A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Diet-induced obesity alters the differentiation potential of stem cells isolated from bone marrow, adipose tissue and infrapatellar fat pad: the effects of free fatty acids.

INTRODUCTION: Obesity is a major risk factor for several musculoskeletal conditions that are characterized by an imbalance of tissue remodeling. Adult stem cells are closely associated with the remodeling and potential repair of several mesodermally derived tissues such as fat, bone and cartilage. We hypothesized that obesity would alter the frequency, proliferation, multipotency and immunophenotype of adult stem cells from a variety of tissues. MATERIALS AND METHODS: Bone marrow-derived mesenchymal stem cells (MSCs), subcutaneous adipose-derived stem cells (sqASCs) and infrapatellar fat pad-derived stem cells (IFP cells) were isolated from lean and high-fat diet-induced obese mice, and their cellular properties were examined. To test the hypothesis that changes in stem cell properties were due to the increased systemic levels of free fatty acids (FFAs), we further investigated the effects of FFAs on lean stem cells in vitro. RESULTS: Obese mice showed a trend toward increased prevalence of MSCs and sqASCs in the stromal tissues. While no significant differences in cell proliferation were observed in vitro, the differentiation potential of all types of stem cells was altered by obesity. MSCs from obese mice demonstrated decreased adipogenic, osteogenic and chondrogenic potential. Obese sqASCs and IFP cells showed increased adipogenic and osteogenic differentiation, but decreased chondrogenic ability. Obese MSCs also showed decreased CD105 and increased platelet-derived growth factor receptor α expression, consistent with decreased chondrogenic potential. FFA treatment of lean stem cells significantly altered their multipotency but did not completely recapitulate the properties of obese stem cells. CONCLUSIONS: These findings support the hypothesis that obesity alters the properties of adult stem cells in a manner that depends on the cell source. These effects may be regulated in part by increased levels of FFAs, but may involve other obesity-associated cytokines. These findings contribute to our understanding of mesenchymal tissue remodeling with obesity, as well as the development of autologous stem cell therapies for obese patients.

WNT3 is a biomarker capable of predicting the definitive endoderm differentiation potential of hESCs.

Generation of functional cells from human pluripotent stem cells (PSCs) through in vitro differentiation is a promising approach for drug screening and cell therapy. However, the observed large and unavoidable variation in the differentiation potential of different human embryonic stem cell (hESC)/induced PSC (iPSC) lines makes the selection of an appropriate cell line for the differentiation of a particular cell lineage difficult. Here, we report identification of WNT3 as a biomarker capable of predicting definitive endoderm (DE) differentiation potential of hESCs. We show that the mRNA level of WNT3 in hESCs correlates with their DE differentiation efficiency. In addition, manipulations of hESCs through WNT3 knockdown or overexpression can respectively inhibit or promote DE differentiation in a WNT3 level-dependent manner. Finally, analysis of several hESC lines based on their WNT3 expression levels allowed accurate prediction of their DE differentiation potential. Collectively, our study supports the notion that WNT3 can serve as a biomarker for predicting DE differentiation potential of hESCs.

Differentiation of mouse induced pluripotent stem cells (iPSCs) into nucleus pulposus-like cells in vitro.

A large percentage of the population may be expected to experience painful symptoms or disability associated with intervertebral disc (IVD) degeneration - a condition characterized by diminished integrity of tissue components. Great interest exists in the use of autologous or allogeneic cells delivered to the degenerated IVD to promote matrix regeneration. Induced pluripotent stem cells (iPSCs), derived from a patient's own somatic cells, have demonstrated their capacity to differentiate into various cell types although their potential to differentiate into an IVD cell has not yet been demonstrated. The overall objective of this study was to assess the possibility of generating iPSC-derived nucleus pulposus (NP) cells in a mouse model, a cell population that is entirely derived from notochord. This study employed magnetic activated cell sorting (MACS) to isolate a CD24(+) iPSC subpopulation. Notochordal cell-related gene expression was analyzed in this CD24(+) cell fraction via real time RT-PCR. CD24(+) iPSCs were then cultured in a laminin-rich culture system for up to 28 days, and the mouse NP phenotype was assessed by immunostaining. This study also focused on producing a more conducive environment for NP differentiation of mouse iPSCs with addition of low oxygen tension and notochordal cell conditioned medium (NCCM) to the culture platform. iPSCs were evaluated for an ability to adopt an NP-like phenotype through a combination of immunostaining and biochemical assays. Results demonstrated that a CD24(+) fraction of mouse iPSCs could be retrieved and differentiated into a population that could synthesize matrix components similar to that in native NP. Likewise, the addition of a hypoxic environment and NCCM induced a similar phenotypic result. In conclusion, this study suggests that mouse iPSCs have the potential to differentiate into NP-like cells and suggests the possibility that they may be used as a novel cell source for cellular therapy in the IVD.

Wnt Protein Signaling Reduces Nuclear Acetyl-CoA Levels to Suppress Gene Expression during Osteoblast Differentiation.

Developmental signals in metazoans play critical roles in inducing cell differentiation from multipotent progenitors. The existing paradigm posits that the signals operate directly through their downstream transcription factors to activate expression of cell type-specific genes, which are the hallmark of cell identity. We have investigated the mechanism through which Wnt signaling induces osteoblast differentiation in an osteoblast-adipocyte bipotent progenitor cell line. Unexpectedly, Wnt3a acutely suppresses the expression of a large number of genes while inducing osteoblast differentiation. The suppressed genes include Pparg and Cebpa, which encode adipocyte-specifying transcription factors and suppression of which is sufficient to induce osteoblast differentiation. The large scale gene suppression induced by Wnt3a corresponds to a global decrease in histone acetylation, an epigenetic modification that is associated with gene activation. Mechanistically, Wnt3a does not alter histone acetyltransferase or deacetylase activities but, rather, decreases the level of acetyl-CoA in the nucleus. The Wnt-induced decrease in histone acetylation is independent of β-catenin signaling but, rather, correlates with suppression of glucose metabolism in the tricarboxylic acid cycle. Functionally, preventing histone deacetylation by increasing nucleocytoplasmic acetyl-CoA levels impairs Wnt3a-induced osteoblast differentiation. Thus, Wnt signaling induces osteoblast differentiation in part through histone deacetylation and epigenetic suppression of an alternative cell fate.