Treecodes for Potential and Force Approximations

N-body problems encompass a variety of fields such as electrostatics, molecularbiology and astrophysics. If there are N particles in the system, the brute force algorithmfor these problems based on particle-particle interaction takes O(N2), whichis clearly expensive for large values of N. There have been some approximation algorithmslike the Barnes-Hut Method and the Fast Multipole Method (FMM) proposedfor these problems to reduce the complexity. However, the applicability of these algorithmsare limited to operators with analytic multipole expansions or restricted tosimulations involving low accuracy. The shortcoming of N-body treecodes are moreevident for particles in motion where the movement of the particles are not consideredwhen evaluating the potential. If the displacement of the particles are small, thenupdating the multipole coefficients for all the nodes in the tree may not be requiredfor computing the potential to a reasonable accuracy. This study focuses on some ofthe limitations of the existing approximation schemes and presents new algorithmsthat can be used for N-body simulations to efficiently compute potentials and forces.In the case of electrostatics, existing algorithms use Cartesian coordinates to evaluatethe potentials of the form r−, where 1. The use of such coordinates toseparate the variables results in cumbersome expressions and does not exploit the inherent spherical symmetry found in these kernels. For such potentials, we providea new multipole expansion series and construct a method which is asymptoticallysuperior than the current treecodes. The advantage of this expansion series is furtherdemonstrated by an algorithm that can compute the forces to the desired accuracy.For particles in motion, we introduce a new method in which we retain the multipolecoefficients when performing multipole updates (to the parent nodes) at every timestep. This results in considerable savings in time while maintaining the accuracy. Wefurther illustrate the efficiency of our algorithms through numerical experiments

Spatial Context of Tumor Immune Microenvironment of Matched Primary and Recurrent Glioblastomas

https://openworks.mdanderson.org/sumexp22/1078/thumbnail.jp

Spatial modelling of the tumor microenvironment from multiplex immunofluorescence images: methods and applications

Spatial modelling methods have gained prominence with developments in high throughput imaging platforms. Multiplex immunofluorescence (mIF) provides the scope to examine interactions between tumor and immune compartment at single cell resolution using a panel of antibodies that can be chosen based on the cancer type or the clinical interest of the study. The markers can be used to identify the phenotypes and to examine cellular interactions at global and local scales. Several translational studies rely on key understanding of the tumor microenvironment (TME) to identify drivers of immune response in immunotherapy based clinical trials. To improve the success of ongoing trials, a number of retrospective approaches can be adopted to understand differences in response, recurrence and progression by examining the patient’s TME from tissue samples obtained at baseline and at various time points along the treatment. The multiplex immunofluorescence (mIF) technique provides insight on patient specific cell populations and their relative spatial distribution as qualitative measures of a favorable treatment outcome. Spatial analysis of these images provides an understanding of the intratumoral heterogeneity and clustering among cell populations in the TME. A number of mathematical models, which establish clustering as a measure of deviation from complete spatial randomness, can be applied to the mIF images represented as spatial point patterns. These mathematical models, developed for landscape ecology and geographic information studies, can be applied to the TME after careful consideration of the tumor type (cold vs. hot) and the tumor immune landscape. The spatial modelling of mIF images can show observable engagement of T cells expressing immune checkpoint molecules and this can then be correlated with single-cell RNA sequencing data

Transcriptional diversity of long-term glioblastoma survivors

BACKGROUND: Glioblastoma (GBM) is a highly aggressive type of glioma with poor prognosis. However, a small number of patients live much longer than the median survival. A better understanding of these long-term survivors (LTSs) may provide important insight into the biology of GBM. METHODS: We identified 7 patients with GBM, treated at Memorial Sloan-Kettering Cancer Center (MSKCC), with survival \u3e48 months. We characterized the transcriptome of each patient and determined rates of MGMT promoter methylation and IDH1 and IDH2 mutational status. We identified LTSs in 2 independent cohorts (The Cancer Genome Atlas [TCGA] and NCI Repository for Molecular Brain Neoplasia Data [REMBRANDT]) and analyzed the transcriptomal characteristics of these LTSs. RESULTS: The median overall survival of our cohort was 62.5 months. LTSs were distributed between the proneural (n = 2), neural (n = 2), classical (n = 2), and mesenchymal (n = 1) subtypes. Similarly, LTS in the TCGA and REMBRANDT cohorts demonstrated diverse transcriptomal subclassification identities. The majority of the MSKCC LTSs (71%) were found to have methylation of the MGMT promoter. None of the patients had an IDH1 or IDH2 mutation, and IDH mutation occurred in a minority of the TCGA LTSs as well. A set of 60 genes was found to be differentially expressed in the MSKCC and TCGA LTSs. CONCLUSIONS: While IDH mutant proneural tumors impart a better prognosis in the short-term, survival beyond 4 years does not require IDH mutation and is not dictated by a single transcriptional subclass. In contrast, MGMT methylation continues to have strong prognostic value for survival beyond 4 years. These findings have substantial impact for understanding GBM biology and progression

DNA methylation-based classification of central nervous system tumours.

Accurate pathological diagnosis is crucial for optimal management of patients with cancer. For the approximately 100 known tumour types of the central nervous system, standardization of the diagnostic process has been shown to be particularly challenging-with substantial inter-observer variability in the histopathological diagnosis of many tumour types. Here we present a comprehensive approach for the DNA methylation-based classification of central nervous system tumours across all entities and age groups, and demonstrate its application in a routine diagnostic setting. We show that the availability of this method may have a substantial impact on diagnostic precision compared to standard methods, resulting in a change of diagnosis in up to 12% of prospective cases. For broader accessibility, we have designed a free online classifier tool, the use of which does not require any additional onsite data processing. Our results provide a blueprint for the generation of machine-learning-based tumour classifiers across other cancer entities, with the potential to fundamentally transform tumour pathology

Nuclear cGMP-Dependent Kinase Regulates Gene Expression via Activity-Dependent Recruitment of a Conserved Histone Deacetylase Complex

Elevation of the second messenger cGMP by nitric oxide (NO) activates the cGMP-dependent protein kinase PKG, which is key in regulating cardiovascular, intestinal, and neuronal functions in mammals. The NO-cGMP-PKG signaling pathway is also a major therapeutic target for cardiovascular and male reproductive diseases. Despite widespread effects of PKG activation, few molecular targets of PKG are known. We study how EGL-4, the Caenorhabditis elegans PKG ortholog, modulates foraging behavior and egg-laying and seeks the downstream effectors of EGL-4 activity. Using a combination of unbiased forward genetic screen and proteomic analysis, we have identified a conserved SAEG-1/SAEG-2/HDA-2 histone deacetylase complex that is specifically recruited by activated nuclear EGL-4. Gene expression profiling by microarrays revealed >40 genes that are sensitive to EGL-4 activity in a SAEG-1–dependent manner. We present evidence that EGL-4 controls egg laying via one of these genes, Y45F10C.2, which encodes a novel protein that is expressed exclusively in the uterine epithelium. Our results indicate that, in addition to cytoplasmic functions, active EGL-4/PKG acts in the nucleus via a conserved Class I histone deacetylase complex to regulate gene expression pertinent to behavioral and physiological responses to cGMP. We also identify transcriptional targets of EGL-4 that carry out discrete components of the physiological response

Why do mutant allele frequencies in oncogenes peak around .40 and rapidly decrease?

<p>The mutant allele frequencies in oncogenes peak around .40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we estimate the selection coefficients of the mutant alleles as a function of germline allele frequencies. Under complete dominance of oncogenic mutations, this selection function is expected to be linearly correlated with the distribution of the mutant alleles. We demonstrate that this is the case by investigating the allele frequencies of mutations in oncogenes across various cancer types, validating our model for mean effective selection. Consistent with the population genetics model of fitness, the selection function fits a gamma-distribution curve that accurately describes the trend of the mutant allele frequencies. While existing equations for selection explain evolution at low allele frequencies, our equations are general formulas for natural selection under complete dominance operating at all frequencies. We show that selection exhibits linear behaviour at all times, favouring dominant alleles with respect to the change in recessive allele frequencies. Also, these equations show, selection behaves like power law against the recessive alleles at low dominant allele frequencies.</p

Gibbs process distinguishes survival and reveals contact-inhibition genes in Glioblastoma multiforme.

Tumor growth is a spatiotemporal birth-and-death process with loss of heterotypic contact-inhibition of locomotion (CIL) of tumor cells promoting invasion and metastasis. Therefore, representing tumor cells as two-dimensional points, we can expect the tumor tissues in histology slides to reflect realizations of spatial birth-and-death process which can be mathematically modeled to reveal molecular mechanisms of CIL, provided the mathematics models the inhibitory interactions. Gibbs process as an inhibitory point process is a natural choice since it is an equilibrium process of the spatial birth-and-death process. That is if the tumor cells maintain homotypic contact inhibition, the spatial distributions of tumor cells will result in Gibbs hard core process over long time scales. In order to verify if this is the case, we applied the Gibbs process to 411 TCGA Glioblastoma multiforme patient images. Our imaging dataset included all cases for which diagnostic slide images were available. The model revealed two groups of patients, one of which - the "Gibbs group," showed the convergence of the Gibbs process with significant survival difference. Further smoothing the discretized (and noisy) inhibition metric, for both increasing and randomized survival time, we found a significant association of the patients in the Gibbs group with increasing survival time. The mean inhibition metric also revealed the point at which the homotypic CIL establishes in tumor cells. Besides, RNAseq analysis between patients with loss of heterotypic CIL and intact homotypic CIL in the Gibbs group unveiled cell movement gene signatures and differences in Actin cytoskeleton and RhoA signaling pathways as key molecular alterations. These genes and pathways have established roles in CIL. Taken together, our integrated analysis of patient images and RNAseq data provides for the first time a mathematical basis for CIL in tumors, explains survival as well as uncovers the underlying molecular landscape for this key tumor invasion and metastatic phenomenon