Stochastic modelling suggests that an elevated superoxide anion - hydrogen peroxide ratio can drive extravascular phagocyte transmigration by lamellipodium formation

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval [Formula: see text] and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity.

The life of the cell membrane: A paradigmatic reading from Deleuze and Guattari

While the Fluid Mosaic model (FMM) is widely accepted as an account of the cell membrane's structure-function, its inability to explain certain phenomena has led to the lipid rafts hypothesis (nanodomains) that spontaneous spatiotemporal enriched zones of sphingolipids-cholesterol-protein exist within the membrane. In this text, we propose a novel approach that conceives the cell membrane as a living entity. The questions regarding the FMM revolve around the fact that, although these molecular components are present in many cell types, the membrane does not react in the same way to every external agent; for example, a virus evokes a particular response: why is there some marked specificity of virus (or toxin) attack on one (or some) of these cell types and not to other cell types that nevertheless have a similar membrane protein constitution? The crucial question, to explain this selectivity, would be what determines the specificity of attack on some cells and not others? While FMN assumes a dynamism between macrostates at the intramolecular, intermolecular, and/or collective levels in the membrane, the approach of the lipid raft model presupposes a much greater and more complex dynamics of microstates (even nano-states) of these molecular components. In other words, it implies higher and instantaneous mobility as assemblages ("intentional") and thus, of the membrane itself (as a collective), in response to changes in the internal and external physicochemical environment over a broad spatiotemporal scale. This suggests a mechanism of membrane adaptation in the face of evolutionary constraints. In this text, we propose a paradigmatic approach, from Deleuze-Guattari's philosophy: to conceive the cell membrane as living and not as a mere molecular conglomerate with particular functions and mechanical processes between molecules. For this, we employ the functional concepts of territory and machinic assemblage, whence the vitality of the membrane would allow us to postulate instantaneous updates, within wider spatiotemporal scales in its composition in contrast with the model that dominates as a more plausible explanation nowadays, that does not include smaller spatiotemporal events. If we resort to the concept of territory and its different media components, we could offer a more plausible explanation of the vigorous dynamism in the composition of the cell membrane since it would allow more subtle and complex differentiations between media and thus make visible the constant and instant changes. We propose that the model of nanodomains, understood as a process of dynamic territorialization, offers a more complex and subtle explanation of the instantaneous changes in the cell membrane's composition. This approach expands the explanatory framework for cellular phenomena and reveals their spatiotemporal complexity in accordance with other research.

ReDirection: an R-package to compute the probable dissociation constant for every reaction of a user-defined biochemical network

Biochemical networks integrate enzyme-mediated substrate conversions with non-enzymatic complex formation and disassembly to accomplish complex biochemical and physiological functions. The choice of parameters and constraints used in most of these studies is numerically motivated and network-specific. Although sound in theory, the outcomes that result depart significantly from the intracellular milieu and are less likely to retain relevance in a clinical setting. There is a need for a computational tool which is biochemically relevant, mathematically rigorous, and unbiased, and can ascribe functionality to and generate potentially testable hypotheses for a user-defined biochemical network. Here, we present "ReDirection," an R-package which computes the probable dissociation constant for every reaction of a biochemical network directly from a null space-generated subspace of the stoichiometry number matrix of the modeled network. "ReDirection" delineates this subspace by excluding all trivial and redundant or duplicate occurrences of non-trivial vectors, combinatorially summing the vectors that remain and verifying that the upper or lower bounds of the sequence of terms formed by each row of this subspace belong to the open real-valued intervals - ∞ , - 1 or 1 , ∞ or whether the number of terms that are differently signed are almost equal. "ReDirection" iterates these steps until these bounds are consistent and unambiguous for all reactions of the modeled biochemical network. Thereafter, "ReDirection" filters the terms from each row of this subspace, bins them to outcome-specific subsets, sums and maps this to an outcome-specific reaction vector, and computes the p1-norm, which is the probable dissociation constant for a reaction. "ReDirection" works on first principles, does not discriminate between enzymatic and non-enzymatic reactions, offers a biochemically relevant and mathematically rigorous environment to explore user-defined biochemical networks under baseline and perturbed conditions, and can be used to address empirically intractable biochemical problems. The utility and relevance of "ReDirection" are highlighted by numerical studies on stoichiometric number models of biochemical networks of galactose metabolism and heme and cholesterol biosynthesis. "ReDirection" is freely available and accessible from the comprehensive R archive network (CRAN) with the URL (https://cran.r-project.org/package=ReDirection).

Mathematical modeling and stochastic simulations suggest that low-affinity peptides can bisect MHC1-mediated export of high-affinity peptides into "early"- and "late"-phases

The peptide loading complex (PLC) is a multi-protein complex of the endoplasmic reticulum (ER) which optimizes major histocompatibility I (MHC1)-mediated export of intracellular high-affinity peptides. Whilst, the molecular biology of MHC1-mediated export is well supported by empirical data, the stoichiometry, kinetics and spatio-temporal profile of the participating molecular entities are a matter of considerable debate. Here, a low-affinity peptide-driven (LAPD)-model of MHC1-mediated high-affinity peptide export is formulated, implemented, analyzed and simulated. The model is parameterized in terms of the contribution of the shunt reaction to the concentration of exportable MHC1. Theoretical analyses and simulation studies of the model suggest that low-affinity peptides can bisect MHC1-mediated export of high-affinity peptides into time-dependent distinct “early”- and “late”-phases. The net exportable MHC1 (eM1β(t)) is a function of the retrograde (rM1β(t))- and anterograde (aM1β(t))-derived fractions. The “early”-phase is dominated by the contribution of the retrograde/recyclable (rM1β≈61%,aM1β≈39%) pathway to exportable MHC1, is characterized by Tapasin-mediated peptide-editing and is ATP-independent. The “late”-phase on the other hand, is characterized by de novo PLC-assembly, rapid disassembly and a significant contribution of the anterograde pathway to exportable MHC1 (rM1β≈21%,aM1β≈79%). The shunt reaction is rate limiting and may integrate peptide translocation with PLC-assembly/disassembly thereby, regulating peptide export under physiological and pathological (viral infections, dysplastic alterations) conditions.