On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.

Implantation of mouse embryonic stem cell-derived cardiac progenitor cells preserves function of infarcted murine hearts.

Stem cell transplantation holds great promise for the treatment of myocardial infarction injury. We recently described the embryonic stem cell-derived cardiac progenitor cells (CPCs) capable of differentiating into cardiomyocytes, vascular endothelium, and smooth muscle. In this study, we hypothesized that transplanted CPCs will preserve function of the infarcted heart by participating in both muscle replacement and neovascularization. Differentiated CPCs formed functional electromechanical junctions with cardiomyocytes in vitro and conducted action potentials over cm-scale distances. When transplanted into infarcted mouse hearts, CPCs engrafted long-term in the infarct zone and surrounding myocardium without causing teratomas or arrhythmias. The grafted cells differentiated into cross-striated cardiomyocytes forming gap junctions with the host cells, while also contributing to neovascularization. Serial echocardiography and pressure-volume catheterization demonstrated attenuated ventricular dilatation and preserved left ventricular fractional shortening, systolic and diastolic function. Our results demonstrate that CPCs can engraft, differentiate, and preserve the functional output of the infarcted heart.