Continuum states of the Dirac equation are calculated numerically for the electrostatic field generated by the charge distribution of an atomic nucleus. The behavior of the wave functions of an incoming electron with a given asymptotic momentum in the nuclear region is discussed in detail and the results are compared to different approximations used in the data analysis for quasielastic electron scattering off medium and highly charged nuclei. It is found that most of the approximations provide an accurate description of the electron wave functions in the range of electron energies above 100 MeV typically used in experiments for quasielastic electron scattering off nuclei only near the center of the nucleus. It is therefore necessary that the properties of exact wave functions are investigated in detail in order to obtain reliable results in the data analysis of quasielastic (e, e ′ p) knockout reactions or inclusive quasielastic (e, e ′ ) scattering. Detailed arguments are given that the effective momentum approximation with a fitted potential parameter is a viable method for a simplified treatment of Coulomb corrections for certain kinematical regions used in experiments. Numerical calculations performed within the framework of the single particle shell model for nucleons lead to the conclusion that our results are incompatible with calculations performed about a decade ago, where exact electron wave functions were used in order to calculate Coulomb corrections in distorted wave Born approximation. A discussion of the exact solutions of the Dirac equation for free electrons in a Coulomb field generated by a point-like charge and some details relevant for the numerical calculations are given in the appendix.

Bacteria adapt their growth rate to their metabolic status and environmental conditions by modulating the length of their G1 period. Here we demonstrate that a gradual increase in the concentration of the second messenger c-di-GMP determines precise gene expression during G1/S transition in Caulobacter crescentus. We show that c-di-GMP stimulates the kinase ShkA by binding to its central pseudo-receiver domain, activates the TacA transcription factor, and initiates a G1/S-specific transcription program leading to cell morphogenesis and S-phase entry. Activation of the ShkA-dependent genetic program causes c-di-GMP to reach peak levels, which triggers S-phase entry and promotes proteolysis of ShkA and TacA. Thus, a gradual increase of c-di-GMP results in precise control of ShkA-TacA activity, enabling G1/Sspecific gene expression that coordinates cell cycle and morphogenesis.

Cytosolic hybrid histidine kinases (HHKs) constitute major signaling nodes that control various biological processes, but their input signals and how these are processed are largely unknown. In Caulobacter crescentus, the HHK ShkA is essential for accurate timing of the G1-S cell cycle transition and is regulated by the corresponding increase in the level of the second messenger c-di-GMP. Here, we use a combination of X-ray crystallography, NMR spectroscopy, functional analyses, and kinetic modeling to reveal the regulatory mechanism of ShkA. In the absence of c-di-GMP, ShkA predominantly adopts a compact domain arrangement that is catalytically inactive. C-di-GMP binds to the dedicated pseudoreceiver domain Rec1, thereby liberating the canonical Rec2 domain from its central position where it obstructs the large-scale motions required for catalysis. Thus, c-di-GMP cannot only stabilize domain interactions, but also engage in domain dissociation to allosterically invoke a downstream effect. Enzyme kinetics data are consistent with conformational selection of the ensemble of active domain constellations by the ligand and show that autophosphorylation is a reversible process.

29Bacteria adapt their growth rate to their metabolic status and environmental 30 conditions by modulating the length of their quiescent G1 period. But the molecular 31 mechanisms controlling G1 length and exit from G1 are poorly understood. Here we 32 identify a key role for the second messenger c-di-GMP, and demonstrate that a gradual 33 increase in c-di-GMP concentration determines precise gene expression during G1/S in 34 Caulobacter crescentus. We show that c-di-GMP strongly stimulates the kinase ShkA, 35activates the TacA transcription factor, and initiates a G1/S-specific transcription 36 program leading to cell morphogenesis and S-phase entry. C-di-GMP activates ShkA by 37 binding to its central pseudo-receiver domain uncovering this wide-spread domain as a 38 novel signal input module of bacterial kinases. Activation of the ShkA-dependent 39 genetic program also causes c-di-GMP to reach peak levels, which triggers S-phase 40 entry and, in parallel, promotes proteolysis of ShkA and TacA. Thus, a gradual 41 increase of c-di-GMP results in a precisely tuned ShkA-TacA activity window enabling 42 G1/S specific gene expression before cells commit to replication initiation. By defining 43 a regulatory mechanism for G1/S control, this study contributes to understanding 44 bacterial growth control at the molecular level. cell division (D or G2) 1 . Since chromosome replication and cell division (C and D 49 periods) remain constant over a wide range of growth rates 2,3 , the step committing 50 cells to initiate chromosome replication largely determines bacterial proliferation rates. 51Bacteria like Escherichia coli or Bacillus subtilis can increase their growth rate by 52 bypassing the B period and by initiating replication multiple times per division cycle 2 . 53In contrast, Caulobacter crescentus strictly separates its cell cycle stages. An 54 asymmetric division generates a sessile stalked (ST) cell, which directly re-enters S-55 phase, and a motile swarmer (SW) cell that remains in G1 for a variable time 56 depending on nutrient availability 4,5 . Coincident with G1/S transition, motile SW cells 57 undergo morphogenesis to gain sessility ( Fig. 1a). But what determines the length of 58 G1 in this organism has remained unclear. 59In C. crescentus, replication initiation is regulated by the cell cycle kinase CckA. 60CckA is a bifunctional enzyme that acts as a kinase for the replication initiation 61 inhibitor CtrA in G1, but switches to being a phosphatase in S phase, resulting in the 62 inactivation of CtrA and clearance of the replication block 6 (Fig. 1a). The CckA switch 63 is governed by two response regulators, DivK and PleD. While DivK controls CckA 64 activity through protein-protein interactions 7-9 , PleD is a diguanylate cyclase, which is 65 responsible for the characteristic oscillation of c-di-GMP during the cell cycle 10 . The 66 concentration of c-di-GMP, below the detection limit in G1, increases during G1/S to 67 reach peak levels at the onset of S-phase 11 where it allosterically stimulates Cc...