Clique topology reveals intrinsic geometric structure in neural correlations

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.Neural activity and connectivity data are often presented in the form of a matrix whose entries, C_ij,  indicate the strength of correlation or connectivity between pairs of neurons, cell types, or imaging voxels. Detecting structure in such a matrix is a critical step toward understanding the organization and function of the underlying neural circuits. In this work, we focus on neural activity, whose structure may reflect the coding properties of neurons, rather than their physical locations within the brain. For example, place cells in rodent hippocampus act as position sensors, exhibiting a high firing rate when the animal’s position lies inside the neuron’s “place field,” its preferred region of the spatial environment (1). Without knowledge of the coding properties, however, it is unclear whether such a geometric organization could be detected purely from the pattern of neural correlations. Alternatively, a correlation or connectivity matrix could be truly unstructured, such as the connectivity pattern observed in the fly olfactory system (2), indicating random network organization.Can we distinguish these possibilities, using only the intrinsic features of the matrix C_ij? The most common approach is to use standard tools from matrix analysis that rely on quantities, such as eigenvalues, that are invariant under linear change of basis. This strategy is natural in physics, where meaningful quantities should be preserved by linear coordinate transformations. In contrast, measurements in biological settings are often obtained as nonlinear transformations of the underlying “real” variables, whereas the choice of basis is meaningful and fixed. For example, basis elements might represent particular neurons or genes, and measurements (matrix elements) could consist of pairwise correlations in neural activity, or the coexpression of pairs of genes. Instead of change of basis, the relevant structure in these data should be invariant under matrix transformations of the following form:C_ij = f(A_ij), [1]where f is a nonlinear monotonic function (Fig. 1A). In the case of hippocampal place cells, f captures the manner in which pairwise correlations C_ij decrease with distance between place field centers (3). In less studied contexts, the represented stimuli—and the function f—may be completely unknown.Open in a separate windowFig. 1.Order-based analysis of symmetric matrices. (A) A symmetric matrix A is related to another matrix C via a nonlinear monotonically increasing function f(x), applied entrywise. (B, Left) Distribution of eigenvalues for a random symmetric N × N matrix A,  whose entries were drawn independently from the normal distribution with zero mean and variance 1/N (N = 500). (Right) Distribution of eigenvalues for the transformed matrix with entries C_ij = f(A_ij), for f(x) = 1 ? e^?30x. Red curves show Wigner’s semicircle distribution with matching mean and variance. (C, Top) The order complex of A is represented as a sequence of binary adjacency matrices, indexed by the density ρ of nonzero entries. (Bottom) Graphs corresponding to the adjacency matrices. Minimal examples of a 1-cycle (yellow square), a 2-cycle (red octahedron), and a 3-cycle (blue orthoplex) appear at ρ = 0.1, 0.25,  and 0.45, respectively. (D) At edge density ρ₀, there are no cycles. Cliques of size 3 and 4 are depicted with light and dark gray shading. As the edge density increases, a new 1-cycle (yellow) is created, persists, and is eventually destroyed at densities ρ₁, ρ₂,  and ρ₃, respectively. (E) For a distribution of 1,000 random N × N symmetric matrices (N = 88), average Betti curves β₁(ρ), β₂(ρ),  and β₃(ρ) are shown (yellow, red, and blue dashed curves), together with 95% confidence intervals (shaded areas).Unfortunately, eigenvalues are not invariant under transformations of the form (Eq. 1) (Fig. 1B and SI Appendix, Fig. S1). Although large random matrices have a reliable eigenvalue spectrum [e.g., Wigner’s semicircle law (4)], it is possible that a random matrix with independent and identically distributed (i.i.d.) entries could be mistaken as structured, purely as an artifact of a monotonic nonlinearity (Fig. 1B).^* The results of eigenvalue-based analyses can thus be difficult to interpret, and potentially misleading.Here, we introduce a new tool to reliably detect signatures of structure and randomness that are invariant under nonlinear monotone transformations of the form (Eq. 1). Using pairwise correlations of hippocampal place cells recorded during both spatial and nonspatial behaviors, we demonstrate that our method is capable of detecting geometric structure from neural activity alone. To our knowledge, this is the first example of a method that detects geometric organization intrinsically from neural activity, without appealing to external stimuli or receptive fields.     

Homologous trans-editing factors with broad tRNA specificity prevent mistranslation caused by serine/threonine misactivation

Aminoacyl-tRNA synthetases (ARSs) establish the rules of the genetic code, whereby each amino acid is attached to a cognate tRNA. Errors in this process lead to mistranslation, which can be toxic to cells. The selective forces exerted by species-specific requirements and environmental conditions potentially shape quality-control mechanisms that serve to prevent mistranslation. A family of editing factors that are homologous to the editing domain of bacterial prolyl-tRNA synthetase includes the previously characterized trans-editing factors ProXp-ala and YbaK, which clear Ala-tRNA^Pro and Cys-tRNA^Pro, respectively, and three additional homologs of unknown function, ProXp-x, ProXp-y, and ProXp-z. We performed an in vivo screen of 230 conditions in which an Escherichia coli proXp-y deletion strain was grown in the presence of elevated levels of amino acids and specific ARSs. This screen, together with the results of in vitro deacylation assays, revealed Ser- and Thr-tRNA deacylase function for this homolog. A similar activity was demonstrated for Bordetella parapertussis ProXp-z in vitro. These proteins, now renamed “ProXp-ST1” and “ProXp-ST2,” respectively, recognize multiple tRNAs as substrates. Taken together, our data suggest that these free-standing editing domains have the ability to prevent mistranslation errors caused by a number of ARSs, including lysyl-tRNA synthetase, threonyl-tRNA synthetase, seryl-tRNA synthetase, and alanyl-tRNA synthetase. The expression of these multifunctional enzymes is likely to provide a selective growth advantage to organisms subjected to environmental stresses and other conditions that alter the amino acid pool.A high level of accuracy in protein synthesis is essential for normal cell function and proliferation. A critical step in this process is pairing the correct amino acid with the cognate tRNA species by aminoacyl-tRNA synthetases (ARSs). ARSs catalyze the aminoacyl-tRNA (aa-tRNA) formation in two steps involving amino acid activation (step 1) and transfer of the activated amino acid to tRNAs (step 2). Although ARSs have evolved to exhibit specific tRNA-recognition capabilities with an estimated error frequency of 10⁻⁶, a greater number of mistakes arise from the lack of discrimination of near-cognate amino acids, with an estimated error rate of 10⁻⁴ to 10⁻⁵ at this step (1). Misincorporation of amino acids into proteins can be harmful to both eukaryotic and prokaryotic cells (2, 3).Quality control of aa-tRNA formation is achieved by hydrolysis of the aminoacyl-adenylate (“pre-transfer editing”) or deacylation of the mischarged aa-tRNA (“post-transfer editing”) (4, 5). Editing mechanisms are used by both classes of ARSs, and 7 of 22 ARSs possess posttransfer editing sites that are distinct from the aminoacylation active site. The connective polypeptide 1 editing domain is found in class I isoleucyl-tRNA synthetase (IleRS) (6), leucyl-tRNA synthetase (LeuRS) (7, 8), and valyl-tRNA synthetase (ValRS) (9). Editing domains of class II ARSs are more diverse and include the N-terminal domain of threonyl-tRNA synthetase (ThrRS) (10), the related editing domain of alanyl-tRNA synthetase (AlaRS) (11), the β3/ β4 domain of phenylalanine-tRNA synthetase (12), and the insertion domain (INS) of prolyl-tRNA synthetase (ProRS) (13, 14). Mutations in editing domains can have detrimental effects on cells. For example, a mutation in the editing site of AlaRS, which results in only a twofold increase in misacylation in vitro, results in a severe neurodegeneration phenotype in mice (15). Cellular degradation and apoptosis caused by a mutation in the editing domain of ValRS have been reported in murine cells (16). In addition, editing defects in bacteria often result in slower growth rates, delayed growth, or even death (17–22).In addition to the cis-editing domain appended to ARSs, free-standing homologs of editing domains are distributed throughout organisms in all three kingdoms of life as additional checkpoints to maintain translational fidelity in trans. Autonomous trans-editing factors that are evolutionarily related to three class II ARSs, namely, AlaRS, ThrRS and ProRS, have been identified. A homolog of the AlaRS editing domain, AlaXp, is widely distributed and is shown to hydrolyze seryl-tRNA synthetase (Ser-tRNA^Ala) (23, 24). ThrRS-ed is an autonomous editing domain of Ser-tRNA^Thr in crenarchaeal genomes where thrS genes are truncated (25). Bacterial ProRS INS domain homologs include five proteins previously named “YbaK,” “ProXp-ala,” “ProXp-x,” “ProXp-y” (annotated YeaK), and “ProXp-z” (annotated PA2301) (Fig. 1) (26). These domains together with the INS domain of ProRS are collectively known as the “INS superfamily.” Although the INS domain edits mischarged Ala-tRNA^Pro (13, 14), YbaK deacylates Cys-tRNA^Pro (27), which is formed in the active site of ProRS because of the similar size of Cys and Pro (28). ProXp-ala is capable of clearing Ala-tRNA^Pro and compensates for the lack of an INS posttransfer editing domain in many bacteria (23, 26). Functions for ProXp-x, -y, and -z have not yet been reported. Here, for the first time to our knowledge, we explore the in vivo and in vitro substrate specificities of ProXp-y and ProXp-z. These two domains are phylogenetically distinct (26) and differ in length and in the identity of several highly conserved residues. Most notably, proXp-y encodes a functionally critical Lys residue that is present in all other INS superfamily members with the exception of proXp-z, which instead contains a strictly conserved Asn (26).Open in a separate windowFig. 1.Domain structure of E. coli and B. parapertussis ProRS and the INS superfamily. Conserved motifs 1, 2, and 3 (M1–M3, purple), the anticodon-binding domain (ABD, green), and the editing domain (INS domain, blue) are shown. Single-domain INS-like proteins YbaK, ProXp-ala, ProXp-x, ProXp-y, and ProXp-z encoded in the indicated species are shown together with the INS and a truncated mini-INS present in the corresponding ProRS. C. crescentus is Caulobacter crescentus, and R. palustris is Rhodopseudomonas palustris. The known activities of INS, YbaK, and ProXp-ala are color coded as follows: blue, Ala deacylation; red, Cys deacylation. The domains investigated in this work are in orange, and domains of unknown function are in gray.     

Implementing an Innovative Cardiac Assist System in a Nonuniversity Hospital—Feasibility,Complications, and First Results

To evaluate the feasibility of implementing a cardiac assist system in a nonuniversity hospital we analyzed 18 consecutive patients treated with venoarterial membrane oxygenation. The system was used electively in 5/18 (27.8%) patients during high‐risk interventions. Thirteen patients (72.2%) were treated in emergency situations. The extracorporal system could be initiated successfully in all patients. Periprocedural complications were hemolysis in 3/18 (16.7%), disseminated intravascular coagulation in 2/18 (11.1%), cerebral ischemia in 1/18 (5.6%), and local infection in 2/18 (11.1%) patients. None of these led to a discontinuation of the therapy. All electively treated patients were successfully weaned from the extracorporeal system. In 9/13 (69.2%) emergency patients the system was removed successfully. The 60‐day survival rate of the emergency patients was 53.8% (7/13). Our experience confirms that an innovative extracorporeal circulatory support system can be implemented in a nonuniversity hospital at a tolerable risk and a low complication and high procedural success rate.     

Malignant Adenomyoepithelioma of the Breast: A Review

Malignant adenomyoepithelioma (MAME) of the breast is a rare lesion characterized by dual population of epithelial and myoepithelial cells which one or both components show malignant features. We report a case of MAME of the breast in a 46‐year‐old woman diagnosed by fine‐needle aspiration with extensive review of the literature. Classification, clinical presentation, cyto‐pathologic, and immunohistochemical features are described. This lesion showed both malignant components of epithelial and myoepithelial cells in cytology and histology. The malignancy was convincingly supported by high mitotic figures, pleomorphism, and invasion in tissue sections. This review of MAMEs showed that cyto‐histologic diagnosis is difficult and should be supported by immunohistochemical study.     

The Effect of Radiation on Complication Rates and Patient Satisfaction in Breast Reconstruction using Temporary Tissue Expanders and Permanent Implants

The optimal method of reconstruction following mastectomy for breast cancer patients receiving radiation therapy (RT) is controversial. This study evaluated patient satisfaction and complication rates among patients who received implant‐based breast reconstruction. The specific treatment algorithm analyzed included patients receiving mastectomy and immediate temporary tissue expander (TE), followed by placement of a permanent breast implant (PI). If indicated, RT was delivered to the fully expanded TE. Records of 218 consecutive patients with 222 invasive (85%) or in situ (15%) breast lesions from the Salt Lake City region treated between 1998 and 2009 were retrospectively reviewed, 28% of whom received RT. Median RT dose was 50.4 Gy, and 41% received a scar boost at a median dose of 10 Gy. Kaplan–Meier analyses were performed to evaluate the cumulative incidence of surgical complications, including permanent PI removal. Risk factors associated with surgical events were analyzed. To evaluate cosmetic results and patient satisfaction, an anonymous survey was administered. Mean follow‐up was 44 months (range 6–144). Actuarial 5‐year PI removal rates for non‐RT and RT patients were 4% and 22%, respectively. On multivariate analysis (MVA), the only factor associated with PI removal was RT (p = 0.009). Surveys were returned describing the outcomes of 149 breasts. For the non‐RT and RT groups, those who rated their breast appearance as good or better were 63% versus 62%, respectively. Under 1/3 of each group was dissatisfied with their reconstruction. RT did not significantly affect patient satisfaction scores, but on MVA RT was the only factor associated with increased PI removal. This reconstruction technique may be considered an acceptable option even if RT is needed, but the increased complication risk with RT must be recognized.