Monte Carlo simulations of single- and multistep enzyme-catalyzed reaction sequences: effects of diffusion, cell size, enzyme fluctuations, colocalization, and segregation

Enzyme Trafficking and Co-Clustering Precede and Accurately Predict Human Breast Cancer Recurrences: An Interdisciplinary Review

Although great effort has been expended to understand cancer's origins, less attention has been given to the primary cause of cancer deaths - cancer recurrences and their sequelae. This interdisciplinary review addresses mechanistic features of aggressive cancer by studying metabolic enzyme patterns within ductal carcinoma in situ (DCIS) of the breast lesions. DCIS lesions from patients who did or did not experience a breast cancer recurrence were compared. Several proteins, including phospho-Ser226-glucose transporter type 1, phosphofructokinase type L and phosphofructokinase/fructose 2,6-bisphosphatase type 4 are found in nucleoli of ductal epithelial cells in samples from patients who will not subsequently recur, but traffic to the cell periphery in samples from patients who will experience a cancer recurrence. Large co-clusters of enzymes near plasmalemmata will enhance product formation because enzyme concentrations in clusters are very high while solvent molecules and solutes diffuse through small channels. These structural changes will accelerate aerobic glycolysis. Agglomerations of pentose phosphate pathway and glutathione synthesis enzymes enhance GSH formation. As aggressive cancer lesions are incomplete at early stages, they may be unrecognizable. We have found that machine learning provides superior analyses of tissue images and may be used to identify biomarker patterns associated with recurrent and non-recurrent patients with high accuracy. This suggests a new prognostic test to predict DCIS patients who are likely to recur and those who are at low risk for recurrence. Mechanistic interpretations provide a deeper understanding of anti-cancer drug action and suggest that aggressive metastatic cancer cells are sensitive to reductive chemotherapy.

Consequences of Heterogeneous Crowding on an Enzymatic Reaction: A Residence Time Monte Carlo Approach

Translational diffusion of a free substrate in crowded metabolically active spaces such as cell cytoplasm or mitochondrial matrix is punctuated by collisions and nonspecific interactions with soluble/immobile macromolecules/macrostructures in a variety of shapes/sizes. It is not understood how such disruptions alter enzyme reaction kinetics in such spaces. A novel Monte Carlo (MC) technique, "residence time MC", has been developed to study the kinetics of a simple enzyme-substrate reaction in a crowded milieu using a single immobile enzyme in the midst of diffusing substrates and products. The reaction time lost while the substrate nonspecifically interacts or is transiently trapped with ambient macromolecules is quantified by introducing the residence time "tau". Tau scales with the size of crowding macromolecules but makes the knowledge of their shape redundant. The residence time thus presents a convenient parameter to realistically mimic the sticky surroundings encountered by a diffusing substrate in heterogeneously crowded physiological spaces. Results reveal that for identical substrate concentration and excluded volume, increase in tau significantly diminished enzymatic product yield and reaction rate, slowed down substrate/product diffusion, and prolonged their relaxation times. A smooth transition from the anomalous subdiffusive motion to normal diffusion at long time limits was observed irrespective of the value of tau. The predictions from the model are shown to be in qualitative agreement with in vitro experimental data revealing the rate of alkaline phosphatase-catalyzed hydrolysis of p-nitrophenyl phosphate in the midst of 40/500/2000 kDa dextrans. Our findings from the residence time MC model also attempt to rationalize previously unexplained experimental observations in crowded enzyme kinetics literature. Furthermore, major insights to emerge from this study are the reasons why free diffusion of the substrate in crowded physiological spaces is detrimental to enzyme function. It is argued that organized enzyme clusters such as "metabolon" may perhaps exist to regulate the substrate translocation in such sticky physiological spaces to maintain optimal enzyme function. In summary, this work provides key insights explaining why absence of substrate channeling can dramatically slow down enzyme reaction rate in crowded metabolically active spaces.

Molecular mechanisms underlying striatal synaptic plasticity: relevance to chronic alcohol consumption and seeking

The striatum, the input structure of the basal ganglia, is a major site of learning and memory for goal-directed actions and habit formation. Spiny projection neurons of the striatum integrate cortical, thalamic, and nigral inputs to learn associations, with cortico-striatal synaptic plasticity as a learning mechanism. Signaling molecules implicated in synaptic plasticity are altered in alcohol withdrawal, which may contribute to overly strong learning and increased alcohol seeking and consumption. To understand how interactions among signaling molecules produce synaptic plasticity, we implemented a mechanistic model of signaling pathways activated by dopamine D1 receptors, acetylcholine receptors, and glutamate. We use our novel, computationally efficient simulator, NeuroRD, to simulate stochastic interactions both within and between dendritic spines. Dopamine release during theta burst and 20-Hz stimulation was extrapolated from fast-scan cyclic voltammetry data collected in mouse striatal slices. Our results show that the combined activity of several key plasticity molecules correctly predicts the occurrence of either LTP, LTD, or no plasticity for numerous experimental protocols. To investigate spatial interactions, we stimulate two spines, either adjacent or separated on a 20-μm dendritic segment. Our results show that molecules underlying LTP exhibit spatial specificity, whereas 2-arachidonoylglycerol exhibits a spatially diffuse elevation. We also implement changes in NMDA receptors, adenylyl cyclase, and G protein signaling that have been measured following chronic alcohol treatment. Simulations under these conditions suggest that the molecular changes can predict changes in synaptic plasticity, thereby accounting for some aspects of alcohol use disorder.

Diffusion-limited attachment of large spherical particles to flexible membrane-immobilized receptors

Relatively large (~100 nm) spherical particles, e.g., virions, vesicles, or metal nanoparticles, often interact with short (<10 nm) flexible receptors immobilized in a lipid membrane or on other biologically relevant surfaces. The attachment kinetics of such particles may be limited globally by their diffusion toward a membrane or locally by diffusion around receptors. The detachment kinetics, also, can be limited by diffusion. Focusing on local diffusion limitations and using suitable approximations, we present expressions for the corresponding rate constants and identify their dependence on particle size and receptor length. We also illustrate features likely to be observed in such kinetics for particles (e.g., vesicles) with a substantial size distribution. The results obtained are generic and can be used to interpret a variety of situations. For example, we estimate upper values of virion attachment rate constants and clarify the likely effect of vesicle size distribution on previously observed non-exponential kinetics of vesicle detachment.