Biological clock mutants and parameter changes in mathematical models

A number of recent experiments have revealed the existence of mutants with different free run periods in their circadian rhythms. Parameter variations in mathematical models can be used to simulate such changes. In addition, phase response curves (PRC) are derived and the effect of parameter variation in their shape is studied. It is shown that changes in global parameters can also distort their shape. Therefore one cannot conclude that genetic experiments provide evidence in favor of “chronon” models since “kinetic” models can also simulate their outcome.     

Combining cell culture analogue reactor designs and PBPK models to probe mechanisms of naphthalene toxicity

An alternative method of evaluating the toxicology of a chemical is to use cultured mammalian cells in a novel cell culture analogue reactor (CCA) together with a corresponding physiologically based pharmacokinetic model (PBPK). The PBPK is a mathematical model that divides the body into compartments representing organs, integrating the kinetic, thermodynamic, and anatomical parameters of the animal. The bioreactor is a physical replica of the PBPK; where the PBPK specifies an organ or tissue compartment, the bioreactor contains compartments with a corresponding cell type. The device is a continuous, dynamic system composed of multiple cell types that interact through a common circulating cell culture medium. The bioreactor and the model are coupled to evaluate the plausibility of the molecular mechanism that is input into the model. This concept is tested with naphthalene as a model of PAH (polycyclic aromatic hydrocarbons) toxicants. Two physically different CCA reactors were tested with naphthalene, and different results were observed. In the prototype system using cells attached to glass dilution bottles, naphthalene dosing resulted in generation of a circulating metabolite from the liver compartment (based on H4IIE cells from a rat hepatoma) that caused cell death in the lung compartment (L2 cells from a rat lung), as well as depletion of glutathione in the L2 cells. An improved CCA using packed bed reactors of microcarrier cultured cells did not show differences between naphthalene-dosed and nondosed controls. To explain the different responses of the two CCA designs, PBPKs of the two reactors were tested with variations in physical and kinetic parameters, and toxic mechanism. When the toxic metabolite of naphthalene was naphthoquinone rather than naphthalene epoxide as initially assumed, the PBPK results were consistent with the results of the two CCA designs. This result indicates that the mechanism of naphthalene toxicity in the CCAs may be mediated through naphthoquinone formation. The CCA-PBPK concept is demonstrated to be applicable to the study of toxic mechanisms. In particular, use of this approach suggests that in vitro naphthalene toxicity is mediated through the naphthoquinone metabolite.     

Combining genetic and geospatial analyses to infer population extinction in mygalomorph spiders endemic to the Los Angeles region

Although hyperdiverse groups like terrestrial arthropods are almost certainly severely impacted by habitat fragmentation and destruction, few studies have formally documented such effects. In this paper, we summarize the results of a multifaceted research approach to assess the magnitude and importance of anthropogenic population extinction on the narrowly endemic trapdoor spider genus Apomastus . We used geographical information systems modeling to reconstruct the likely historical distribution of Apomastus , and used molecular phylogeographic data to discern population genetic structure and detect genetic signatures of population extinction. In combination, these complementary lines of inference support direct observations of population extinction, and lead us to conclude that population extinction via urbanization has played an important role in defining the modern-day distribution of Apomastus species. This population loss implies coincident loss of genetic and adaptive diversity within this genus, and more generally, suggests a loss of ground-dwelling arthropod population diversity throughout the Los Angeles Basin. Strategies for minimizing this loss are proposed.     

Successional changes in an evolving anaerobic chlorophenol-degrading community used to infer relationships between population structure and system-level processes.

The response of a complex methanogenic sediment community to 2-chlorophenol (2-CP) was evaluated by monitoring the concentrations of this model contaminant and important metabolic intermediates and products and by using rRNA-targeted probes to track several microbial populations. Key relationships between the evolving population structure, formation of metabolic intermediates, and contaminant mineralization were identified. The nature of these relationships was intrinsically linked to the metabolism of benzoate, an intermediate that transiently accumulated during the mineralization of 2-CP. Before the onset of benzoate fermentation, reductive dehalogenation of 2-CP competed with methanogenesis for endogenous reducing equivalents. This suppressed H(2) levels, methane production, and archaeal small-subunit (SSU)-rRNA concentrations in the sediment community. The concentrations of bacterial SSU rRNA, including SSU rRNA derived from "Desulfovibrionaceae" populations, tracked with 2-CP levels, presumably reflecting changes in the activity of dehalogenating organisms. After the onset of benzoate fermentation, the abundance of Syntrophus-like SSU rRNA increased, presumably because these syntrophic organisms fermented benzoate to methanogenic substrates. Consequently, although the parent substrate 2-CP served as an electron acceptor, cleavage of its aromatic nucleus also influenced the sediment community by releasing the electron donors H(2) and acetate. Increased methane production and archaeal SSU-rRNA levels, which tracked with the Syntrophus-like SSU-rRNA concentrations, revealed that methanogenic populations in particular benefited from the input of reducing equivalents derived from 2-CP.     

Stretch-induced changes in heart rate and rhythm: clinical observations, experiments and mathematical models

Clinical and research data indicate that active and passive changes in the mechanical environment of the heart are capable of influencing both the initiation and the spread of cardiac excitation via pathways that are intrinsic to the heart. This direction of the cross-talk between cardiac electrical and mechanical activity is referred to as mechano-electric feedback (MEF). MEF is thought to be involved in the adjustment of heart rate to changes in mechanical load and would help to explain the precise beat-to-beat regulation of cardiac performance as it occurs even in the recently transplanted (and, thus, denervated) heart. Furthermore, there is clinical evidence that MEF may be involved in mechanical initiation of arrhythmias and fibrillation, as well as in the re-setting of disturbed heart rhythm by 'mechanical' first aid procedures. This review will outline the clinical relevance of cardiac MEF, describe cellular correlates to the responses observed in situ, and discuss the role that quantitative mathematical models may play in identifying the involvement of cardiac MEF in the regulation of heart rate and rhythm.     

Microcephaly models in the developing zebrafish retinal neuroepithelium point to an underlying defect in metaphase progression

Autosomal recessive primary microcephaly (MCPH) is a congenital disorder characterized by significantly reduced brain size and mental retardation. Nine genes are currently known to be associated with the condition, all of which encode centrosomal or spindle pole proteins. MCPH is associated with a reduction in proliferation of neural progenitors during fetal development. The cellular mechanisms underlying the proliferation defect, however, are not fully understood. The zebrafish retinal neuroepithelium provides an ideal system to investigate this question. Mutant or morpholino-mediated knockdown of three known MCPH genes (stil, aspm and wdr62) and a fourth centrosomal gene, odf2, which is linked to several MCPH proteins, results in a marked reduction in head and eye size. Imaging studies reveal a dramatic rise in the fraction of proliferating cells in mitosis in all cases, and time-lapse microscopy points to a failure of progression through prometaphase. There was also increased apoptosis in all the MCPH models but this appears to be secondary to the mitotic defect as we frequently saw mitotically arrested cells disappear, and knocking down p53 apoptosis did not rescue the mitotic phenotype, either in whole retinas or clones.     

Experimental models and mechanisms underlying the protective effects of n-3 polyunsaturated fatty acids in Alzheimer's disease

Dementia such as Alzheimer's disease (AD) is a growing health problem in aging populations in many countries around the world. Currently, there is no cure for AD; consequently, alternative therapies are urgently needed. Recent studies suggest that nutritional intervention may have therapeutic benefits for AD. Specifically, an increased intake of n-3 polyunsaturated fatty acids (PUFA) from fish and marine oils may lower AD risk. This review will summarize the current body of knowledge regarding the association between n-3 PUFA and AD, including human studies and experimental models, and potential mechanisms of action.     

Combining mathematical models and statistical methods to understand and predict the dynamics of antibiotic-sensitive mutants in a population of resistant bacteria during experimental evolution

Temporarily discontinuing the use of antibiotics has been proposed as a means to eliminate resistant bacteria by allowing sensitive clones to sweep through the population. In this study, we monitored a tetracycline-sensitive subpopulation that emerged during experimental evolution of E. coli K12 MG1655 carrying the multiresistance plasmid pB10 in the absence of antibiotics. The fraction of tetracycline-sensitive mutants increased slowly over 500 generations from 0.1 to 7%, and loss of resistance could be attributed to a recombination event that caused deletion of the tet operon. To help understand the population dynamics of these mutants, three mathematical models were developed that took into consideration recurrent mutations, increased host fitness (selection), or a combination of both mechanisms (full model). The data were best explained by the full model, which estimated a high mutation frequency (lambda = 3.11 x 10(-5)) and a significant but small selection coefficient (sigma = 0.007). This study emphasized the combined use of experimental data, mathematical models, and statistical methods to better understand and predict the dynamics of evolving bacterial populations, more specifically the possible consequences of discontinuing the use of antibiotics.     

Molecular adaptations underlying susceptibility and resistance to social defeat in brain reward regions

While stressful life events are an important cause of psychopathology, most individuals exposed to adversity maintain normal psychological functioning. The molecular mechanisms underlying such resilience are poorly understood. Here, we demonstrate that an inbred population of mice subjected to social defeat can be separated into susceptible and unsusceptible subpopulations that differ along several behavioral and physiological domains. By a combination of molecular and electrophysiological techniques, we identify signature adaptations within the mesolimbic dopamine circuit that are uniquely associated with vulnerability or insusceptibility. We show that molecular recapitulations of three prototypical adaptations associated with the unsusceptible phenotype are each sufficient to promote resistant behavior. Our results validate a multidisciplinary approach to examine the neurobiological mechanisms of variations in stress resistance, and illustrate the importance of plasticity within the brain's reward circuits in actively maintaining an emotional homeostasis.     

Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors

Background

Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results

We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions

The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

Reviewers

This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).     

Development and disease: how susceptibility to an emerging pathogen changes through anuran development

Ranaviruses have caused die-offs of amphibians across the globe. In North America, these pathogens cause more amphibian mortality events than any other pathogen. Field observations suggest that ranavirus epizootics in amphibian communities are common during metamorphosis, presumably due to changes in immune function. However, few controlled studies have compared the relative susceptibility of amphibians to ranaviruses across life stages. Our objectives were to measure differences in mortality and infection prevalence following exposure to ranavirus at four developmental stages and determine whether the differences were consistent among seven anuran species. Based on previous studies, we hypothesized that susceptibility to ranavirus would be greatest at metamorphosis. Our results did not support this hypothesis, as four of the species were most susceptible to ranavirus during the larval or hatchling stages. The embryo stage had the lowest susceptibility among species probably due to the protective membranous layers of the egg. Our results indicate that generalizations should be made cautiously about patterns of susceptibility to ranaviruses among amphibian developmental stages and species. Further, if early developmental stages of amphibians are susceptible to ranaviruses, the impact of ranavirus epizootic events may be greater than realized due to the greater difficulty of detecting morbid hatchlings and larvae compared to metamorphs.     

Molecular mechanisms and global dynamics of fibrillation: an integrative approach to the underlying basis of vortex-like reentry

Art Winfree's scientific legacy has been particularly important to our laboratory whose major goal is to understand the mechanisms of ventricular fibrillation (VF). Here, we take an integrative approach to review recent studies on the manner in which nonlinear electrical waves organize to result in VF. We describe the contribution of specific potassium channel proteins and of the myocardial fiber structure to such organization. The discussion centers on data derived from a model of stable VF in the Langendorff-perfused guinea pig heart that demonstrates distinct patterns of organization in the left (LV) and right (RV) ventricles. Analysis of optical mapping data reveals that VF excitation frequencies are distributed throughout the ventricles in clearly demarcated domains. The highest frequency domains are found on the anterior wall of the LV at a location where sustained reentrant activity is present. The optical data suggest that a high frequency rotor that remains stationary in the LV is the mechanism that sustains VF in this model. Computer simulations predict that the inward rectifying potassium current (IK1) is an essential determinant of rotor stability and frequency, and patch-clamp results strongly suggest that the outward component of IK1 of cells in the LV is significantly larger than in the RV. Additional computer simulations and analytical procedures predict that the filaments of the reentrant activity (scroll waves) adopt a non-random configuration depending on fiber organization within the ventricular wall. Using the minimal principle we have concluded that filaments align with the trajectory of least resistance (i.e. the geodesic) between their endpoints. Overall, the data discussed have opened new and potentially exciting avenues of research on the possible role played by inward rectifier channels in the mechanism of VF, as well as the organization of its reentrant sources in three-dimensional cardiac muscle. Such an integrative approach may lead us toward an understanding of the molecular and structural basis of VF and hopefully to new preventative approaches.     

Cellular models of macrophage tumoricidal effector mechanisms in vitro. Characterization of cytolytic responses to tumor necrosis factor and nitric oxide pathways in vitro

The recently described L-arginine-dependent nitric oxide (NO) pathway has been proposed to interact synergistically with the TNF pathway in murine macrophage-mediated tumor cytotoxicity in vitro. We have employed an experimental construct in which these two pathways were independently expressed by two different effector cell populations. The TNF-dependent pathway was committed by murine 3T3 cells transfected with the cDNA encoding human pro-TNF. The NO pathway was executed by the murine EMT-6 mammary adenocarcinoma cell line treated with murine rIFN-gamma and LPS. Controls for the TNF pathway committed by the transfectant included lysis of the TNF-sensitive murine L929 cell in coculture, secretion of TNF, and absence of nitrite synthesis. For the NO pathway controls included lysis of the murine P815 mastocytoma cocultured with activated EMT-6 cells that had been pretreated with murine rIFN-gamma and LPS, production of nitrite by this activated effector cell, and an absence of TNF secretion. The target cell panel included L929, EMT-6, P815, and murine B16 melanoma and TU-5 sarcoma cell lines. All targets on this panel were susceptible to lysis by LPS-triggered murine bacillus Calmette-Guérin-activated macrophages. The 3T3 transfectant caused significant lysis of cocultured L929 and TU-5 targets. The EMT-6 effector cell only caused significant lysis of the P815 target. When both effector cells were cocultured with these target cells, lysis of the P815 target was observed to be additive or superadditive; however, for all the other targets, cytotoxicity was comparable with or subadditive compared with that seen with the 3T3 transfectant effector cell alone. Thus, these two pathways do not appear to account for the broad, potent tumoricidal activity observed for activated macrophages in vitro.     

Theme and variations in the evolutionary pathways to virulence of an RNA plant virus species

The diversity of a highly variable RNA plant virus was considered to determine the range of virulence substitutions, the evolutionary pathways to virulence, and whether intraspecific diversity modulates virulence pathways and propensity. In all, 114 isolates representative of the genetic and geographic diversity of Rice yellow mottle virus (RYMV) in Africa were inoculated to several cultivars with eIF(iso)4G-mediated Rymv1-2 resistance. Altogether, 41 virulent variants generated from ten wild isolates were analyzed. Nonconservative amino acid replacements at five positions located within a stretch of 15 codons in the central region of the 79-aa-long protein VPg were associated with virulence. Virulence substitutions were fixed predominantly at codon 48 in most strains, whatever the host genetic background or the experimental conditions. There were one major and two isolate-specific mutational pathways conferring virulence at codon 48. In the prevalent mutational pathway I, arginine (AGA) was successively displaced by glycine (GGA) and glutamic acid (GAA). Substitutions in the other virulence codons were displaced when E48 was fixed. In the isolate-specific mutational pathway II, isoleucine (ATA) emerged and often later coexisted with valine (GTA). In mutational pathway III, arginine, with the specific S2/S3 strain codon usage AGG, was displaced by tryptophane (TGG). Mutational pathway I never arose in the widely spread West African S2/S3 strain because G48 was not infectious in the S2/S3 genetic context. Strain S2/S3 least frequently overcame resistance, whereas two geographically localized variants of the strain S4 had a high propensity to virulence. Codons 49 and 26 of the VPg, under diversifying selection, are candidate positions in modulating the genetic barriers to virulence. The theme and variations in the evolutionary pathways to virulence of RYMV illustrates the extent of parallel evolution within a highly variable RNA plant virus species.     

The rate and character of spontaneous mutation in an RNA virus

Estimates of spontaneous mutation rates for RNA viruses are few and uncertain, most notably due to their dependence on tiny mutation reporter sequences that may not well represent the whole genome. We report here an estimate of the spontaneous mutation rate of tobacco mosaic virus using an 804-base cognate mutational target, the viral MP gene that encodes the movement protein (MP). Selection against newly arising mutants was countered by providing MP function from a transgene. The estimated genomic mutation rate was on the lower side of the range previously estimated for lytic animal riboviruses. We also present the first unbiased riboviral mutational spectrum. The proportion of base substitutions is the same as that in a retrovirus but is lower than that in most DNA-based organisms. Although the MP mutant frequency was 0.02-0.05, 35% of the sequenced mutants contained two or more mutations. Therefore, the mutation process in populations of TMV and perhaps of riboviruses generally differs profoundly from that in populations of DNA-based microbes and may be strongly influenced by a subpopulation of mutator polymerases.     

Inhibitory and excitatory mechanisms underlying auditory responses to learned vocalizations in the songbird nucleus HVC

Speech and birdsong require auditory feedback for their development and maintenance, necessitating precise auditory encoding of vocal sounds. In songbirds, the telencephalic song premotor nucleus HVC contains neurons that respond highly selectively to the bird's own song (BOS), a property distinguishing HVC from its auditory afferents. We examined the contribution of inhibitory and excitatory synaptic inputs to BOS-evoked firing in those HVC neurons innervating a pathway essential for audition-dependent vocal plasticity. Using in vivo intracellular techniques, we found that G protein-coupled, potassium-mediated inhibition, tuned to the BOS, interacts with BOS-tuned excitation through several mechanisms to shape neuronal firing patterns. Furthermore, in the absence of this inhibition, the response bias to the BOS increases, reminiscent of cancellation mechanisms in other sensorimotor systems.