Spatial Rule-Based Simulations: The SRSim Software.

SRSim combines rule-based reaction network models with spatial particle simulations allowing to simulate the dynamics of large molecular complexes changing according to a set of chemical reaction rules. As the rule can contain patterns of molecular complexes and specific states of certain binding sites, a combinatorially complex or even infinitely sized reaction network can be defined. Particles move in a three-dimensional space according to molecular dynamics implemented by LAMMPS, while the BioNetGen language is used to formulate reaction rules. Geometric information is added in a specific XML format. The simulation protocol is exemplified by two different variants of polymerization as well as a toy model of DNA helix formation. SRSim is open source and available for download.

Multi-scale stochastic organization-oriented coarse-graining exemplified on the human mitotic checkpoint.

The complexity of biological models makes methods for their analysis and understanding highly desirable. Here, we demonstrate the orchestration of various novel coarse-graining methods by applying them to the mitotic spindle assembly checkpoint. We begin with a detailed fine-grained spatial model in which individual molecules are simulated moving and reacting in a three-dimensional space. A sequence of manual and automatic coarse-grainings finally leads to the coarsest deterministic and stochastic models containing only four molecular species and four states for each kinetochore, respectively. We are able to relate each more coarse-grained level to a finer one, which allows us to relate model parameters between coarse-grainings and which provides a more precise meaning for the elements of the more abstract models. Furthermore, we discuss how organizational coarse-graining can be applied to spatial dynamics by showing spatial organizations during mitotic checkpoint inactivation. We demonstrate how these models lead to insights if the model has different "meaningful" behaviors that differ in the set of (molecular) species. We conclude that understanding, modeling and analyzing complex bio-molecular systems can greatly benefit from a set of coarse-graining methods that, ideally, can be automatically applied and that allow the different levels of abstraction to be related.

A Dynamical Model for Activating and Silencing the Mitotic Checkpoint.

The spindle assembly checkpoint (SAC) is an evolutionarily conserved mechanism, exclusively sensitive to the states of kinetochores attached to microtubules. During metaphase, the anaphase-promoting complex/cyclosome (APC/C) is inhibited by the SAC but it rapidly switches to its active form following proper attachment of the final spindle. It had been thought that APC/C activity is an all-or-nothing response, but recent findings have demonstrated that it switches steadily. In this study, we develop a detailed mathematical model that considers all 92 human kinetochores and all major proteins involved in SAC activation and silencing. We perform deterministic and spatially-stochastic simulations and find that certain spatial properties do not play significant roles. Furthermore, we show that our model is consistent with in-vitro mutation experiments of crucial proteins as well as the recently-suggested rheostat switch behavior, measured by Securin or CyclinB concentration. Considering an autocatalytic feedback loop leads to an all-or-nothing toggle switch in the underlying core components, while the output signal of the SAC still behaves like a rheostat switch. The results of this study support the hypothesis that the SAC signal varies with increasing number of attached kinetochores, even though it might still contain toggle switches in some of its components.

Structural analysis of in silico mutant experiments of human inner-kinetochore structure.

Large multi-molecular complexes like the kinetochore are lacking of suitable methods to determine their spatial structure. Here, we use and evaluate a novel modeling approach that combines rule-bases reaction network models with spatial molecular geometries. In particular, we introduce a method that allows to study in silico the influence of single interactions (e.g. bonds) on the spatial organization of large multi-molecular complexes and apply this method to an extended model of the human inner-kinetochore. Our computational analysis method encompasses determination of bond frequency, geometrical distances, statistical moments, and inter-dependencies between bonds using mutual information. For the analysis we have extend our previously reported human inner-kinetochore model by adding 13 new protein interactions and three protein geometry details. The model is validated by comparing the results of in silico with reported in vitro single protein deletion experiments. Our studies revealed that most simulations mimic the in vitro behavior of the kinetochore complex as expected. To identify the most important bonds in this model, we have created 39 mutants in silico by selectively disabling single protein interactions. In a total of 11,800 simulation runs we have compared the resulting structures to the wild-type. In particular, this allowed us to identify the interaction Cenp-W-H3 and Cenp-S-Cenp-X as having the strongest influence on the inner-kinetochore's structure. We conclude that our approach can become a useful tool for the in silico dynamical study of large, multi-molecular complexes.

Active transport can greatly enhance Cdc20:Mad2 formation.

To guarantee genomic integrity and viability, the cell must ensure proper distribution of the replicated chromosomes among the two daughter cells in mitosis.The mitotic spindle assembly checkpoint (SAC) is a central regulatory mechanism to achieve this goal. A dysfunction of this checkpoint may lead to aneuploidy and likely contributes to the development of cancer. Kinetochores of unattached or misaligned chromosomes are thought to generate a diffusible ''wait-anaphase'' signal, which is the basis for downstream events to inhibit the anaphase promoting complex/cyclosome (APC/C). The rate of Cdc20:C-Mad2 complex formation at the kinetochore is a key regulatory factor in the context of APC/C inhibition. Computer simulations of a quantitative SAC model show that the formation of Cdc20:C-Mad2 is too slow for checkpoint maintenance when cytosolic O-Mad2 has to encounter kinetochores by diffusion alone. Here, we show that an active transport of O-Mad2 towards the spindle mid-zone increases the efficiency of Mad2-activation. Our data indicate that this mechanism can greatly enhance the formation of Cdc20:Mad2 and furthermore gives an explanation on how the ''wait-anaphase'' signal can dissolve abruptly within a short time. Our results help to understand parts of the SAC mechanism that remain unclear.

Spatial rule-based modeling: a method and its application to the human mitotic kinetochore.

A common problem in the analysis of biological systems is the combinatorial explosion that emerges from the complexity of multi-protein assemblies. Conventional formalisms, like differential equations, Boolean networks and Bayesian networks, are unsuitable for dealing with the combinatorial explosion, because they are designed for a restricted state space with fixed dimensionality. To overcome this problem, the rule-based modeling language, BioNetGen, and the spatial extension, SRSim, have been developed. Here, we describe how to apply rule-based modeling to integrate experimental data from different sources into a single spatial simulation model and how to analyze the output of that model. The starting point for this approach can be a combination of molecular interaction data, reaction network data, proximities, binding and diffusion kinetics and molecular geometries at different levels of detail. We describe the technique and then use it to construct a model of the human mitotic inner and outer kinetochore, including the spindle assembly checkpoint signaling pathway. This allows us to demonstrate the utility of the procedure, show how a novel perspective for understanding such complex systems becomes accessible and elaborate on challenges that arise in the formulation, simulation and analysis of spatial rule-based models.

Surgical correction of a congenital coronary arterial fistula and a massive sinus of Valsalva aneurysm.

The case of a 22-year old male patient who presented with a congenital coronary arterial fistula from the right coronary artery to the right ventricle is described. The arterial fistula had led to an aneurysm of the right sinus of Valsalva and the proximal right coronary artery. The aneurysm was incised from the aorta and the fistula closed with a pericardial patch. The diameter of the aneurysm was reduced by plication. Successful occlusion of the fistula and the competence of the aortic valve were confirmed by transoesophageal echocardiography.

Beneficial effect of sodium nitroprusside after coronary artery bypass surgery: pump function correlates inversely with cardiac release of proinflammatory cytokines.

The authors studied the relationship between cardiac cytokine release and pump function and whether low-dose application of sodium nitroprusside (SNP) improves cardiac performance during coronary artery bypass graft (CABG) creation. Cardiac reperfusion and application of nitric oxide have an influence on cytokine release. However, the functional consequences are unclear. Patients with CABGs (n = 30) with severely compromised left ventricular ejection fraction (<40%) were treated with either SNP (0.5 microg/kg/min) or placebo for the first 60 minutes of reperfusion after cardiac arrest. Interleukin (IL)-6, IL-8, and tumor necrosis factor (TNF)-alpha were determined in blood samples from the radial artery and coronary sinus during reperfusion (5, 35, and 75 minutes). Hemodynamic measurements were performed before and after cardiopulmonary bypass and at the end of surgery. In all patients, the cardiac index at the end of surgery correlated negatively with levels of TNF-alpha at 5 minutes (r = 0.398; P < 0.05), IL-8 at 35 minutes (r = 0.394; P < 0.05), and IL-6 at 75 minutes of reperfusion (r = 0.421; P < 0.025). Sodium nitroprusside improved the cardiac index immediately after reperfusion (4.4 L/min/m2 +/- 0.3 vs. 3.7 L/min/m2 +/- 0.1; P = 0.014) and at the end of surgery (3.8 L/min/m2 +/- 0.3 vs. 3.0 L/min/m2 +/- 0.2; P = 0.023). The negative correlation between cardiac index and transcardiac cytokines suggests that reducing cardiac inflammatory reaction improves postischemic cardiac function. This was achieved by treating CABG patients with the nitric oxide donor SNP at a dosage without vasodilatory action.