16.7 Encapsulation Statistics and Copy Number

Encapsulation Statistics and Copy Number describes the statistical treatment of how many copies of a given cargo molecule end up within individual compartments across a population, addressing the inherently random nature of passive cargo capture and the resulting variability from one compartment to the next. It treats copy number not as a fixed, guaranteed quantity per compartment but as a distributed outcome governed by probability, particularly significant when compartment volumes are small relative to cargo concentration.

Describing Occupancy Across a Population

Compartment Cargo Occupancy

Compartment cargo occupancy refers to the presence or absence, and the amount, of a given cargo species within an individual compartment, serving as the basic unit of observation from which population-level encapsulation statistics are built.

Empty Compartment Fraction

Empty compartment fraction is the proportion of compartments within a population that contain zero copies of the cargo of interest, representing compartments that failed to capture any cargo despite cargo being present in the surrounding bulk medium during formation.

Single-Cargo Compartment Fraction

Single-cargo compartment fraction is the proportion of compartments within a population that contain exactly one copy of the cargo of interest, relevant for applications requiring precisely one cargo copy per compartment.

Multi-Cargo Compartment Fraction

Multi-cargo compartment fraction is the proportion of compartments within a population that contain more than one copy of the cargo of interest, representing outcomes above the single-copy case.

Copy Number as a Distributed Quantity

Encapsulated Molecular Copy Number

Encapsulated molecular copy number is the actual count of individual cargo molecules present within a specific compartment, the fundamental quantity that varies from compartment to compartment within a population subjected to passive, statistically governed encapsulation.

Encapsulated Copy Number Distribution

Encapsulated copy number distribution describes the full spread of copy number values observed across a compartment population, characterizing not just an average copy number but the relative frequency of each possible copy number outcome.

Low-Copy and Zero-Copy Regimes

Low-Copy Molecular Encapsulation

Low-copy molecular encapsulation refers to situations in which the expected number of cargo copies per compartment is small, on the order of a few molecules or fewer, a regime in which statistical variability between compartments becomes especially pronounced relative to the average copy number.

Zero-Copy Compartment Occurrence

Zero-copy compartment occurrence is the specific outcome in which a compartment ends up with no cargo copies at all despite cargo being present in the source medium, an outcome that becomes increasingly likely as expected copy number decreases.

Governing Relationships

Compartment Volume-Copy Number Relationship

Compartment volume-copy number relationship describes how the internal volume of a compartment directly scales the expected number of cargo copies it will capture at a given bulk concentration, since larger compartments sample a larger volume of the surrounding medium during closure.

Random Molecular Sampling

Random molecular sampling refers to the fundamentally stochastic nature of which specific cargo molecules end up within a given compartment's enclosed volume at the moment of closure, underlying why copy number varies across a population even when every compartment forms under identical bulk conditions.

Poisson-Like Cargo Partitioning

Poisson-like cargo partitioning describes the statistical pattern that emerges when cargo molecules are randomly and independently distributed throughout a bulk medium and then sampled into compartments of a defined volume, following a distribution shape characteristic of random, independent sampling events.

This relationship expresses the probability of a compartment containing exactly a given number of cargo copies as a function of the average expected copy number, capturing the characteristic pattern of random, independent cargo partitioning across a compartment population.

Cargo Concentration-to-Occupancy Relationship

Cargo concentration-to-occupancy relationship describes how the bulk cargo concentration used during encapsulation directly sets the average expected copy number per compartment, linking a controllable assembly input to the resulting statistical occupancy outcome across the population.

Consequences of Statistical Variability

Small-Volume Encapsulation Variability

Small-volume encapsulation variability describes the heightened relative fluctuation in copy number that occurs when compartment volumes are small, since a small enclosed volume captures a comparatively small and therefore more variable sample of the surrounding bulk medium.

Encapsulation Population Heterogeneity

Encapsulation population heterogeneity is the overall consequence of the statistical effects described throughout this branch, describing a compartment population that, even when formed under uniform bulk conditions, contains individual compartments varying meaningfully in their cargo occupancy and copy number.