Fiber depolymerization

Depolymerization is, by definition, a crucial process in the reversible assembly of various biopolymers. It may also be an important factor in the pathology of sickle cell disease. If sickle hemoglobin fibers fail to depolymerize fully during passage through the lungs then they will reintroduce aggregates into the systemic circulation and eliminate or shorten the protective delay (nucleation) time for the subsequent growth of fibers. We study how depolymerization depends on the rates of end- and side-depolymerization, kend and kside, which are, respectively, the rates at which fiber length is lost at each end and the rate at which new breaks appear per unit fiber length. We present both an analytic mean field theory and supporting simulations showing that the characteristic fiber depolymerization time View the MathML source depends on both rates, but not on the fiber length L, in a large intermediate regime 1 much less-than ksideL2/kend much less-than (L/d)2, with d the fiber diameter. We present new experimental data which confirms that both mechanisms are important and shows how the rate of side depolymerization depends strongly on the concentration of CO, acting as a proxy for oxygen. Our theory remains rather general and could be applied to the depolymerization of an entire class of linear aggregates, not just sickle hemoglobin fibers

Microtubule depolymerization by the kinesin-8 motor Kip3p: a mathematical model

Proteins from the kinesin-8 family promote microtubule (MT) depolymerization, a process thought to be important for the control of microtubule length in living cells. In addition to this MT shortening activity, kinesin 8s are motors that show plus-end directed motility on MTs. Here we describe a simple model that incorporates directional motion and destabilization of the MT plus end by kinesin 8. Our model quantitatively reproduces the key features of length-vs-time traces for stabilized MTs in the presence of purified kinesin 8, including length-dependent depolymerization. Comparison of model predictions with experiments suggests that kinesin 8 depolymerizes processively, i.e., one motor can remove multiple tubulin dimers from a stabilized MT. Fluctuations in MT length as a function of time are related to depolymerization processivity. We have also determined the parameter regime in which the rate of MT depolymerization is length dependent: length-dependent depolymerization occurs only when MTs are sufficiently short; this crossover is sensitive to the bulk motor concentration.Comment: 34 pages, 11 figure

Analysis of gas chromatography/mass spectrometry data for catalytic lignin depolymerization using positive matrix factorization

Various catalytic technologies are being developed to efficiently convert lignin into renewable chemicals. However, due to its complexity, catalytic lignin depolymerization often generates a wide and complex distribution of product compounds. Gas chromatography/mass spectrometry (GC-MS) is a common analytical technique to profile the compounds that comprise lignin depolymerization products. GC-MS is applied not only to determine the product composition, but also to develop an understanding of the catalytic reaction pathways and of the relationships among catalyst structure, reaction conditions, and the resulting compounds generated. Although a very useful tool, the analysis of lignin depolymerization products with GC-MS is limited by the quality and scope of the available mass spectral libraries and the ability to correlate changes in GC-MS chromatograms to changes in lignin structure, catalyst structure, and other reaction conditions. In this study, the GC-MS data of the depolymerization products generated from organosolv hybrid poplar lignin using a copper-doped porous metal oxide catalyst and a methanol/dimethyl carbonate co-solvent was analyzed by applying a factor analysis technique, positive matrix factorization (PMF). Several different solutions for the PMF model were explored. A 13-factor solution sufficiently explains the chemical changes occurring to lignin depolymerization products as a function of lignin, reaction time, catalyst, and solvent. Overall, seven factors were found to represent aromatic compounds, while one factor was defined by aliphatic compounds

Simultaneous quantification of depolymerization and mineralization rates by a novel 15N tracing model

The depolymerization of soil organic matter, such as proteins and (oligo-)peptides, into monomers (e.g. amino acids) is currently considered to be the rate-limiting step for nitrogen (N) availability in terrestrial ecosystems. The mineralization of free amino acids (FAAs), liberated by the depolymerization of peptides, is an important fraction of the total mineralization of organic N. Hence, the accurate assessment of peptide depolymerization and FAA mineralization rates is important in order to gain a better process-based understanding of the soil N cycle. In this paper, we present an extended numerical 15N tracing model Ntrace, which incorporates the FAA pool and related N processes in order to provide a more robust and simultaneous quantification of depolymerization and gross mineralization rates of FAAs and soil organic N. We discuss analytical and numerical approaches for two forest soils, suggest improvements of the experimental work for future studies, and conclude that (i) when about half of all depolymerized peptide N is directly mineralized, FAA mineralization can be as important a rate-limiting step for total gross N mineralization as peptide depolymerization rate; (ii) gross FAA mineralization and FAA immobilization rates can be used to develop FAA use efficiency (NUEFAA), which can reveal microbial N or carbon (C) limitation

Long-time asymptotics for polymerization models

This study is devoted to the long-term behavior of nucleation, growth and fragmentation equations, modeling the spontaneous formation and kinetics of large polymers in a spatially homogeneous and closed environment. Such models are, for instance, commonly used in the biophysical community in order to model in vitro experiments of fibrillation. We investigate the interplay between four processes: nucleation, polymeriza-tion, depolymerization and fragmentation. We first revisit the well-known Lifshitz-Slyozov model, which takes into account only polymerization and depolymerization, and we show that, when nucleation is included, the system goes to a trivial equilibrium: all polymers fragmentize, going back to very small polymers. Taking into account only polymerization and fragmentation, modeled by the classical growth-fragmentation equation, also leads the system to the same trivial equilibrium, whether or not nucleation is considered. However, also taking into account a depolymer-ization reaction term may surprisingly stabilize the system, since a steady size-distribution of polymers may then emerge, as soon as polymeriza-tion dominates depolymerization for large sizes whereas depolymerization dominates polymerization for smaller ones-a case which fits the classical assumptions for the Lifshitz-Slyozov equations, but complemented with fragmentation so that " Ostwald ripening " does not happen.Comment: https://link.springer.com/article/10.1007/s00220-018-3218-

Direct Depolymerization Coupled to Liquid Extraction Surface Analysis-High-Resolution Mass Spectrometry for the Characterization of the Surface of Plant Tissues

The cuticle, the outermost layer covering the epidermis of most aerial organs of land plants, can have a heterogeneous composition even on the surface of the same organ. The main cuticle component is the polymer cutin which, depending on its chemical composition and structure, can have different biophysical properties. In this study, we introduce a new on-surface depolymerization method coupled to liquid extraction surface analysis (LESA) high-resolution mass spectrometry (HRMS) for a fast and spatially resolved chemical characterization of the cuticle of plant tissues. The method is composed of an on-surface saponification, followed by extraction with LESA using a chloroform-acetonitrile-water (49:49:2) mixture and direct HRMS detection. The method is also compared with LESA-HRMS without prior depolymerization for the analysis of the surface of the petals of Hibiscus richardsonii flowers, which have a ridged cuticle in the proximal region and a smooth cuticle in the distal region. We found that on-surface saponification is effective enough to depolymerize the cutin into its monomeric constituents thus allowing detection of compounds that were not otherwise accessible without a depolymerization step. The effect of the depolymerization procedure was more pronounced for the ridged/proximal cuticle, which is thicker and richer in epicuticular waxes compared with the cuticle in the smooth/distal region of the petal

Growth and dissolution of macromolecular Markov chains

The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle

Kinetics and thermodynamics of first-order Markov chain copolymerization

We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer

Distribution of lifetimes of kinetochore-microtubule attachments: interplay of energy landscape, molecular motors and microtubule (de-)polymerization

Before a cell divides into two daughter cells, chromosomes are replicated resulting in two sister chromosomes embracing each other. Each sister chromosome is bound to a separate proteinous structure, called kinetochore (kt), that captures the tip of a filamentous protein, called microtubule (MT). Two oppositely oriented MTs pull the two kts attached to two sister chromosomes thereby pulling the two sisters away from each other. Here we theoretically study an even simpler system, namely an isolated kt coupled to a single MT; this system mimics an {\it in-vitro} experiment where a single kt-MT attachment is reconstituted using purified extracts from budding yeast. Our models not only account for the experimentally observed "catch-bond-like" behavior of the kt-MT coupling, but also make new predictions on the probability distribution of the lifetimes of the attachments. In principle, our new predictions can be tested by analyzing the data collected in the {\it in-vitro} experiments provided the experiment is repeated sufficiently large number of times. Our theory provides a deep insight into the effects of (a) size, (b) energetics, and (c) stochastic kinetics of the kt-MT coupling on the distribution of the lifetimes of these attachments.Comment: This is an author-created, un-copyedited version of an article accepted for publication in "Physical Biology" (IOP). IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Length control of microtubules by depolymerizing motor proteins

In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.Comment: Added section with figures and significantly expanded text, current version to appear in Europhys. Let