The motion of point particles in curved spacetime

This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a smooth field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative) field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (part II). It continues with a thorough discussion of Green's functions in curved spacetime (part III). The review concludes with a detailed derivation of each of the three equations of motion (part IV).Comment: LaTeX2e, 116 pages, 10 figures. This is the final version, as it will appear in Living Reviews in Relativit

Regulatory Architecture of the Neuronal Cacng2/Tarpγ2 Gene Promoter: Multiple Repressive Domains, a Polymorphic Regulatory Short Tandem Repeat, and Bidirectional Organization with Co-regulated lncRNAs

CACNG2 (TARPγ2, Stargazin) is a multi-functional regulator of excitatory neurotransmission and has been implicated in the pathological processes of several brain diseases. Cacng2 function is dependent upon expression level, but currently, little is known about the molecular mechanisms that control expression of this gene. To address this deficit and investigate disease-related gene variants, we have cloned and characterized the rat Cacng2 promoter and have defined three major features: (i) multiple repressive domains that include an array of RE-1 silencing transcription factor (REST) elements, and a calcium regulatory element-binding factor (CaRF) element, (ii) a (poly-GA) short tandem repeat (STR), and (iii) bidirectional organization with expressed lncRNAs. Functional activity of the promoter was demonstrated in transfected neuronal cell lines (HT22 and PC12), but although selective removal of REST and CaRF domains was shown to enhance promoter-driven transcription, the enhanced Cacng2 promoter constructs were still about fivefold weaker than a comparable rat Synapsin-1 promoter sequence. Direct evidence of REST activity at the Cacng2 promoter was obtained through co-transfection with an established dominant-negative REST (DNR) construct. Investigation of the GA-repeat STR revealed polymorphism across both animal strains and species, and size variation was also observed in absence epilepsy disease model cohorts (Genetic Absence Epilepsy Rats, Strasbourg [GAERS] and non-epileptic control [NEC] rats). These data provide evidence of a genotype (STR)-phenotype correlation that may be unique with respect to proximal gene regulatory sequence in the demonstrated absence of other promoter, or 3′ UTR variants in GAERS rats. However, although transcriptional regulatory activity of the STR was demonstrated in further transfection studies, we did not find a GAERS vs. NEC difference, indicating that this specific STR length variation may only be relevant in the context of other (Cacna1h and Kcnk9) gene variants in this disease model. Additional studies revealed further (bidirectional) complexity at the Cacng2 promoter, and we identified novel, co-regulated, antisense rat lncRNAs that are paired with Cacng2 mRNA. These studies have provided novel insights into the organization of a synaptic protein gene promoter, describing multiple repressive and modulatory domains that can mediate diverse regulatory inputs