Finitely Generated Nil but Not Nilpotent Evolution Algebra

To use evolution algebras to model population dynamics that both allow extinction and introduction of certain gametes in finite generations, nilpotency must be built into the algebraic structures of these algebras with the entire algebras not to be nilpotent if the populations are assumed to evolve for a long period of time. To adequately address this need, evolution algebras over rings with nilpotent elements must be considered instead of evolution algebras over fields. This paper develops some criteria, which are computational in nature, about the nilpotency of these algebras, and shows how to construct finitely generated evolution algebras which are nil but not nilpotent

Finite-Time Perturbations of Dynamical Systems and Applications to Tumor Therapy

We study finite-time perturbations of dynamical systems. We prove that finite-time perturbed dynamical systems are asymptotically equivalent to unperturbed dynamical systems. And so the asymptotical behavior of finite-time perturbed systems can be studied by unperturbed systems. As an example, we study a system perturbed by drug treatments

Lytic cycle: A defining process in oncolytic virotherapy

The viral lytic cycle is an important process in oncolytic virotherapy. Most mathematical models for oncolytic virotherapy do not incorporate this process. In this article, we propose a mathematical model with the viral lytic cycle based on the basic mathematical model for oncolytic virotherapy. The viral lytic cycle is characterized by two parameters, the time period of the viral lytic cycle and the viral burst size. The time period of the viral lytic cycle is modeled as a delay parameter. The model is a nonlinear system of delay differential equations. The model reveals a striking feature that the critical value of the period of the viral lytic cycle is determined by the viral burst size. There are two threshold values for the burst size. Below the first threshold, the system has an unstable trivial equilibrium and a globally stable virus free equilibrium for any nonnegative delay, while the system has a third positive equilibrium when the burst size is greater than the first threshold. When the burst size is above the second threshold, there is a functional relation between the bifurcation value of the delay parameter for the period of the viral lytic cycle and the burst size. If the burst size is greater than the second threshold, the positive equilibrium is stable when the period of the viral lytic cycle is smaller than the bifurcation value, while the system has orbitally stable periodic solutions when the period of the lytic cycle is longer than the bifurcation value. However, this bifurcation value becomes smaller when the burst size becomes bigger. The viral lytic cycle may explain the oscillation phenomena observed in many studies. An important clinic implication is that the burst size should be carefully modified according to its effect on the lytic cycle when a type of a virus is modified for virotherapy, so that the period of the viral lytic cycle is in a suitable range which can break away the stability of the positive equilibria or periodic solutions. (C) 2012 Elsevier Inc. All rights reserved

The Role of the Innate Immune System in Oncolytic Virotherapy

The complexity of the immune responses is a major challenge in current virotherapy. This study incorporates the innate immune response into our basic model for virotherapy and investigates how the innate immunity affects the outcome of virotherapy. The viral therapeutic dynamics is largely determined by the viral burst size, relative innate immune killing rate, and relative innate immunity decay rate. The innate immunity may complicate virotherapy in the way of creating more equilibria when the viral burst size is not too big, while the dynamics is similar to the system without innate immunity when the viral burst size is big

Lumpability Abstractions of Rule-based Systems

The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

The trans-ancestral genomic architecture of glycemic traits

Glycemic traits are used to diagnose and monitor type 2 diabetes and cardiometabolic health. To date, most genetic studies of glycemic traits have focused on individuals of European ancestry. Here we aggregated genome-wide association studies comprising up to 281,416 individuals without diabetes (30% non-European ancestry) for whom fasting glucose, 2-h glucose after an oral glucose challenge, glycated hemoglobin and fasting insulin data were available. Trans-ancestry and single-ancestry meta-analyses identified 242 loci (99 novel; P < 5 x 10(-8)), 80% of which had no significant evidence of between-ancestry heterogeneity. Analyses restricted to individuals of European ancestry with equivalent sample size would have led to 24 fewer new loci. Compared with single-ancestry analyses, equivalent-sized trans-ancestry fine-mapping reduced the number of estimated variants in 99% credible sets by a median of 37.5%. Genomic-feature, gene-expression and gene-set analyses revealed distinct biological signatures for each trait, highlighting different underlying biological pathways. Our results increase our understanding of diabetes pathophysiology by using trans-ancestry studies for improved power and resolution. A trans-ancestry meta-analysis of GWAS of glycemic traits in up to 281,416 individuals identifies 99 novel loci, of which one quarter was found due to the multi-ancestry approach, which also improves fine-mapping of credible variant sets.Peer reviewe

Mapping genomic loci implicates genes and synaptic biology in schizophrenia

Schizophrenia has a heritability of 60-80%1, much of which is attributable to common risk alleles. Here, in a two-stage genome-wide association study of up to 76,755 individuals with schizophrenia and 243,649 control individuals, we report common variant associations at 287 distinct genomic loci. Associations were concentrated in genes that are expressed in excitatory and inhibitory neurons of the central nervous system, but not in other tissues or cell types. Using fine-mapping and functional genomic data, we identify 120 genes (106 protein-coding) that are likely to underpin associations at some of these loci, including 16 genes with credible causal non-synonymous or untranslated region variation. We also implicate fundamental processes related to neuronal function, including synaptic organization, differentiation and transmission. Fine-mapped candidates were enriched for genes associated with rare disruptive coding variants in people with schizophrenia, including the glutamate receptor subunit GRIN2A and transcription factor SP4, and were also enriched for genes implicated by such variants in neurodevelopmental disorders. We identify biological processes relevant to schizophrenia pathophysiology; show convergence of common and rare variant associations in schizophrenia and neurodevelopmental disorders; and provide a resource of prioritized genes and variants to advance mechanistic studies

A Genome-Wide Association Study of Diabetic Kidney Disease in Subjects With Type 2 Diabetes

dentification of sequence variants robustly associated with predisposition to diabetic kidney disease (DKD) has the potential to provide insights into the pathophysiological mechanisms responsible. We conducted a genome-wide association study (GWAS) of DKD in type 2 diabetes (T2D) using eight complementary dichotomous and quantitative DKD phenotypes: the principal dichotomous analysis involved 5,717 T2D subjects, 3,345 with DKD. Promising association signals were evaluated in up to 26,827 subjects with T2D (12,710 with DKD). A combined T1D+T2D GWAS was performed using complementary data available for subjects with T1D, which, with replication samples, involved up to 40,340 subjects with diabetes (18,582 with DKD). Analysis of specific DKD phenotypes identified a novel signal near GABRR1 (rs9942471, P = 4.5 x 10(-8)) associated with microalbuminuria in European T2D case subjects. However, no replication of this signal was observed in Asian subjects with T2D or in the equivalent T1D analysis. There was only limited support, in this substantially enlarged analysis, for association at previously reported DKD signals, except for those at UMOD and PRKAG2, both associated with estimated glomerular filtration rate. We conclude that, despite challenges in addressing phenotypic heterogeneity, access to increased sample sizes will continue to provide more robust inference regarding risk variant discovery for DKD.Peer reviewe