Breakdown of Random-Matrix Universality in Persistent Lotka-Volterra Communities.

The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed without proof in applications. In this Letter, we offer a pertinent counterexample in the context of the generalized Lotka-Volterra equations. Using dynamic mean-field theory, we derive the statistics of the interactions between species in an evolved ecological community. We then show that the full statistics of these interactions, beyond those of a Gaussian ensemble, are required to correctly predict the eigenvalue spectrum and therefore stability. Consequently, the universality principle fails in this system. We thus show that the eigenvalue spectra of random matrices can be used to deduce the stability of "feasible" ecological communities, but only if the emergent non-Gaussian statistics of the interactions between species are taken into account.

Eigenvalues of Random Matrices with Generalized Correlations: A Path Integral Approach.

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical systems. In this Letter, we study the eigenvalue spectrum of an ensemble of random matrices with correlations between any pair of elements. To this end, we introduce an analytical method that maps the resolvent of the random matrix onto the response functions of a linear dynamical system. The response functions are then evaluated using a path integral formalism, enabling us to make deductions about the eigenvalue spectrum. Our central result is a simple, closed-form expression for the leading eigenvalue of a large random matrix with generalized correlations. This formula demonstrates that correlations between matrix elements that are not diagonally opposite, which are often neglected, can have a significant impact on stability.

Analytical and Numerical Treatment of Continuous Ageing in the Voter Model.

The conventional voter model is modified so that an agent's switching rate depends on the 'age' of the agent-that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Markovian dynamics and concentration-dependent rates can be handled both computationally and analytically. The thinning algorithm of Lewis and Shedler can be modified in order to provide an efficient simulation method. Analytically, we demonstrate how the asymptotic approach to an absorbing state (consensus) can be deduced. We discuss three special cases of the age-dependent switching rate: one in which the concentration of voters can be approximated by a fractional differential equation, another for which the approach to consensus is exponential in time, and a third case in which the system reaches a frozen state instead of consensus. Finally, we include the effects of a spontaneous change of opinion, i.e., we study a noisy voter model with continuous ageing. We demonstrate that this can give rise to a continuous transition between coexistence and consensus phases. We also show how the stationary probability distribution can be approximated, despite the fact that the system cannot be described by a conventional master equation.

Quercetin Therapy for Selected Patients with PIM1 Kinase-Positive Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma: A Pilot Study.

We reported that PIM1 kinase is expressed in the lymphocytes of patients with chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL). Quercetin, a naturally occurring flavonoid, is a dietary supplement and inhibits many kinases, including PIM1, in vitro. Under an Institutional Review Board-approved protocol, we performed an open-label, single-arm pilot study to evaluate the antitumor activity of quercetin in patients with CLL/SLL. Q-ForceTM chews were administered orally, 500 mg twice daily, for 3 months. Eligible patients had failed prior therapies, had had no other standard treatment, or refused other therapies. Response was assessed based on objective change in disease parameters. Patients were included if their lymphocyte counts were rising and ≥10,000/µL but not > 100,000/µL. Three patients received quercetin treatment. There was no toxicity. Two responded with stabilization of rising lymphocyte counts (p < 0.001 for each), which remained stable during their follow-up (5 and 11 months after cessation of treatment, respectively). The CLL cells in the nonresponder harbored a TP53 mutation. Although our data from this pilot translational study are based on a small sample, further studies of quercetin as a potential therapeutic agent in selected patients with CLL/SLL appear warranted.

The ITM2B (BRI2) gene is a target of BCL6 repression: Implications for lymphomas and neurodegenerative diseases.

The human BCL6 gene encodes a transcriptional repressor that is crucial for germinal center B cell development and T follicular helper cell differentiation. It is involved in the pathogenesis of certain human lymphomas. In an effort to identify targets of BCL6 repression, we used a previously described cell system in which BCL6 repressive effects are inhibited, followed by subtractive hybridization, and identified the integral membrane 2B gene (ITM2B, formerly BRI2) as a potential target. Here we show that BCL6 can bind to its preferential consensus binding site within the first intron of ITM2B and represses its transcription. Knockdown of endogenous BCL6 in a human B cell lymphoma line increases ITM2B expression. Further, there is an inverse relationship between the expression levels of BCL6 and ITM2B proteins in 16 human B- and T-cell lymphomas studied by immunohistochemistry. Both the BCL6 and ITM2B proteins are expressed ubiquitously. Similar to some other targets of BCL6, a short form of the ITM2B protein generated by alternative splicing induces apoptosis in hematopoietic cell lines. Molecular alterations in the ITM2B gene are associated with two neurodegenerative diseases, Familial British and Familial Danish dementia. ITM2B dysfunction also may be relevant for the development of Alzheimer's disease. Our data confirm ITM2B as a target of BCL6 repression in lymphoma. A further understanding of the genes that function as regulators of the ITM2B protein may provide insights for the development of new molecular tools not only for targeted lymphoma therapy but also for the treatment of these dementias.

PIM1 gene cooperates with human BCL6 gene to promote the development of lymphomas.

Diffuse large B-cell lymphomas in humans are associated with chromosomal rearrangements (∼40%) and/or mutations disrupting autoregulation (∼16%) involving the BCL6 gene. Studies of lymphoma development in humans and mouse models have indicated that lymphomagenesis evolves through the accumulation of multiple genetic alterations. Based on our prior studies, which indicated that carcinogen-induced DNA mutations enhance the incidence of lymphomas in our mouse model expressing a human BCL6 transgene, we hypothesized that mutated genes are likely to play an important cooperative role in BCL6-associated lymphoma development. We used retroviral insertional mutagenesis in an effort to identify which genes cooperate with BCL6 in lymphomagenesis in our BCL6 transgenic mice. We identified PIM1 as the most frequently recurring cooperating gene in our murine BCL6-associated lymphomas (T- and B-cell types), and we observed elevated levels of PIM1 mRNA and protein expression in these neoplasms. Further, immunohistochemical staining, which was performed in 20 randomly selected BCL6-positive human B- and T-cell lymphomas, revealed concurrent expression of BCL6 and PIM1 in these neoplasms. As PIM1 encodes a serine/threonine kinase, PIM1 kinase inhibition may be a promising therapy for BCL6/PIM1-positive human lymphomas.

GFI1B, EVI5, MYB--additional genes that cooperate with the human BCL6 gene to promote the development of lymphomas.

The BCL6 gene, which is expressed in certain B- and T-cell human lymphomas, is involved with chromosomal rearrangements and mutations in a number of these neoplasms. Lymphomagenesis is believed to evolve through a multi-step accumulation of genetic alterations in these tumors. We used retroviral insertional mutagenesis in transgenic mice expressing the human BCL6 transgene in order to identify genes that cooperate with BCL6 during lymphomatous transformation. We previously reported PIM1 as the most frequently recurring cooperating gene in this model. We now report three newly identified cooperating genes-GFI1B, EVI5, and MYB-that we identified in the lymphomas of retroviral-injected BCL6 transgenic mice (but not in retroviral-injected non-transgenic controls); mRNA and protein expression of GFI1B and EVI5 were decreased in the murine tumors, whereas MYB mRNA and protein expression were increased or decreased. These findings correlated with protein expression in human lymphomas, both B- and T-cell. Improved therapy of lymphomas may necessitate the development of combinations of drugs that target the alterations specific to each neoplasm.

Eigenvalue spectra of finely structured random matrices.

Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are applicable in a myriad of different contexts. However, it is often assumed that all components of the complex system in question are statistically equivalent, which is unrealistic in many applications. Here we introduce the concept of a finely structured random matrix. These are random matrices with element-specific statistics, which can be used to model systems in which the individual components are statistically distinct. By supposing that the degree of "fine structure" in the matrix is small, we arrive at a succinct "modified" elliptical law. We demonstrate the direct applicability of our results to the niche and cascade models in theoretical ecology, as well as a model of a neural network, and a directed network with arbitrary degree distribution. The simple closed form of our central results allow us to draw broad qualitative conclusions about the effect of fine structure on stability.

Reducing the risk of hyperammonemia from transfusion of stored red blood cells.

Ammonia concentration increases in red cell units (RBCs) during storage. We measured absolute amounts of ammonia (AA) per unit serially in stored RBCs and before and after removal of the supernatant by volume reduction (VR) or washing. Ammonia increased 6.4-fold in untreated units over 31 days. VR decreased AA 3.7-fold, whereas washing decreased it 38-fold (p<0.0001). At least for certain patients, e.g., infants receiving large volume transfusions and patients in liver failure, it may be advisable to use RBCs as fresh as possible and to limit infusion (by VR or washing) of ammonia in the supernatant.

Generalized Lotka-Volterra model with hierarchical interactions.

In the analysis of complex ecosystems it is common to use random interaction coefficients, which are often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by imposing hierarchical interspecies interactions. These are incorporated into a generalized Lotka-Volterra dynamical system. In a hierarchical community species benefit more, on average, from interactions with species further below them in the hierarchy than from interactions with those above. Using dynamic mean-field theory, we demonstrate that a strong hierarchical structure is stabilizing, but that it reduces the number of species in the surviving community, as well as their abundances. Additionally, we show that increased heterogeneity in the variances of the interaction coefficients across positions in the hierarchy is destabilizing. We also comment on the structure of the surviving community and demonstrate that the abundance and probability of survival of a species are dependent on its position in the hierarchy.

PR1P, a VEGF-stabilizing peptide, reduces injury and inflammation in acute lung injury and ulcerative colitis animal models.

Acute Respiratory Distress Syndrome (ARDS) and Ulcerative Colitis (UC) are each characterized by tissue damage and uncontrolled inflammation. Neutrophils and other inflammatory cells play a primary role in disease progression by acutely responding to direct and indirect insults to tissue injury and by promoting inflammation through secretion of inflammatory cytokines and proteases. Vascular Endothelial Growth Factor (VEGF) is a ubiquitous signaling molecule that plays a key role in maintaining and promoting cell and tissue health, and is dysregulated in both ARDS and UC. Recent evidence suggests a role for VEGF in mediating inflammation, however, the molecular mechanism by which this occurs is not well understood. We recently showed that PR1P, a 12-amino acid peptide that binds to and upregulates VEGF, stabilizes VEGF from degradation by inflammatory proteases such as elastase and plasmin thereby limiting the production of VEGF degradation products (fragmented VEGF (fVEGF)). Here we show that fVEGF is a neutrophil chemoattractant in vitro and that PR1P can be used to reduce neutrophil migration in vitro by preventing the production of fVEGF during VEGF proteolysis. In addition, inhaled PR1P reduced neutrophil migration into airways following injury in three separate murine acute lung injury models including from lipopolysaccharide (LPS), bleomycin and acid. Reduced presence of neutrophils in the airways was associated with decreased pro-inflammatory cytokines (including TNF-α, IL-1ß, IL-6) and Myeloperoxidase (MPO) in broncho-alveolar lavage fluid (BALF). Finally, PR1P prevented weight loss and tissue injury and reduced plasma levels of key inflammatory cytokines IL-1ß and IL-6 in a rat TNBS-induced colitis model. Taken together, our data demonstrate that VEGF and fVEGF may each play separate and pivotal roles in mediating inflammation in ARDS and UC, and that PR1P, by preventing proteolytic degradation of VEGF and the production of fVEGF may represent a novel therapeutic approach to preserve VEGF signaling and inhibit inflammation in acute and chronic inflammatory diseases.

The diagnostic value of biopsy of small peripheral lymph nodes in patients with suspected lymphoma.

In a patient with suspected lymphoma, it is considered desirable to confirm the diagnosis by excisional biopsy of enlarged lymph nodes. However, sometimes the ideal nodes are positioned internally, requiring a deep invasive procedure for access, or the patient may have underlying medical conditions that make it risky to perform such an invasive procedure. Under a protocol approved by our institution's review board (IRB), we reviewed five patients in whom superficial lymph nodes were biopsied which were smaller than usually considered optimal for diagnosis (=2 cm). In each of these cases, the biopsy yielded diagnostic information upon which treatment could be based, sparing the patient a deep invasive procedure. We suggest that in situations in which large internal lymph nodes are not easily accessible and/or the patient's clinical situation precludes more invasive procedures, including deep core needle biopsy of a large mass, it is worthwhile to consider the removal of smaller, superficial lymph nodes with minimal risk which may suffice for diagnosis.

Eigenvalue spectra and stability of directed complex networks.

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction network between components has on the eigenvalue spectrum. We build on previous results, which usually only take into account the mean degree of the network, by allowing for nontrivial network degree heterogeneity. We derive closed-form expressions for the eigenvalue spectrum of the adjacency matrix of a general weighted and directed network. Using these results, which are valid for any large well-connected complex network, we then derive compact formulas for the corrections (due to nonzero network heterogeneity) to well-known results in random matrix theory. Specifically, we derive modified versions of the Wigner semicircle law, the Girko circle law, and the elliptic law and any outlier eigenvalues. We also derive a surprisingly neat analytical expression for the eigenvalue density of a directed Barabási-Albert network. We are thus able to deduce that network heterogeneity is mostly a destabilizing influence in complex dynamical systems.

Sampling rare trajectories using stochastic bridges.

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. Further, we also compare the stochastic bridges we produce to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the generated paths, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that the method can also be used to judge the accuracy of the WKB approximation at finite levels of noise.

Persistent hypocalcemia associated with therapeutic plasma exchange performed to reduce HLA antibody levels in cardiac transplant recipients.

BACKGROUND: Patients who receive heart transplants may undergo therapeutic plasma exchange to reduce high levels of HLA antibodies which may increase the risk of allograft rejection. Plasma exchange may predispose to hypocalcemia because of chelation of calcium by sodium citrate, used as an anticoagulant both during the procedure and in thawed fresh frozen plasma often used for replacement. METHODS: We report three adults with dilated cardiomyopathy who underwent cardiac transplantation and serial plasma exchange for high levels of HLA antibodies. We followed these patients' pre-exchange serum calcium levels and the quantity of calcium supplementation they received. Further, we examined myocardial tissue sections post-transplantation for calcium deposition. RESULTS: Our patients' serum calcium levels were initially normal, but, despite aggressive calcium repletion, remained low (nadirs for pre-exchange ionized calcium in two patients 4.48 and 3.8mg/dL, respectively, reference range 4.6-5.4mg/dL). For patient 3, pre-exchange total calcium on day 2 was 7.9mg/dL (reference range 8.4-10.2mg/dL). Two patients had intermittent symptoms of hypocalcemia. Studies of cardiac tissue sections (available only from these two patients) were consistent with the presence of calcium deposition post transplantation. In comparison, six patients who underwent lung transplantation and plasma exchange for high levels of HLA antibodies did not manifest significant hypocalcemia. CONCLUSIONS: We emphasize the need for prompt and sufficient calcium replacement, monitored by serum ionized calcium levels, in the early post-cardiac transplantation period when plasma exchange is performed with thawed fresh frozen plasma replacement. The persistently low serum calcium levels we observed post heart transplantation were possibly contributed to by increased myocardial calcium influx.

Persistent individual bias in a voter model with quenched disorder.

Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level of the individual. In this work, we ask which factors contribute to a single voter maintaining a long-term statistical bias for one opinion over the other in the face of social influence. To this end, a modified version of the network voter model is proposed, which also incorporates quenched disorder in the interaction strengths between individuals and the possibility of antagonistic relationships. We find that a sparse interaction network and heterogeneity in interaction strengths give rise to the possibility of arbitrarily long-lived individual biases, even when there is no population-averaged bias for one opinion over the other. This is demonstrated by calculating the eigenvalue spectrum of the weighted network Laplacian using the theory of sparse random matrices.

Consensus, polarization, and coexistence in a continuous opinion dynamics model with quenched disorder.

A model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that consensus, polarization and a spread of moderate opinions are all possible within this model. Using dynamic mean-field theory, we are able to identify the statistical features of the interactions between individuals that give rise to each of the aforementioned emergent phenomena. The nature of the transitions between each of the observed macroscopic states is also studied. It is demonstrated that heterogeneity of interactions between individuals can lead to polarization, that mostly antagonistic or contrarian interactions can promote consensus at a moderate opinion, and that mostly reinforcing interactions encourage the majority to take an extreme opinion.

PDCD2, a protein whose expression is repressed by BCL6, induces apoptosis in human cells by activation of the caspase cascade.

We have previously reported that the human programmed cell death-2 gene (PDCD2), a target of BCL6 repression, is likely to be important in the pathogenesis of certain human lymphomas. We now demonstrate that transfection of a construct expressing PDCD2 induces apoptosis in human cell lines, that this occurs, at least in part, through activation of the caspase cascade, and, furthermore, that caspase inhibitors block this effect. Immunohistochemical studies in human benign lymphoid and lymphoma tissues support these findings. In addition, transfection of a VP16-BCL6 zinc fingers fusion protein, which competes with the binding of endogenous BCL6 in a Burkitt lymphoma cell line, increases PDCD2 protein expression and apoptosis, and knockdown of the PDCD2 protein in this cell line by PDCD2-specific small interfering RNA duplexes inhibits apoptosis. These studies indicate that one function of PDCD2 is to promote apoptosis in several human and mammalian cell lines and tissues, including lymphoma. Although the pathways involved in lymphomagenesis are likely to be multiple and complex, it is plausible that repression of PDCD2 expression by BCL6, which, in turn, leads to downregulation of apoptosis, is one mechanism involved in BCL6-associated lymphomatous transformation. The usefulness of increasing PDCD2 expression in the treatment of certain lymphomas merits further investigation.