Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Adherence to a lifestyle physical activity program: Trends over time and associations with processes of change and physical activity

Research on lifestyle physical activity interventions suggests that they help individuals meet the new recommendations for physical activity made by the Centers for Disease Control and Prevention (CDC) and the American College of Sports Medicine (ACSM). The purpose of this research was to describe the rates of adherence to two lifestyle physical activity intervention arms and to examine the association between adherence and outcome variables, using data from Project PRIME, a lifestyle physical activity intervention based on the transtheoretical model and conducted by the Cooper Institute of Aerobics Research, Dallas, Texas. Participants were 250 sedentary healthy adults, aged 35 to 70 years, primarily non-Hispanic White, and in the contemplation and preparation stages of readiness to change. They were randomized to a group (PRIME G) or a mail- and telephone-delivered condition (PRIME C). Adherence measures included attending class (PRIME G), completing a monthly telephone call with a health educator (PRIME C), and completing homework assignments and self-monitoring minutes of moderate- to vigorous physical activity (both groups). In the first results paper, adherence over time and between conditions was examined: Attendance in group, completing the monthly telephone call, and homework completion decreased over time, and participants in PRIME G were more likely to complete homework than those in PRIME C. Paper 2 aimed to determine whether the adherence measures predicted achievement of the CDC/ACSM physical activity guideline. In separate models for the two conditions, a latent variable measuring adherence was found to predict achievement of the guideline. Paper 3 examined the association between adherence measures and the transtheoretical model's processes of change within each condition. For both, participants who completed at least two thirds of the homework assignments improved their use of the processes of change more than those who completed less than that amount. These results suggest that encouraging adherence to a lifestyle physical activity intervention, at least among already motivated volunteers, may increase the likelihood of beneficial changes in the outcomes. ^

A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Focal white matter changes in spasmodic dysphonia: a combined diffusion tensor imaging and neuropathological study.

Spasmodic dysphonia is a neurological disorder characterized by involuntary spasms in the laryngeal muscles during speech production. Although the clinical symptoms are well characterized, the pathophysiology of this voice disorder is unknown. We describe here, for the first time to our knowledge, disorder-specific brain abnormalities in these patients as determined by a combined approach of diffusion tensor imaging (DTI) and postmortem histopathology. We used DTI to identify brain changes and to target those brain regions for neuropathological examination. DTI showed right-sided decrease of fractional anisotropy in the genu of the internal capsule and bilateral increase of overall water diffusivity in the white matter along the corticobulbar/corticospinal tract in 20 spasmodic dysphonia patients compared to 20 healthy subjects. In addition, water diffusivity was bilaterally increased in the lentiform nucleus, ventral thalamus and cerebellar white and grey matter in the patients. These brain changes were substantiated with focal histopathological abnormalities presented as a loss of axonal density and myelin content in the right genu of the internal capsule and clusters of mineral depositions, containing calcium, phosphorus and iron, in the parenchyma and vessel walls of the posterior limb of the internal capsule, putamen, globus pallidus and cerebellum in the postmortem brain tissue from one patient compared to three controls. The specificity of these brain abnormalities is confirmed by their localization, limited only to the corticobulbar/corticospinal tract and its main input/output structures. We also found positive correlation between the diffusivity changes and clinical symptoms of spasmodic dysphonia (r = 0.509, P = 0.037). These brain abnormalities may alter the central control of voluntary voice production and, therefore, may underlie the pathophysiology of this disorder.

Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory.

Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular Ca2+ release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. This dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that (1) the dual-time structure similarly confers resistance to internal noise due to molecule number fluctuations, and (2) model variants with altered coupling, which better represent some specific biochemical systems, share all the above advantages. We also develop a similar bistable model with coupling of a fast autoactivation loop to a slow loop. This model's topology was suggested by positive feedback proposed to play a role in long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance are also present in this autoactivation model. Empirically, LTP develops resistance to reversal over approximately 1h . The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback.

Diffusion tensor imaging of rat spinal cord in vivo

Magnetic resonance imaging, with its exquisite soft tissue contrast, is an ideal modality for investigating spinal cord pathology. While conventional MRI techniques are very sensitive for spinal cord pathology, their specificity is somewhat limited. Diffusion MRI is an advanced technique which is a very sensitive and specific indicator of the integrity of white matter tracts. Diffusion imaging has been shown to detect early ischemic changes in white matter, while conventional imaging demonstrates no change. By acquiring the complete apparent diffusion tensor (ADT), tissue diffusion properties can be expressed in terms of quantitative and rotationally invariant parameters. ^ Systematic study of SCI in vivo requires controlled animal models such as the popular rat model. To date, studies of spinal cord using ADT imaging have been performed exclusively in fixed, excised spinal cords, introducing inevitable artifacts and losing the benefits of MRI's noninvasive nature. In vivo imaging reflects the actual in vivo tissue properties, and allows each animal to be imaged at multiple time points, greatly reducing the number of animals required to achieve statistical significance. Because the spinal cord is very small, the available signal-to-noise ratio (SNR) is very low. Prior spin-echo based ADT studies of rat spinal cord have relied on high magnetic field strengths and long imaging times—on the order of 10 hours—for adequate SNR. Such long imaging times are incompatible with in vivo imaging, and are not relevant for imaging the early phases following SCI. Echo planar imaging (EPI) is one of the fastest imaging methods, and is popular for diffusion imaging. However, EPI further lowers the image SNR, and is very sensitive to small imperfections in the magnetic field, such as those introduced by the bony spine. Additionally, The small field-of-view (FOV) needed for spinal cord imaging requires large imaging gradients which generate EPI artifacts. The addition of diffusion gradients introduces yet further artifacts. ^ This work develops a method for rapid EPI-based in vivo diffusion imaging of rat spinal cord. The method involves improving the SNR using an implantable coil; reducing magnetic field inhomogeneities by means of an autoshim, and correcting EPI artifacts by post-processing. New EPI artifacts due to diffusion gradients described, and post-processing correction techniques are developed. ^ These techniques were used to obtain rotationally invariant diffusion parameters from 9 animals in vivo, and were validated using the gold-standard, but slow, spinecho based diffusion sequence. These are the first reported measurements of the ADT in spinal cord in vivo . ^ Many of the techniques described are equally applicable toward imaging of human spinal cord. We anticipate that these techniques will aid in evaluating and optimizing potential therapies, and will lead to improved patient care. ^

The dynamics of calmodulin signaling revealed using optical methods

The Ca2+-binding protein calmodulin (CaM) is a key transducer of Ca2+ oscillations by virtue of its ability to bind Ca 2+ selectively and then interact specifically with a large number of downstream enzymes and proteins. It remains unclear whether Ca2+ -dependent signaling alone can activate the full range of Ca 2+/CaM regulated processes or whether other regulatory schemes in the cell exist that allow specific targeting of CaM to subsets of Ca 2+/CaM binding sites or regions of the cell. Here we investigate the possibility that alterations of the availability of CaM may serve as a potential cellular mechanism for regulating the activation of CaM-dependent targets. By utilizing sensitive optical techniques with high spatial and temporal resolution, we examine the intracellular dynamics of CaM signaling at a resolution previously unattainable. After optimizing and characterizing both the optical methods and fluorescently labeled probes for intracellular measurements, the diffusion of CaM in the cytoplasm of HEK293 cells was analyzed. It was discovered that the diffusion characteristics of CaM are similar to that of a comparably sized inert molecule. Independent manipulation of experimental parameters, including increases in total concentrations of CaM and intracellular Ca2+ levels, did not change the diffusion of CaM in the cytoplasm. However, changes in diffusion were seen when the concentration of Ca2+/CaM-binding targets was increased in conjunction with elevated Ca2+. This indicates that CaM is not normally limiting for the activation of Ca 2+/CaM-dependent enzymes in HEK293 cells but reveals that the ratio of CaM to CaM-dependent targets is a potential mechanism for changing CaM availability. Next we considered whether cellular compartmentalization may act to regulate concentrations of available Ca2+/CaM in hippocampal neurons. We discovered changes in diffusion parameters of CaM under elevated Ca2+ conditions in the soma, neurite and nucleus which suggest that either the composition of cytoplasm is different in these compartments and/or they are composed of unique families of CaM-binding proteins. Finally, we return to the HEK293 cell and for the first time directly show the intracellular binding of CaM and CaMKII, an important target for CaM critical for neuronal function and plasticity. Furthermore, we analyzed the complex binding stoichiometry of this molecular interaction in the basal, activated and autophosphorylated states of CaMKII and determined the impact of this binding on CaM availability in the cell. Overall these results demonstrate that regulation of CaM availability is a viable cellular mechanism for regulating the output of CaM-dependent processes and that this process is tuned to the specific functional needs of a particular cell type and subcellular compartment. ^

In-vivo diffusion tensor imaging of rat spinal cord with a phased array coil at 7T

Magnetic resonance imaging (MRI) is a non-invasive technique that offers excellent soft tissue contrast for characterizing soft tissue pathologies. Diffusion tensor imaging (DTI) is an MRI technique that has shown to have the sensitivity to detect subtle pathology that is not evident on conventional MRI. ^ Rats are commonly used as animal models in characterizing the spinal cord pathologies including spinal cord injury (SCI), cancer, multiple sclerosis, etc. These pathologies could affect both thoracic and cervical regions and complete characterization of these pathologies using MRI requires DTI characterization in both the thoracic and cervical regions. Prior to the application of DTI for investigating the pathologic changes in the spinal cord, it is essential to establish DTI metrics in normal animals. ^ To date, in-vivo DTI studies of rat spinal cord have used implantable coils for high signal-to-noise ratio (SNR) and spin-echo pulse sequences for reduced geometric distortions. Implantable coils have several disadvantages including: (1) the invasive nature of implantation, (2) loss of SNR due to frequency shift with time in the longitudinal studies, and (3) difficulty in imaging the cervical region. While echo planar imaging (EPI) offers much shorter acquisition times compared to spin-echo imaging, EPI is very sensitive to static magnetic field inhomogeneities and the existing shimming techniques implemented on the MRI scanner do not perform well on spinal cord because of its geometry. ^ In this work, an integrated approach has been implemented for in-vivo DTI characterization of rat spinal cord in the thoracic and cervical regions. A three element phased array coil was developed for improved SNR and extended spatial coverage. A field-map shimming technique was developed for minimizing the geometric distortions in EPI images. Using these techniques, EPI based DWI images were acquired with optimized diffusion encoding scheme from 6 normal rats and the DTI-derived metrics were quantified. ^ The phantom studies indicated higher SNR and smaller bias in the estimated DTI metrics than the previous studies in the cervical region. In-vivo results indicated no statistical difference in the DTI characteristics of either gray matter or white matter between the thoracic and cervical regions. ^

A look at parent-adolescent processes and adolescent sexual intentions among urban, minority, middle school youth

Background. The United States continues to have the highest rates in teenage pregnancy among industrialized nations and approximately 46% of high school students engaged in sex by the time they graduated. Various family adolescent processes (family connectedness, perceived parental beliefs about sex, parent-child communication about sex) have been linked to adolescent sexual behavior. However, the association between family adolescent and adolescent sexual intentions has not often been studied in middle school minority youth.^ Methods. Research hypotheses were tested using a secondary data analysis from a HIV, STI, and pregnancy prevention program for urban middle school students.^ Results. At baseline, 77% of students reported low intentions to engage in vaginal or oral sex within a year and 87% reported they would use a condom if having sex within the next 3 months. After adjusting for gender, age, and race/ethnicity, family connectedness and perceived parental beliefs about sex were significantly associated with vaginal and oral sex intentions. Only perceived parental beliefs was associated with condom use intentions. ^ Conclusions. Family adolescent processes appear to be associated with adolescents’ intentions regarding sex and condom use. Early interventions are needed that take into account the importance of healthy, supportive parent-adolescent relationships and encourage parents to share their beliefs about sex to adolescents before the onset of sexual activity. ^

Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^