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| The binding of individual components to form composite structures is a ubiquitous phenomenon within the sciences. Nucleation and growth have been extensively studied in the past decades, often assuming infinitely large numbers of building blocks and unbounded cluster sizes. These assumptions led to the use of mass-action, mean field descriptions such as the well known Becker D\"oering equations. In cellular biology, however, nucleation events often take place in confined spaces, with a finite number of components, so that discrete and stochastic effects must be taken into account. We examine finite sized nucleation by considering a fully stochastic master equation, solved via Monte-Carlo simulations and via analytical insight. We find striking differences between the mean cluster sizes obtained from our discrete, stochastic treatment and those predicted by mean field treatments, even in the limits of large system sizes. We discuss homogeneous and heterogeneous nucleation, coagulation and fragmentation events, and first assembly times. |
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