a cell-expansion or persistence model.

Relating States to Measurements

A model state is often not observed directly. An assay supplies an observation related to the state through a measurement process: for example, a viability assay classifies cells under its own criterion, a genome assay reports copies in a sampled material, and an expression assay has a detection threshold. The quantity recorded by an assay should be named precisely, including the sampled compartment and denominator where relevant.

For each proposed state, ask:

• What is counted or measured, and what is excluded?
• Where is it measured, and what are the units?
• Is the quantity physical, viable, transduced, expressing, or functionally competent?
• Does the assay measure that state directly, or a related quantity?
• Could two biologically different populations produce the same reported measurement?

When the model tracks only a lumped quantity, it assumes that distinctions within that quantity are irrelevant to the modeled question or can be represented adequately by fixed relationships. When that assumption is not defensible, states should be split. Conversely, adding a state without a distinct biological role or a way to constrain it from data can make the model harder to identify without improving the interpretation.

A minimal model may use a single measured cell population when the purpose is to describe that measurement and no relevant subpopulation differences are needed. A more resolved model can separate viable, nonviable, transduced, or expressing populations when their behavior or measurements differ. A direct input-output description may instead relate administered dose to an observed product or response without representing intermediate biological quantities. That can be useful for a narrow prediction task, but it cannot answer mechanistic questions about the omitted stages.

Diagnostics, Pitfalls, and Limitations

Several warning signs indicate that state definitions may be obscuring the biology:

• Unit mismatch: a calculation treats cell counts, particle counts, genome copies, or product mass as directly interchangeable.
• Unstated denominator: a percentage is applied to total cells when it was measured among viable cells, or vice versa.
• Function inferred from presence: detectable genomes or a marker are treated as proof of expression, viability, or therapeutic activity without a stated criterion.
• Assay and state are conflated: a measurement is named as if it were the biological state, despite sampling or detection limits that may alter what it represents.
• Unnecessary detail: multiple states are introduced even though the model question cannot distinguish them and the available data cannot inform them.

A common mistake is to reason, “The administered dose contains \(X\) units, so the model starts with \(X\) functional units.” That conclusion does not follow unless the dose definition and evidence establish that every administered unit meets the functional-state criterion at the relevant time. The correction is to name the administered quantity and the proposed functional quantity separately, state their operational definitions, and represent their relationship only when it is supported. Even a carefully defined state model remains limited by assay validity, sampling, and uncertainty about which biological distinctions matter for the question.