The correct statement is: “the smaller polymers can push the larger proteins together to maximize their own entropy.” This is the classic entropic depletion attraction between large globular proteins in a solution of short, non‑adsorbing polymers.​​

Introduction

When large globular proteins are homogeneously mixed with short, non‑adsorbing polymer chains, the system exhibits an important soft‑matter phenomenon called depletion interaction. This interaction is entropic in origin and can generate an effective attraction between the big protein particles, strongly influencing aggregation, phase separation, and crystallization of proteins in solution. Understanding which statement correctly describes this situation is crucial for biophysics, colloid science, and competitive exam questions.​

Correct option: polymers push proteins together (entropic depletion)

Statement: “the smaller polymers can push the larger proteins together to maximize their own entropy”

• Short polymers are excluded from a thin shell (excluded volume) around each large globular protein, because they cannot penetrate close to the protein surface.​

• When two large proteins approach so that their excluded volumes overlap, the total excluded volume available to polymers decreases, thereby increasing the free volume accessible to polymers in the rest of the solution; this increases polymer configurational entropy.​

• The osmotic pressure of polymers outside the overlap region becomes higher than in the depleted region between proteins, producing an effective “push” that drives the big proteins together, i.e., a short‑range attractive force known as depletion attraction.​

Thus, the smaller polymers effectively push the larger proteins together to maximize their own entropy, so this option is true and is the correct answer.​

Why “depletion interaction will keep the mixture homogeneous” is wrong

Statement: “Depletion interaction will keep the mixture homogeneous”

• Depletion interaction is an effective attraction between large particles in the presence of smaller depletants (here, short polymers).​

• At sufficiently high polymer concentration or appropriate size ratio, this attraction actually promotes aggregation or phase separation (demixing) of the protein–polymer mixture, leading to clustering, gelation, or a protein‑rich and protein‑poor phase, rather than maintaining homogeneity.​

Therefore, depletion interaction does not inherently “keep the mixture homogeneous”; it more often destabilizes a homogeneous mixture by inducing phase separation or crystallization of proteins. Hence this option is false.​

Why “smaller polymers will keep proteins separated to maximize protein entropy” is wrong

Statement: “the smaller polymers will keep the larger proteins separated to maximize the protein entropy”

• Maximizing the entropy of the proteins alone would favor them being more spatially disordered, but the dominant effect here is the entropy of the polymers, which strongly outnumber proteins and have many more configurational states.​

• Depletion forces arise because polymers gain entropy when large particles come closer, not when they stay separated; thus the polymers do not keep proteins apart, they favor clustering of the proteins.​

So the direction of the entropic drive is opposite to what this statement claims: it is polymer entropy, not protein entropy, that controls the interaction, and it favors proteins coming together, not staying separated. This option is false.

Why “smaller polymers will bind to the larger proteins” is wrong

Statement: “the smaller polymers will bind to the larger proteins”

• Depletion interaction is defined for non‑adsorbing (non‑binding) polymers: they do not bind or strongly adsorb to the protein surface.​

• If polymers actually bound to proteins, the mechanism would shift to polymer–protein association or bridging flocculation, which is a different, specific interaction, not the classic entropic depletion mechanism described in this question.​

Therefore, saying that “the smaller polymers will bind to the larger proteins” contradicts the basic assumption of depletion interaction and is incorrect.

Key takeaways for exams

• Correct option: The smaller polymers can push the larger proteins together to maximize their own entropy (entropic depletion attraction).​

• Depletion interaction: Short, non‑adsorbing polymers excluded from around proteins create an osmotic imbalance that effectively attracts the proteins when they come close enough for exclusion zones to overlap.​

• Homogeneity vs phase separation: Depletion attraction usually tends to promote aggregation or phase separation, not maintain perfect homogeneity, especially at higher polymer concentrations.​