Fig. 1

Main components of our computational framework for Bayesian inference of chromatin parameters from whole nucleus simulations. a Simulations: we consider a number n =144 of different parameter values Π _i  = (P _i , C _i , W _i , L _i ), where P _i is the chromatin persistence length, C _i the chromatin compaction, W _i the chromatin width, and L _i the length of microtubules (see Table 1, Additional file 2). The discretization of the parameter space is illustrated on the left (crosses), highlighting persistence length P and compaction C. Each Π _i defines a separate model M _i  = M(Π _i ), for which we run two to six independent dynamic simulations of all 16 chromosomes in the nucleus with random initializations. Three-dimensional snapshots are shown for a model with high P and high C (top) and a model with low P and low C (bottom). Each simulation run calculates changes in chromosome configurations over millions of time steps, as illustrated for two time points t ₁ and t _N (only chromosome 4 is shown). By sampling these simulation runs, we predict various observables, \( {Y}_k^{M_i} \), such as the average distance \( \left\langle {\mathrm{d}}_{AB}^{M_i}\right\rangle \) between two loci A and B, or the average contact frequencies between chromosomes i and j. b For any value of the parameters Π (within the allowed range), an interpolation scheme calculates the predicted value of the observables Y _k ^M(Π), e.g. 〈d _AB ^Π〉 shown here as a heat map, from the discrete models M _i (crosses). c Experimental data Y _k ^E, such as the average distance between loci A and B measured by imaging, 〈d _AB ^E〉, are compared to the predictions 〈d _AB ^Π〉 for all Π. d, e Similarly, contact frequencies between chromosomes i and j are predicted for all Π (here i=j) (d) and compared to measurements from Hi-C experiments (e). f, g Parameter inference: given an experimental dataset, using the Bayes rule and Markov chain Monte Carlo sampling, we calculate the posterior probability density of any subset of parameters, such as (P, C). Isocontour lines enclose the region of high probability. This can be done for individual experimental data, e.g. 〈d _AB ^E〉 (f), or for a combination of multiple datasets, e.g. mean distances between loci and chromosome contact frequencies (g). The maximum a posteriori estimate of the parameters (MAP) defines a model that provides the best match to the experimental data