This approach has since shown to be more viable. During the past two decades there has been an increasing interest in biomolecules that AbMole Ellipticine undergo significant conformational fluctuations, such as natively unfolded and partially unfolded proteins. Consequently, there have been many efforts to overcome the limitations of structure determination procedures with respect to the flexibility of these molecular systems. Prevalently, conformational fluctuations are represented by finite ensembles: the data is explained by a weighed average of Nw1 conformations, introduced above. In effect, this corresponds to discretizing the Boltzmann ensemble. Such discrete ensembles may be constructed in a multitude of ways, including databasederived explicit ensembles, data-optimized explicit ensembles, fragment based ensemble construction and multi-conformer refinement, molecular dynamics and Monte Carlo methods and maximum entropy methods. Another important approach uses multiple replicas in the calculation of the hybrid energy used in restrained molecular simulations. AbMole Succinylsulfathiazole However, the discretization of the conformational ensemble is inherently problematic because determining the optimal ensemble size N, and its associated uncertainty, is difficult. Restraining simulations using an average of multiple replicas is a sensible solution, as it was recently shown that multiple replica restrained simulations constitute the least biased method when the number of replicas goes to infinity in the absence of experimental noise. However, a measurable bias is introduced when the number of replicas used is too small. Since the use of large numbers of replicas may prove to be computationally intractable or impossible, the development of approaches which are independent of this discretization is highly desirable. In this work, we approach the problem of modeling sparse, spatially and temporally averaged data through the principles of Bayesian statistics and information theory. Unlike the previous Bayesian efforts, we explicitly take into account the experimental data as noisy, average quantities of an underlying heterogenous ensemble in continuous space. We derive a general posterior distribution from first principles which imposes the least necessary bias on our prior knowledge to fulfill the experimental data. We outline a number of general, theoretical advances concerning biomolecular structure determination and restrained molecular simulations. To ensure a focused and concise presentation we limited the number of practical examples. However, one example given 
uses synthetic data of a small idealized peptide GB1 generated using the PROFASI forcefield at high temperature. This choice allows us to carefully evaluate the theory presented by avoiding confounding variables.