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Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and thus gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of state-of-the-art methods for parameter and model inference, with an emphasis on scalability., To appear in the book "Gene Regulatory Networks: Methods and Protocols"

The elucidation of sources of heterogeneity in cell populations is crucial to fully understand biological processes. A suitable method to identify causes of heterogeneity is reaction rate equation (RRE) constrained mixture modeling, which enables the analysis of subpopulation structures and dynamics. These mixture models are calibrated using single cell snapshot data to estimate model parameters which are not measured or which cannot be assessed experimentally. In this manuscript, we evaluate different optimization methods for estimating the parameters of RRE constrained mixture models under the normal distribution assumption. We compare gradient-based optimization using sensitivity analysis with two other optimization methods – gradient-based optimization with finite differences and a stochastic optimization method – for simulation examples with artificial data. Furthermore, we compare different numerical schemes for the evaluation of the log-likelihood function. We found that gradient-based optimization using sensitivity analysis outperforms the other optimization methods in terms of convergence and computation time.

Carolin Loos introduces two novel approaches for the analysis of single-cell data. Both approaches can be used to study cellular heterogeneity and therefore advance a holistic understanding of biological processes. The first method, ODE constrained mixture modeling, enables the identification of subpopulation structures and sources of variability in single-cell snapshot data. The second method estimates parameters of single-cell time-lapse data using approximate Bayesian computation and is able to exploit the temporal cross-correlation of the data as well as lineage information.

Inflammation plays an important role in the initiation, development, progression and complications of atherosclerotic vascular disease. Our present knowledge of the elementary role of inflammation for the onset of plaque rupture in atherosclerotic coronary lesions primarily stems from autopsy studies. However, the introduction of directional coronary atherectomy catheters has provided a unique opportunity to directly investigate the role of inflammation in coronary syndromes. In this report we describe the role of coronary plaque inflammation, as determined by immunohistochemistry, on the presentation of coronary syndromes and on the clinical outcome following percutaneous interventions.

An immunocytochemical staining method has been developed for simultaneous staining of both cell surface markers (CD4 and CD8) and intracellular cytokine proteins IFN-gamma, IL-4 and IL-5. Cell surface molecules were visualized with alkaline phosphatase, which was developed by Fast Blue BB. Intracellular cytokine proteins were detected by amino-ethyl carbazole. We applied this technique to T cells from T-cell lines and T-cell clones, peripheral blood mononuclear cells and broncho-alveolar lavage fluid cells. Cells were used either unstimulated or stimulated for 4 h with 1 ng/ml PMA and 1 microg/ml ionomycin, which proved to be an optimal stimulus taking cytokine staining, cell recovery and cell viability into account. We studied peripheral blood mononuclear cells from healthy subjects and found that without in vitro stimulation on average 0.4% of the cells were IFN-gamma positive cells. In unstimulated broncho-alveolar lavage fluid cells of the 2 allergic asthmatic subjects studied so far we found higher numbers of cytokine-positive cells (up to 22% of the lymphocytes being IL-4+ cells). By in vitro stimulation, the numbers of cytokine-positive peripheral blood mononuclear cells from the healthy subjects were increased to maximally 5% IFN-gamma+ cells. In stimulated lavage fluid cells from allergic asthmatic subjects maximally 34% of the lymphocytes became IFN-gamma+. We conclude that this method allows detection of intracellular cytokine proteins in both CD4+ and CD8+ T cells without the need for stimulating the cells in vitro. In vitro stimulation may change the cytokine profile detected

BACKGROUND: C-type natriuretic peptide (CNP) belongs to the natriuretic peptide family and is considered to have regulatory effects on vascular tone and smooth muscle growth. Since these features play a role in atherogenesis, the presence of CNP at such sites was studied. METHODS AND RESULTS: Thirty-three coronary artery segments were harvested at autopsy: 10 normal, with diffuse intimal thickening, and 23 atherosclerotic lesions. Samples were snap-frozen and processed for immunohistochemical staining. For the identification of CNP, a mouse monoclonal antibody (KY-CNP-1) was used. 1A4, EBM-11 (CD68), and von Willebrand factor antibodies were used to stain smooth muscle cells, macrophages, and endothelial cells, respectively. CNP is present in several cell types. Normal arterial segments show CNP-positive endothelial cells. Hypercellular atherosclerotic lesions show distinct CNP positivity of smooth muscle cells and macrophages but a decrease in positivity of endothelial cells. Advanced atherosclerotic lesions contain CNP-positive macrophages, but the smooth muscle cells within the fibrous cap and the surface endothelial cells are almost all CNP-negative. CONCLUSIONS: These observations suggest that CNP has functional significance in atherogenesis

The study was designed to verify the concept of plaques "at risk" and whether inflammation could play a role in plaque rupture and thrombosis. In 20 patients who had died of acute myocardial infarction, the thrombosed coronary artery was identified and the site of plaque rupture was traced in serial sections. The cellular characteristics of the fibrous cap at the immediate site of rupture were analyzed and compared with the adjacent cap tissue by use of monoclonal antibodies reactive with macrophages, T lymphocytes, and smooth muscle cells. A deep intimal rupture, extending into the lipid core, was encountered in 12 plaques, whereas 8 had superficial erosions only. Ten atherosclerotic plaques had a distinctly attenuated fibrous cap covering a large atheroma, 7 showed a thick fibrocellular cap overlying a lipid pool, and 3 showed a fibrocellular lesion without a clear lipid core. Macrophages, and to a lesser extent T lymphocytes, were the dominant cells at the immediate site of either rupture or superficial erosion in each instance. These sites, moreover, were always characterized by abundant expression of HLA-DR antigens on both inflammatory cells and adjacent smooth muscle cells, suggesting an active inflammatory reaction. In terms of overall cellular composition of the ruptured plaques, the dominant cell types were macrophages and T cells in 11, smooth muscle cells in 3, and mixtures of both in 6. The underlying atherosclerotic plaque morphology in complicated coronary artery lesions causing acute myocardial infarction is heterogeneous with respect to both plaque architecture and cellular composition. However, the immediate site of plaque rupture or erosion is always marked by an inflammatory process. This suggests that inflammation plays a role in destabilizing the fibrous cap tissue and, thus, in enhancing the risk of coronary thrombosis

This study has examined the effect of postmortem autolysis, type, and duration of fixation on neurofilament, synaptophysin, and glial fibrillary acidic protein (GFAP) antigen decay as demonstrated by immunohistochemistry, using a streptavidin-biotin peroxidase method. The system used consisted of 5 normal cerebellar cortices. Time intervals, temperature, mode of fixation and storage, and staining technique were well controlled. Anti-neurofilament antibodies comprised SMI-31, MNF, and BF-10 against phosphorylated epitopes, and SMI-32 against a non-phosphorylated epitope. Bouin's and B5 fixative, and Sensofix gave best results, whereas formaldehyde and paraformaldehyde fixation gave much lower immunoreactivity. Phosphorylated neurofilament epitopes were less affected by aldehydes than unphosphorylated epitopes. GFAP staining was most consistent after Bouin fixation while the monoclonal antibody was much more sensitive to the fixative used than the polyclonal one. Aspecific background staining increased considerably after a postmortem interval of 24 hours. Synaptophysin immunoreactivity, as demonstrated by SY-38, proved very sensitive to prolonged fixation and was of poor quality following formaldehyde and paraformaldehyde fixation. Knowledge of antigen decay due to postmortem artifacts is essential for the correct evaluation of immunoperoxidase studies of autolyzed tissues that have been fixed and stored in different modes and for variable time interval