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Adsorption is accumulation of a substance at an interface. Binding a solute to a packing surface can delay its passage through a chromatography column. Ideal size-exclusion chromatography separates through SEC pore access without such binding; extra retention from adsorption requires a different interpretation.

For a gas contacting a solid, adsorption concentrates molecules at the boundary; absorption takes material into the bulk. A porous solid can have a large internal surface area: binding on pore walls is still adsorption, even though those walls lie inside the particle. Both processes can occur together. Desorption returns adsorbed material to the surrounding phase. The useful question is therefore not just how much material disappeared from the gas, but where it went and whether it returns when the pressure falls.

An adsorption site model turns this spatial distinction into counting. With twelve identical adsorption sites and three bound molecules, the surface coverage is $\theta =3/12=1/4$. Filling six gives $\theta =1/2$; filling twelve gives a complete monolayer. These are configurations illustrating the count, rather than measured arrangements or claims that all real surfaces have twelve sites.

The chromatographic stationary phase remains in place during separation. A porous packing in size-exclusion chromatography supplies internal liquid regions with size-dependent accessibility; ideal separation requires no adsorption of the solute to the packing.

A chromatographic stationary phase may instead expose a solid surface for adsorption, or retain an immobilized liquid into which solutes partition. In ordinary silica gel thin-layer chromatography, interactions with the surface delay migration. This mechanism differs from ideal SEC pore access.

Chromatography separates components of a mixture through different migration rates in contact with a chromatographic stationary phase while a chromatographic mobile phase transports them. Liquid chromatography describes the physical state of the transporting phase; size-exclusion chromatography describes a separation mechanism. Classification by phase and classification by mechanism answer different questions. In ideal size-exclusion chromatography, differential access to liquid-filled pores replaces binding as the source of differential migration.

In many other forms of chromatography, a solute repeatedly leaves the chromatographic mobile phase and returns to it. Reversible adsorption holds it at a surface; partition distributes it between the chromatographic mobile phase and an immobilized liquid chromatographic stationary phase. Spending more time stationary means less progress with the moving fluid. Two initially overlapping components can therefore emerge as separate bands without either being permanently trapped. Chromatography is useful both for comparing a sample with reference substances and for collecting separated components; a visible band need not contain just one substance.

Relative retention belongs to the sample together with the chosen chromatographic stationary phase, chromatographic mobile phase, eluent composition, and temperature. Changing these conditions can change the separation order. Chemical polarity helps explain interactions in some systems but is not a universal ranking rule. In thin-layer chromatography, a spot's TLC retardation factor is consequently conditional evidence about identity, rather than a fixed identifier intrinsic to a molecule.

The final substrate-level phosphorylation in glycolysis provides a useful experimental handle: pyruvate kinase transfers a phosphate group from phosphoenolpyruvate to ADP, producing pyruvate and ATP. Adding lactate dehydrogenase couples each pyruvate formed to consumption of one NADH:These equations select free ionic forms consistently: phosphoenolpyruvate has charge $-3$, ADP $-3$, ATP $-4$, and pyruvate and lactate each $-1$; NAD+ has one more positive charge than NADH. Each line conserves charge. Cancelling pyruvate gives one NADH consumed per ATP formed in this coupled system. A whole-pathway NADH measurement has a different meaning, because the earlier glycolysis redox step produces NADH.

The published An Optimized Enzyme-Coupled Spectrophotometric Method for Measuring Pyruvate Kinase Kinetics reports recombinant pyruvate kinase prepared in Escherichia coli, purified by chromatography and size-exclusion chromatography. UV-transparent microplate wells contained ADP, phosphoenolpyruvate, NADH, lactate dehydrogenase and a buffer solution with magnesium ions. An Epoch plate reader used spectrophotometry to follow absorbance at $340\mathrm{nm}$ every five to ten seconds for one minute at $25{}^{\circ }\mathrm{C}$. Its Figure 2 presents $A_0-A_t$, increasing as NADH is consumed. Heat-inactivated pyruvate kinase gave minimal background; a validated active preparation was the positive control. These comparisons support an enzyme-dependent readout in the prepared system, rather than a whole-biological cell glycolysis measurement.^[ref]

The same report uses $0.5\mathrm{cm}$ for optical path length in Procedure B.2.i, but approximately $0.3\mathrm{cm}$ in Data analysis §3. An absolute conversion requires the actual path length and sufficient coupling enzyme activity; no measured ATP rate is inferred here.^[ref]

For an original dimensional example, stipulate a blank-corrected absorbance decline $-d{A}_{340}/dt=0.024\mathrm{mi}{\mathrm{n}}^{-1}$, a calibrated path length $\ell =0.40\mathrm{cm}$ and a chosen calibration coefficient $\epsilon =6000\mathrm{L}\mathrm{mo}{\mathrm{l}}^{-1}\mathrm{c}{\mathrm{m}}^{-1}$. These are invented teaching inputs, not the protocol's measurements or its quoted coefficient. The Beer-Lambert law givesIn a stipulated $0.20\mathrm{mL}$ reaction volume, this is $2\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$ of NADH consumed and, conditionally, $2\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$ of ATP formed. The conditional inference requires rapid pyruvate consumption by the coupling enzyme, no other NADH-consuming chemical reactions, and a linear, correctly calibrated optical response. The readout measures this last glycolysis step; it cannot establish the full two-net-ATP-per-glucose balance by itself.

Measurement of single-particle mass through its contribution to an optical scattering signal. Unlike size-exclusion chromatography, its principal size readout is mass rather than hydrodynamic size.

multi-angle light scattering measures scattered light at multiple angles to infer molecular size and, with appropriate concentration and optical-contrast information, molar mass. Coupling it to size-exclusion chromatography helps distinguish eluting assemblies, although unresolved mixtures complicate inference.

The useful product is a correctly identified, active and reproducible protein preparation, not merely a large expression band. I would first examine the coding sequence, protein sequence and available biological information to identify the likely mature chain, protein domains, signal peptides, transmembrane segments, disulfide bonds and required post-translational modifications. A predicted protein structure can guide construct boundaries, but cannot establish that the expressed product will fold or function. A eukaryotic genomic sequence containing introns generally needs replacement by an intron-free Complementary DNA or synthetic coding region for expression in Escherichia coli. I would verify the chosen isoform and full sequence, since a database annotation can be wrong.

The expression host follows from the biochemical requirements. Escherichia coli is inexpensive and convenient for many soluble proteins; yeast, insect or mammalian cells may be preferable for secreted proteins or essential glycosylation. A membrane protein also requires a suitable membrane environment during expression and an appropriate detergent or membrane mimic after extraction. I would preserve biologically necessary domains and modifications. Removing a flexible region to improve yield creates a different construct whose suitability must be justified by the intended analysis.

For a bacterial preparation, I would clone the coding region into an expression vector with a controllable promoter, a suitable ribosome-binding site, a selectable marker and a removable affinity tag. A terminal polyhistidine tag is a practical initial choice, provided the terminus is compatible with activity. Correct reading frame, both junctions and the complete insert must be checked by DNA sequencing. The T7 expression system offers strong inducible expression through a phage RNA polymerase; the original work established selective expression of cloned genes, but strong transcription alone does not guarantee soluble, active product.^[ref]

I would screen small cultures before scale-up, varying induction strength, induction duration and temperature, and comparing total lysate with soluble and insoluble fractions by SDS-PAGE. Empty-vector and uninduced controls identify host bands and background expression; an immunoblot against the tag can help identify the product. Expression at lower temperature or a weaker rate can improve protein folding; persistent insolubility may require changing the construct, host or folding environment. An inclusion body is evidence of abundant insoluble material, not of correctly folded protein. Refolding may be possible, but its yield and recovered activity need independent validation.

Once a small-scale condition produces active soluble material, I would expand the culture or fermentation while monitoring growth and retaining the validated induction conditions. After harvesting, controlled lysis at low temperature, an appropriate buffer solution and protection against proteolysis preserve the product. Centrifugation removes debris; a membrane-associated target instead requires isolation and solubilization of the relevant fraction. I would use immobilized metal affinity chromatography for a polyhistidine-tagged construct, wash away nonspecific binders, and elute under conditions compatible with activity. Tag cleavage, a second affinity step to remove tag and tagged protease, and an orthogonal separation such as ion-exchange chromatography can improve purity. A final size-exclusion chromatography step removes aggregates and separates different assemblies. No single chromatographic peak proves identity or homogeneity.

At each stage I would record protein concentration, total recovered amount and a suitable activity or binding readout, rather than optimizing yield alone. Final checks would include SDS-PAGE, intact or peptide mass spectrometry, a native-size measurement and the expected biological activity. Buffer-only and host-purification controls test whether apparent activity comes from contaminants; comparing tagged and cleaved material tests tag interference. Small frozen aliquots should be used only after checking stability and freeze–thaw effects. Scale-up is justified by recovery of the desired molecular species with retained function, with any differences from the native protein documented.

A purified sample should be characterized along independent axes: identity, amount, chemical integrity, solution assembly, conformation and function. A high-resolution structural experiment cannot compensate for analysing the wrong protein or a mixture of molecular states. Conversely, useful biochemical information does not require an atomic structure.

First, verify identity and integrity. SDS-PAGE under reducing and nonreducing conditions estimates apparent subunit size and reveals many contaminants or disulfide-linked species. A single band cannot exclude a same-sized contaminant, a small chemical modification or several co-migrating oligomers. An immunoblot adds epitope recognition, while peptide mass spectrometry checks sequence-derived peptides and intact-mass analysis tests the overall molecular mass. Comparing measured and predicted masses can reveal cleavage, retained tags or modifications, but incomplete peptide coverage and heterogeneity constrain the inference. A tag-specific signal establishes the tag's presence rather than the identity of every residue.

Measure protein concentration using absorbance and an appropriate extinction coefficient, or a calibrated colorimetric assay with compatible standards. The Beer-Lambert law, $A=\epsilon lc$, converts absorbance to concentration only when the assumed molecular species and optical conditions apply. tryptophan residues, tyrosine residues and disulfides contribute to ultraviolet absorption; light scattering and nucleic-acid contamination can inflate readings. Buffer blanks, dilution linearity and a second quantification method help identify such problems. A concentration stated as monomer equivalents must not be confused with the concentration of oligomeric particles.

Next, determine whether the material is monodisperse and how it assembles in solution. Size-exclusion chromatography reports hydrodynamic size and can separate aggregates, but elution calibrated with globular standards gives an apparent size, not an absolute molecular mass for an elongated protein. SEC-MALS combines separation with multi-angle light scattering and a concentration detector to estimate the molar mass across the eluting peak; it can distinguish a large monomer from a compact oligomer when the detector models and sample composition are suitable.^[ref] Analytical ultracentrifugation supplies a complementary sedimentation-based approach, and concentration series can reveal reversible association. dynamic light scattering is sensitive to aggregates but is strongly influenced by a small number of large particles; a visually narrow intensity distribution is not a precise count of all molecular species.

Conformation and stability can then be assessed without determining an atomic model. Far-ultraviolet circular dichroism reports ensemble secondary-structure features, while near-ultraviolet circular dichroism and intrinsic aromatic fluorescence probe environments associated with tertiary packing. These signatures support folding and conformational changes but do not uniquely specify a three-dimensional fold. Thermal or chemical unfolding followed spectroscopically estimates stability only within an appropriate model: an irreversible aggregation-driven transition does not give an equilibrium folding free energy. Differential scanning calorimetry measures heat-capacity changes during a transition, and limited proteolysis can reveal exposed regions or stable domains. Buffer-only controls, matched concentrations and repeated heating–cooling cycles help separate reversible conformational change from precipitation.

Finally, test biological competence. For an enzyme, initial-rate measurements over substrate and enzyme concentration ranges establish specific activity and, where justified, Michaelis-Menten kinetics. For a binding protein, isothermal titration calorimetry can estimate binding stoichiometry, affinity and enthalpy, while a kinetic method such as surface plasmon resonance can resolve association and dissociation. Controls must include heat of dilution or nonspecific surface binding, ligand quality and the possibility of multivalent avidity. A measured dissociation constant does not by itself establish physiological function.

The methods should be chosen to answer a defined question and cross-check one another. For example, a clean gel, the expected intact mass, a single SEC-MALS species and concentration-independent native activity jointly support a useful preparation; none establishes complete homogeneity alone. Comparing fresh, stored and freeze–thawed samples identifies conditions suitable for later structural work. The resulting dossier should state what species is present under the actual experimental conditions and which features remain unresolved.

Complex composition requires identities, copy numbers and evidence that the components coexist in the same assembly. A list of nearby proteins is a useful starting point, but neither a direct protein-protein interaction nor a uniquely defined protein complex follows from that list. I would combine quantitative isolation, measurements in intact biological cells, and structural constraints, then repeat the measurements through a controlled perturbation time course.

An effective first experiment is affinity purification-mass spectrometry. Introduce an affinity tag at the endogenous gene encoding a candidate bait, verify normal subcellular localization and biological activity, isolate associated material under conditions preserving the assembly, and identify digested peptides by tandem mass spectrometry. Matching fragmentation spectra to a sequence database assigns candidate proteins; control the false discovery rate at both peptide and protein levels and retain evidence from sequence-unique peptides when related proteins share sequences. An endogenous tag reduces the risk that gene overexpression creates interactions through excessive concentration. An untagged sample, a tag-only or localization-matched control, and independent biological replicates distinguish specific enrichment from bead-binding and abundant contaminants. Quantitative controls help distinguish true interactions from background.^[ref]

Isolation has selective losses. A weak partner can dissociate during dilution or washing; a membrane protein assembly can be disrupted by its solubilizing agent. Compare extraction conditions, check recovery in the soluble and insoluble fractions, and use reciprocal co-immunoprecipitation from an independent subunit. Treatment with a nuclease tests whether the association depends on DNA or RNA, but removal after extraction can itself destabilize a real nucleic-acid-dependent assembly. Purification from mixed tagged and untagged cell populations, with distinguishable stable isotope labeling, can test whether partners exchange after cell disruption. A reciprocal enrichment supports coassociation; demonstrating a direct contact still requires additional evidence.

For stoichiometry, raw mass spectrometry intensity is insufficient because different peptides have different digestion and ionization efficiencies. Use calibrated peptide standards or carefully normalized quantitative estimates, ideally with several reference subunits. native mass spectrometry measures intact assembly masses and can distinguish candidate subunit counts, while controlled dissociation helps assign subcomplexes. Bound lipids, post-translational modifications, gas-phase losses and heterogeneous occupancy complicate assignment, so check the mass against the summed masses of candidate subunits. Size-exclusion chromatography coupled to multi-angle light scattering independently constrains assembly mass, although an unresolved mixture produces an average and the hydrodynamic size alone is not a molecular mass. Quantitative mass spectrometry of protein complexes can combine interaction strengths, abundance and stoichiometry.^[ref]

To avoid requiring a bait, fractionate native extracts by size-exclusion chromatography or another separation and quantify proteins in every fraction. Correlated elution profiles suggest membership of the same protein complex; comparison across an independent separation helps distinguish coincidence. This co-fractionation mass spectrometry can also reveal shifts from a large assembly into smaller forms after treatment. It may merge different assemblies sharing a subunit, and a failure to coelute does not exclude a transient interaction. chemical cross-linking mass spectrometry adds spatial information: identify pairs of linked residues, translate them into distance restraints appropriate to the reagent and residue accessibility, and ask whether a proposed assembly can satisfy them. A cross-link is a proximity constraint, not automatically a permanent interface; intermolecular assignment is especially difficult for identical subunits.

In living biological cells, proximity labeling captures an interaction neighbourhood before disruptive extraction. A bait fused to TurboID marks nearby proteins with biotin, allowing stringent enrichment and mass spectrometry. The original TurboID work demonstrated useful labeling over roughly ten minutes, which is much faster than older long-labeling implementations.^[ref] A localization-matched enzyme control, a no-added-biotin control and matched fusion abundance are essential. The labeling pulse integrates both spatial proximity and residence time; ten-minute labeling cannot resolve a seconds-long interaction sequence. Changes in ATP, biotin availability, enzyme activity or access to reactive residues can change the labeling signal independently of complex membership. A pulse followed by a chase does not make the covalent label disappear when the partner leaves.

Structural methods distinguish alternative interpretations of these measurements. cryo-electron microscopy can assign ordered subunits, estimate occupancy of resolved features, and separate some compositionally different particle classes. Flexible or small subunits may remain invisible despite being present. X-ray crystallography resolves stable interfaces but selects material that crystallizes. Förster resonance energy transfer between appropriately positioned labels tests nanometre-scale proximity in intact biological cells; single-particle tracking and fluorescence correlation spectroscopy can test comobility and exchange. Label placement, spectral cross-talk and accidental colocalization require controls. None of these techniques by itself reliably inventories every component.

The computational analysis should preserve these distinctions. Construct a protein interaction network with separate edge types for copurification, cross-linking and proximity labeling. Cluster reproducibly supported associations to propose modules, distinguish a stable core from variable accessory components, and integrate localization and measured protein abundance. Models such as AlphaFold 3 can propose interfaces for experimentally supported candidate components, but a confident predicted geometry does not demonstrate that an interaction occurs in the tested condition.^[ref] Test interfaces by site-directed mutagenesis, confirming normal protein folding, expression and localization before interpreting a lost interaction. Evaluate a proposed assembly against independently held-out cross-links or other measurements to reduce circular validation.

For perturbations, use vehicle controls, several doses and early-to-late sampling; randomize preparation and instrument order. Quantify input abundance alongside bait-normalized partner recovery. An illustrative relative recruitment statistic for partner $i$ at time $t$ iswhere $I^{\mathrm{IP}}$ is background-corrected recovered intensity, $b$ is the bait and $A_i$ is input abundance. This is an operational comparison under matched extraction and measurement response, not an absolute occupancy or dissociation constant. A doubled recovered partner signal with doubled input abundance and unchanged bait recovery gives $R_i=1$, illustrating why raw enrichment alone would mislead. Values near the detection limit need uncertainty bounds rather than unstable ratios.

A drug-induced loss of several core components could mean disassembly, degradation, changed localization or poor recovery. Distinguish them with input proteomics, microscopy and native fractionation, then test reversibility after washout and rescue by a drug-resistant target when feasible. For stress, monitor viability and extraction-resistant material; for disease-associated mutations, compare otherwise matched genetic backgrounds and rescue with the normal allele. post-translational modifications may recruit an accessory partner without changing the core. hydrogen-deuterium exchange mass spectrometry can then test interface exposure, but its altered exchange reports accessibility and structural dynamics rather than a new subunit by itself. A convincing remodeling claim is a reproducible change in assembly membership or occupancy, separated from changes in abundance, localization and assay recovery, and connected to a functional consequence.

The liposomes could be separated from free proteins by density-gradient flotation: lipid-containing particles float to a different position from soluble protein. Size-exclusion chromatography is another possibility if it resolves the large vesicles from the unincorporated proteins. Simple sedimentation can also collect sufficiently large vesicles, but protein aggregates may sediment too. The important control is to show that the recovered SNARE proteins associate with the lipid bilayer, rather than merely copurifying with it.

The unliganded and peptide-bound preparations elute at almost the same volume, near 14 ml. They therefore have similar effective hydrodynamic sizes in this separation. A conformational change can occur without a large change in that measurement. The GFP–peptide-containing complex elutes earlier, near 10.5–11 ml, consistent with a larger particle; the later peak is consistent with excess unbound GFP–peptide.

The experiment supports ligand association but does not alone determine subunit number. Size-exclusion chromatography separates by access to pores, which depends on size and shape rather than mass alone. The similar peptide-free and peptide-bound elution volumes therefore do not establish identical conformations or exact molecular masses.

Polystyrene is a polymer used as a calibration-standard family in organic-solvent size-exclusion chromatography. Its hydrodynamic size in a specified solvent supplies a conditional SEC molar mass calibration for other dissolved chains.

A protease protection assay asks whether a barrier prevents an added protease from reaching a protein. A membrane-disruption comparison tests whether protection depends on that barrier.

The membrane-disruption test was performed by David D. Sabatini and Günter Blobel in 1970. Rat-liver microsomes purified by sucrose centrifugation incorporated radioactive leucine during cell-free translation. Samples received cold trypsin and chymotrypsin, with or without membrane-solubilizing detergents. Electron microscopy checked vesicle preservation; size-exclusion chromatography separated protected fragment sizes. Large membrane-associated fragments lost protection after disruption, whereas small ribosome-protected fragments persisted. An exposed ribosome preparation remained digestible when mixed with microsomes, checking that membranes did not simply inhibit the proteases.^[ref]

To read the qualitative diagram, first compare untreated aliquots: they establish that detectable cargo exists before digestion. Next compare external protease with intact versus disrupted membranes. Persistence only while the barrier remains intact supports enclosure, provided the exposed-cargo control confirms active protease in both chemical conditions. The detergent-only aliquot checks that disruption itself does not destroy recovery or detection. Adding membranes after synthesis tests a different alternative: capture of a completed product rather than entry during biological translation.

This is an argument from controlled accessibility. Binding predicts membrane association but generally leaves an exposed cargo digestible. Enclosure predicts protection that depends on membrane integrity. However, protein aggregation, intrinsic resistance to proteolysis, inactive protease or undetected small fragments can obscure this distinction. For a transmembrane protein, expect protection of the enclosed portion rather than necessarily the full chain. Combine fragment size, compartment controls and membrane topology; a protected signal alone does not uniquely specify the whole protein's location.

An experimental comparison joined a two-ended diol chain, HOPCLOH, with a bifunctional isocyanate, at reported isocyanate-to-diol ratio $1.14:1$. The researchers used oven-dried $25\mathrm{mL}$ round-bottom flasks and an IKA RET magnetic hotplate with a metal carrier. They varied solvent, concentration, reaction temperature ($50$ or $61{}^{\circ }\mathrm{C}$), and duration ($1$ or $8\mathrm{h}$).^[ref]

A Bruker $500\mathrm{MHz}$ NMR spectroscopy instrument measured residual hydroxy group-adjacent signal relative to an ester signal. Independently, size-exclusion chromatography used ResiPore columns at $70{}^{\circ }\mathrm{C}$, a refractive-index detector, and polystyrene calibration. Figure 8 reports sharply increasing apparent number-average molar mass beyond the reported conversion $0.95$. A deliberately water-exposed isocyanate comparison reproduced a $1625\mathrm{c}{\mathrm{m}}^{-1}$ infrared spectroscopy band assigned to urea-containing products. The authors warn that tiny residual NMR spectroscopy signals reduce integration precision.^[ref]

The inference is increasing chain size alongside depletion of reactive groups, consistent with step-growth polymerization. It is not an exact measurement of $X_n$ in the toy model. The feed contains already extended diol chains: counting their constituent repeat units differs from counting each feed molecule as one unit. Their varying molar masses, calibration against a different polymer, residual starting material, and competing chemical reactions further obstruct a direct conversion-to-$X_n$ substitution. Report which functional groups the conversion readout measures before comparing it with stoichiometric imbalance in step growth.

Useful proposed controls, distinct from the reported water comparison, are pre-reaction spectra and matched mixtures omitting each joining partner in turn. Keep solvent, heating, and signal normalization matched. Disappearance of an isocyanate signal in the omitted-diol control would reveal competing consumption rather than establish chain joining. Agreement between residual-group and independently calibrated chain-size readouts is stronger evidence than calculating both quantities from the same Carothers equation.

Size-exclusion chromatography separates dissolved molecules by their hydrodynamic size in the chosen solvent. A larger species that cannot enter the packing's pores travels with the liquid between particles and elutes earlier. Smaller species explore more internal liquid and elute later. The column is not a sieve that permanently traps the large species: exclusion makes them leave first. “Gel filtration” is common for aqueous separations; “gel permeation chromatography” is common for organic-solvent analysis of polymers. SEC molar mass calibration translates size-dependent elution into a standard-relative estimate of molar mass, rather than a universal absolute measurement.

This makes SEC useful for separating proteins from small dissolved species, comparing protein aggregation, and characterizing dissolved polymer chains. The residual-group monitoring of polyurethane formation experiment already illustrates polymer calibration: its reported molar masses are relative to polystyrene standards. Size-exclusion characterization of chain polymers explains why an elution trace alone cannot count chains or establish their growth mechanism.

Suppose a synthetic polymer population contains three chains of molar mass $10000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for every one chain of molar mass $40000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. Multiplying both chain counts by any common factor leaves the averages unchanged. Substitution into the existing number-average molar mass and weight-average molar mass definitions givesThe larger chains are only one quarter of the chain count but supply $40000/70000=4/7$ of the mass. Thus a weighted mean that emphasizes mass gives a larger result than one that weights each molecule equally. Total mass divided by total chain amount of substance gives $M_n$, while $M_w/N_{\mathrm{A}}$ is not the mean mass of a randomly chosen chain. Inferring chain counts from size-exclusion chromatography still requires the existing SEC detector response and SEC molar mass calibration assumptions.