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The force-extension relation for a semi-flexible polymer such as DNA confinedin a nanoslit is investigated and it is found that both the effectivepersistence length and the form of the force-extension relation change as thechain goes from 3D (very large slit heights) to 2D (very tight confinement).Generalizations of the Marko-Siggia relation appropriate for polymers innanoconfinement are presented. The forms for both strong and weak confinementregimes are characterized by an \textit{effective dimensionality}. At lowforces, the effective dimensionality is given by the correlations along thepolymer in the plane of the confining walls. At high forces, the theoreticalforce must account for reduced conformation space. Together the interpolationsgive good agreement for all slit heights at all forces. As DNA and othersemi-flexible biopolymers are commonly confined \textit{in situ} to variousdegrees, both the idea of an effective dimensionality and the associatedgeneralized Marko-Siggia interpolations are useful for qualitativelyunderstanding and quantitatively modeling polymers in nanoconfinement.

Force-Extension for DNA in a Nanoslit: Using an Effective Dimensionality to Map between the 3D and 2D Limits