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Institute
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Improving permafrost dynamics in land surface models: insights from dual sensitivity experiments
(2024)
The thawing of permafrost and the subsequent release of greenhouse gases constitute one of the most significant and uncertain positive feedback loops in the context of climate change, making predictions regarding changes in permafrost coverage of paramount importance. To address these critical questions, climate scientists have developed Land Surface Models (LSMs) that encompass a multitude of physical soil processes. This thesis is committed to advancing our understanding and refining precise representations of permafrost dynamics within LSMs, with a specific focus on the accurate modeling of heat fluxes, an essential component for simulating permafrost physics.
The first research question overviews fundamental model prerequisites for the representation of permafrost soils within land surface modeling. It includes a first-of-its-kind comparison between LSMs in CMIP6 to reveal their differences and shortcomings in key permafrost physics parameters. Overall, each of these LSMs represents a unique approach to simulating soil processes and their interactions with the climate system. Choosing the most appropriate model for a particular application depends on factors such as the spatial and temporal scale of the simulation, the specific research question, and available computational resources.
The second research question evaluates the performance of the state-of-the-art Community Land Model (CLM5) in simulating Arctic permafrost regions. Our approach overcomes traditional evaluation limitations by individually addressing depth, seasonality, and regional variations, providing a comprehensive assessment of permafrost and soil temperature dynamics. I compare CLM5's results with three extensive datasets: (1) soil temperatures from 295 borehole stations, (2) active layer thickness (ALT) data from the Circumpolar Active Layer Monitoring Network (CALM), and (3) soil temperatures, ALT, and permafrost extent from the ESA Climate Change Initiative (ESA-CCI). The results show that CLM5 aligns well with ESA-CCI and CALM for permafrost extent and ALT but reveals a significant global cold temperature bias, notably over Siberia. These results echo a persistent challenge identified in numerous studies: the existence of a systematic 'cold bias' in soil temperature over permafrost regions. To address this challenge, the following research questions propose dual sensitivity experiments.
The third research question represents the first study to apply a Plant Functional Type (PFT)-based approach to derive soil texture and soil organic matter (SOM), departing from the conventional use of coarse-resolution global data in LSMs. This novel method results in a more uniform distribution of soil organic matter density (OMD) across the domain, characterized by reduced OMD values in most regions. However, changes in soil texture exhibit a more intricate spatial pattern. Comparing the results to observations reveals a significant reduction in the cold bias observed in the control run. This method shows noticeable improvements in permafrost extent, but at the cost of an overestimation in ALT. These findings emphasize the model's high sensitivity to variations in soil texture and SOM content, highlighting the crucial role of soil composition in governing heat transfer processes and shaping the seasonal variation of soil temperatures in permafrost regions.
Expanding upon a site experiment conducted in Trail Valley Creek by \citet{dutch_impact_2022}, the fourth research question extends the application of the snow scheme proposed by \citet{sturm_thermal_1997} to cover the entire Arctic domain. By employing a snow scheme better suited to the snow density profile observed over permafrost regions, this thesis seeks to assess its influence on simulated soil temperatures. Comparing this method to observational datasets reveals a significant reduction in the cold bias that was present in the control run. In most regions, the Sturm run exhibits a substantial decrease in the cold bias. However, there is a distinctive overshoot with a warm bias observed in mountainous areas. The Sturm experiment effectively addressed the overestimation of permafrost extent in the control run, albeit resulting in a substantial reduction in permafrost extent over mountainous areas. ALT results remain relatively consistent compared to the control run. These outcomes align with our initial hypothesis, which anticipated that the reduced snow insulation in the Sturm run would lead to higher winter soil temperatures and a more accurate representation of permafrost physics.
In summary, this thesis demonstrates significant advancements in understanding permafrost dynamics and its integration into LSMs. It has meticulously unraveled the intricacies involved in the interplay between heat transfer, soil properties, and snow dynamics in permafrost regions. These insights offer novel perspectives on model representation and performance.
In recent decades, astronomy has seen a boom in large-scale stellar surveys of the Galaxy. The detailed information obtained about millions of individual stars in the Milky Way is bringing us a step closer to answering one of the most outstanding questions in astrophysics: how do galaxies form and evolve? The Milky Way is the only galaxy where we can dissect many stars into their high-dimensional chemical composition and complete phase space, which analogously as fossil records can unveil the past history of the genesis of the Galaxy. The processes that lead to large structure formation, such as the Milky Way, are critical for constraining cosmological models; we call this line of study Galactic archaeology or near-field cosmology.
At the core of this work, we present a collection of efforts to chemically and dynamically characterise the disks and bulge of our Galaxy. The results we present in this thesis have only been possible thanks to the advent of the Gaia astrometric satellite, which has revolutionised the field of Galactic archaeology by precisely measuring the positions, parallax distances and motions of more than a billion stars. Another, though not less important, breakthrough is the APOGEE survey, which has observed spectra in the near-infrared peering into the dusty regions of the Galaxy, allowing us to determine detailed chemical abundance patterns in hundreds of thousands of stars. To accurately depict the Milky Way structure, we use and develop the Bayesian isochrone fitting tool/code called StarHorse; this software can predict stellar distances, extinctions and ages by combining astrometry, photometry and spectroscopy based on stellar evolutionary models. The StarHorse code is pivotal to calculating distances where Gaia parallaxes alone cannot allow accurate estimates.
We show that by combining Gaia, APOGEE, photometric surveys and using StarHorse, we can produce a chemical cartography of the Milky way disks from their outermost to innermost parts. Such a map is unprecedented in the inner Galaxy. It reveals a continuity of the bimodal chemical pattern previously detected in the solar neighbourhood, indicating two populations with distinct formation histories. Furthermore, the data reveals a chemical gradient within the thin disk where the content of 𝛼-process elements and metals is higher towards the centre. Focusing on a sample in the inner MW we confirm the extension of the chemical duality to the innermost regions of the Galaxy. We find stars with bar shape orbits to show both high- and low-𝛼 abundances, suggesting the bar formed by secular evolution trapping stars that already existed. By analysing the chemical orbital space of the inner Galactic regions, we disentangle the multiple populations that inhabit this complex region. We reveal the presence of the thin disk, thick disk, bar, and a counter-rotating population, which resembles the outcome of a perturbed proto-Galactic disk. Our study also finds that the inner Galaxy holds a high quantity of super metal-rich stars up to three times solar suggesting it is a possible repository of old super-metal-rich stars found in the solar neighbourhood.
We also enter into the complicated task of deriving individual stellar ages. With StarHorse, we calculate the ages of main-sequence turn-off and sub-giant stars for several public spectroscopic surveys. We validate our results by investigating linear relations between chemical abundances and time since the 𝛼 and neutron capture elements are sensitive to age as a reflection of the different enrichment timescales of these elements. For further study of the disks in the solar neighbourhood, we use an unsupervised machine learning algorithm to delineate a multidimensional separation of chrono-chemical stellar groups revealing the chemical thick disk, the thin disk, and young 𝛼-rich stars. The thick disk is shown to have a small age dispersion indicating its fast formation contrary to the thin disk that spans a wide range of ages.
With groundbreaking data, this thesis encloses a detailed chemo-dynamical view of the disk and bulge of our Galaxy. Our findings on the Milky Way can be linked to the evolution of high redshift disk galaxies, helping to solve the conundrum of galaxy formation.
In this thesis we mainly generalize two theorems from Mackaay-Picken and Picken (2002, 2004). In the first paper, Mackaay and Picken show that there is a bijective correspondence between Deligne 2-classes $\xi \in \check{H}^2(M,\mathcal{D}^2)$ and holonomy maps from the second thin-homotopy group $\pi_2^2(M)$ to $U(1)$. In the second one, a generalization of this theorem to manifolds with boundaries is given: Picken shows that there is a bijection between Deligne 2-cocycles and a certain variant of 2-dimensional topological quantum field theories. In this thesis we show that these two theorems hold in every dimension. We consider first the holonomy case, and by using simplicial methods we can prove that the group of smooth Deligne $d$-classes is isomorphic to the group of smooth holonomy maps from the $d^{th}$ thin-homotopy group $\pi_d^d(M)$ to $U(1)$, if $M$ is $(d-1)$-connected. We contrast this with a result of Gajer (1999). Gajer showed that Deligne $d$-classes can be reconstructed by a different class of holonomy maps, which not only include holonomies along spheres, but also along general $d$-manifolds in $M$. This approach does not require the manifold $M$ to be $(d-1)$-connected. We show that in the case of flat Deligne $d$-classes, our result differs from Gajers, if $M$ is not $(d-1)$-connected, but only $(d-2)$-connected. Stiefel manifolds do have this property, and if one applies our theorem to these and compare the result with that of Gajers theorem, it is revealed that our theorem reconstructs too many Deligne classes. This means, that our reconstruction theorem cannot live without the extra assumption on the manifold $M$, that is our reconstruction needs less informations about the holonomy of $d$-manifolds in $M$ at the price of assuming $M$ to be $(d-1)$-connected. We continue to show, that also the second theorem can be generalized: By introducing the concept of Picken-type topological quantum field theory in arbitrary dimensions, we can show that every Deligne $d$-cocycle induces such a $d$-dimensional field theory with two special properties, namely thin-invariance and smoothness. We show that any $d$-dimensional topological quantum field theory with these two properties gives rise to a Deligne $d$-cocycle and verify that this construction is surjective and injective, that is both groups are isomorphic.
Complex emulsions are dispersions of kinetically stabilized multiphasic emulsion droplets comprised of two or more immiscible liquids that provide a novel material platform for the generation of active and dynamic soft materials. In recent years, the intrinsic reconfigurable morphological behavior of complex emulsions, which can be attributed to the unique force equilibrium between the interfacial tensions acting at the various interfaces, has become of fundamental and applied interest. As such, particularly biphasic Janus droplets have been investigated as structural templates for the generation of anisotropic precision objects, dynamic optical elements or as transducers and signal amplifiers in chemo- and bio-sensing applications. In the present thesis, switchable internal morphological responses of complex droplets triggered by stimuli-induced alterations of the balance of interfacial tensions have been explored as a universal building block for the design of multiresponsive, active, and adaptive liquid colloidal systems. A series of underlying principles and mechanisms that influence the equilibrium of interfacial tensions have been uncovered, which allowed the targeted design of emulsion bodies that can alter their shape, bind and roll on surfaces, or change their geometrical shape in response to chemical stimuli. Consequently, combinations of the unique triggerable behavior of Janus droplets with designer surfactants, such as a stimuli-responsive photosurfactant (AzoTAB) resulted for instance in shape-changing soft colloids that exhibited a jellyfish inspired buoyant motion behavior, holding great promise for the design of biological inspired active material architectures and transformable soft robotics.
In situ observations of spherical Janus emulsion droplets using a customized side-view microscopic imaging setup with accompanying pendant dropt measurements disclosed the sensitivity regime of the unique chemical-morphological coupling inside complex emulsions and enabled the recording of calibration curves for the extraction of critical parameters of surfactant effectiveness. The deduced new "responsive drop" method permitted a convenient and cost-efficient quantification and comparison of the critical micelle concentrations (CMCs) and effectiveness of various cationic, anionic, and nonionic surfactants. Moreover, the method allowed insightful characterization of stimuli-responsive surfactants and monitoring of the impact of inorganic salts on the CMC and surfactant effectiveness of ionic and nonionic surfactants. Droplet functionalization with synthetic crown ether surfactants yielded a synthetically minimal material platform capable of autonomous and reversible adaptation to its chemical environment through different supramolecular host-guest recognition events. Addition of metal or ammonium salts resulted in the uptake of the resulting hydrophobic complexes to the hydrocarbon hemisphere, whereas addition of hydrophilic ammonium compounds such as amino acids or polypeptides resulted in supramolecular assemblies at the hydrocarbon-water interface of the droplets. The multiresponsive material platform enabled interfacial complexation and
thus triggered responses of the droplets to a variety of chemical triggers including metal ions, ammonium compounds, amino acids, antibodies, carbohydrates as well as amino-functionalized solid surfaces.
In the final chapter, the first documented optical logic gates and combinatorial logic circuits based on complex emulsions are presented. More specifically, the unique reconfigurable and multiresponsive properties of complex emulsions were exploited to realize droplet-based logic gates of varying complexity using different stimuli-responsive surfactants in combination with diverse readout methods. In summary, different designs for multiresponsive, active, and adaptive liquid colloidal systems were presented and investigated, enabling the design of novel transformative chemo-intelligent soft material platforms.
Selenium (Se) is an essential trace element that is ubiquitously present in the environment in small concentrations. Essential functions of Se in the human body are manifested through the wide range of proteins, containing selenocysteine as their active center. Such proteins are called selenoproteins which are found in multiple physiological processes like antioxidative defense and the regulation of thyroid hormone functions. Therefore, Se deficiency is known to cause a broad spectrum of physiological impairments, especially in endemic regions with low Se content. Nevertheless, being an essential trace element, Se could exhibit toxic effects, if its intake exceeds tolerable levels. Accordingly, this range between deficiency and overexposure represents optimal Se supply. However, this range was found to be narrower than for any other essential trace element. Together with significantly varying Se concentrations in soil and the presence of specific bioaccumulation factors, this represents a noticeable difficulty in the assessment of Se
epidemiological status. While Se is acting in the body through multiple selenoproteins, its intake occurs mainly in form of small organic or inorganic molecular mass species. Thus, Se exposure not only depends on daily intake but also on the respective chemical form, in which it is present.
The essential functions of selenium have been known for a long time and its primary forms in different food sources have been described. Nevertheless, analytical capabilities for a comprehensive investigation of Se species and their derivatives have been introduced only in the last decades. A new Se compound was identified in 2010 in the blood and tissues of bluefin tuna. It was called selenoneine (SeN) since it is an isologue of naturally occurring antioxidant ergothioneine (ET), where Se replaces sulfur. In the following years, SeN was identified in a number of edible fish species and attracted attention as a new dietary Se source and potentially strong antioxidant. Studies in populations whose diet largely relies on fish revealed that SeN
represents the main non-protein bound Se pool in their blood. First studies, conducted with enriched fish extracts, already demonstrated the high antioxidative potential of SeN and its possible function in the detoxification of methylmercury in fish. Cell culture studies demonstrated, that SeN can utilize the same transporter as ergothioneine, and SeN metabolite was found in human urine.
Until recently, studies on SeN properties were severely limited due to the lack of ways to obtain the pure compound. As a predisposition to this work was firstly a successful approach to SeN synthesis in the University of Graz, utilizing genetically modified yeasts. In the current study, by use of HepG2 liver carcinoma cells, it was demonstrated, that SeN does not cause toxic effectsup to 100 μM concentration in hepatocytes. Uptake experiments showed that SeN is not bioavailable to the used liver cells.
In the next part a blood-brain barrier (BBB) model, based on capillary endothelial cells from the porcine brain, was used to describe the possible transfer of SeN into the central nervous system (CNS). The assessment of toxicity markers in these endothelial cells and monitoring of barrier conditions during transfer experiments demonstrated the absence of toxic effects from SeN on the BBB endothelium up to 100 μM concentration. Transfer data for SeN showed slow but substantial transfer. A statistically significant increase was observed after 48 hours following SeN incubation from the blood-facing side of the barrier. However, an increase in Se content was clearly visible already after 6 hours of incubation with 1 μM of SeN. While the transfer rate of SeN after application of 0.1 μM dose was very close to that for 1 μM, incubation with 10 μM of SeN resulted in a significantly decreased transfer rate. Double-sided application of SeN caused no side-specific transfer of SeN, thus suggesting a passive diffusion mechanism of SeN across the BBB. This data is in accordance with animal studies, where ET accumulation was observed in the rat brain, even though rat BBB does not have the primary ET transporter – OCTN1. Investigation of capillary endothelial cell monolayers after incubation with SeN and reference selenium compounds showed no significant increase of intracellular selenium concentration. Speciesspecific Se measurements in medium samples from apical and basolateral compartments, as good as in cell lysates, showed no SeN metabolization. Therefore, it can be concluded that SeN may reach the brain without significant transformation.
As the third part of this work, the assessment of SeN antioxidant properties was performed in Caco-2 human colorectal adenocarcinoma cells. Previous studies demonstrated that the intestinal epithelium is able to actively transport SeN from the intestinal lumen to the blood side and accumulate SeN. Further investigation within current work showed a much higher antioxidant potential of SeN compared to ET. The radical scavenging activity after incubation with SeN was close to the one observed for selenite and selenomethionine. However, the SeN effect on the viability of intestinal cells under oxidative conditions was close to the one caused by ET. To answer the question if SeN is able to be used as a dietary Se source and induce the activity of selenoproteins, the activity of glutathione peroxidase (GPx) and the secretion of selenoprotein P (SelenoP) were measured in Caco-2 cells, additionally. As expected, reference selenium compounds selenite and selenomethionine caused efficient induction of GPx activity. In contrast to those SeN had no effect on GPx activity. To examine the possibility of SeN being embedded into the selenoproteome, SelenoP was measured in a culture medium. Even though Caco-2 cells effectively take up SeN in quantities much higher than selenite or selenomethionine, no secretion of SelenoP was observed after SeN incubation.
Summarizing, we can conclude that SeN can hardly serve as a Se source for selenoprotein synthesis. However, SeN exhibit strong antioxidative properties, which appear when sulfur in ET is exchanged by Se. Therefore, SeN is of particular interest for research not as part of Se metabolism, but important endemic dietary antioxidant.
This thesis rests on two large Active Galactic Nuclei (AGNs) surveys. The first survey deals with galaxies that host low-level AGNs (LLAGN) and aims at identifying such galaxies by quantifying their variability. While numerous studies have shown that AGNs can be variable at all wavelengths, the nature of the variability is still not well understood. Studying the properties of LLAGNs may help to understand better galaxy evolution, and how AGNs transit between active and inactive states. In this thesis, we develop a method to extract variability properties of AGNs. Using multi-epoch deep photometric observations, we subtract the contribution of the host galaxy at each epoch to extract variability and estimate AGN accretion rates. This pipeline will be a powerful tool in connection with future deep surveys such as PANSTARS. The second study in this thesis describes a survey of X-ray selected AGN hosts at redshifts z>1.5 and compares them to quiescent galaxies. This survey aims at studying environments, sizes and morphologies of star-forming high-redshift AGN hosts in the COSMOS Survey at the epoch of peak AGN activity. Between redshifts 1.5<z<3.8, the COSMOS HST/ACS imaging probes the UV regime, where separating the AGN flux from its host galaxy is very challenging. Nevertheless, we successfully derived the structural properties of 249 AGN hosts using two-dimensional surface-brightness profile fitting with the GALFIT package. This is the largest sample of AGN hosts at redshift z>1.5 to date. We analyzed the evolution of structural parameters of AGN and non-AGN host galaxies with redshift, and compared their disturbance rates to identify the more probable AGN triggering mechanism in the 43.5<log_10 L_X<45 luminosity range. We also conducted mock AGN and quiescent galaxies observations to determine errors and corrections for the derived parameters. We find that the size-absolute magnitude relations of AGN hosts and non-AGN galaxies are very similar, with estimated mean sizes in both samples decreasing by ~50% between redshifts z=1.5 and z=3.5. Morphological classification of both active and quiescent galaxies shows that the majority of the AGN host galaxies are disc-dominated, with disturbance rates that are significantly lower than among the non-AGN galaxies. Such a finding suggests that Major Mergers are probably not responsible for triggering AGN accretion in most of these galaxies. Other secular mechanisms should therefore be responsible.
The central gas in half of all galaxy clusters shows short cooling times. Assuming unimpeded cooling, this should lead to high star formation and mass cooling rates, which are not observed. Instead, it is believed that condensing gas is accreted by the central black hole that powers an active galactic nuclei jet, which heats the cluster. The detailed heating mechanism remains uncertain. A promising mechanism invokes cosmic ray protons that scatter on self-generated magnetic fluctuations, i.e. Alfvén waves. Continuous damping of Alfvén waves provides heat to the intracluster medium. Previous work has found steady state solutions for a large sample of clusters where cooling is balanced by Alfvénic wave heating. To verify modeling assumptions, we set out to study cosmic ray injection in three-dimensional magnetohydrodynamical simulations of jet feedback in an idealized cluster with the moving-mesh code arepo. We analyze the interaction of jet-inflated bubbles with the turbulent magnetized intracluster medium.
Furthermore, jet dynamics and heating are closely linked to the largely unconstrained jet composition. Interactions of electrons with photons of the cosmic microwave background result in observational signatures that depend on the bubble content. Those recent observations provided evidence for underdense bubbles with a relativistic filling while adopting simplifying modeling assumptions for the bubbles. By reproducing the observations with our simulations, we confirm the validity of their modeling assumptions and as such, confirm the important finding of low-(momentum) density jets.
In addition, the velocity and magnetic field structure of the intracluster medium have profound consequences for bubble evolution and heating processes. As velocity and magnetic fields are physically coupled, we demonstrate that numerical simulations can help link and thereby constrain their respective observables. Finally, we implement the currently preferred accretion model, cold accretion, into the moving-mesh code arepo and study feedback by light jets in a radiatively cooling magnetized cluster. While self-regulation is attained independently of accretion model, jet density and feedback efficiencies, we find that in order to reproduce observed cold gas morphology light jets are preferred.
Hydraulic-driven fractures play a key role in subsurface energy technologies across several scales. By injecting fluid at high hydraulic pressure into rock with intrinsic low permeability, in-situ stress field and fracture development pattern can be characterised as well as rock permeability can be enhanced. Hydraulic fracturing is a commercial standard procedure for enhanced oil and gas production of rock reservoirs with low permeability in petroleum industry. However, in EGS utilization, a major geological concern is the unsolicited generation of earthquakes due to fault reactivation, referred to as induced seismicity, with a magnitude large enough to be felt on the surface or to damage facilities and buildings. Furthermore, reliable interpretation of hydraulic fracturing tests for stress measurement is a great challenge for the energy technologies. Therefore, in this cumulative doctoral thesis the following research questions are investigated. (1): How do hydraulic fractures grow in hard rock at various scales?; (2): Which parameters control hydraulic fracturing and hydro-mechanical coupling?; and (3): How can hydraulic fracturing in hard rock be modelled?
In the laboratory scale study, several laboratory hydraulic fracturing experiments are investigated numerically using Irazu2D that were performed on intact cubic Pocheon granite samples from South Korea applying different injection protocols. The goal of the laboratory experiments is to test the concept of cyclic soft stimulation which may enable sustainable permeability enhancement (Publication 1).
In the borehole scale study, hydraulic fracturing tests are reported that were performed in boreholes located in central Hungary to determine the in-situ stress for a geological site investigation. At depth of about 540 m, the recorded pressure versus time curves in mica schist with low dip angle foliation show atypical evolution. In order to provide explanation for this observation, a series of discrete element computations using Particle Flow Code 2D are performed (Publication 2).
In the reservoir scale study, the hydro-mechanical behaviour of fractured crystalline rock due to one of the five hydraulic stimulations at the Pohang Enhanced Geothermal site in South Korea is studied. Fluid pressure perturbation at faults of several hundred-meter lengths during hydraulic stimulation is simulated using FracMan (Publication 3).
The doctoral research shows that the resulting hydraulic fracturing geometry will depend “locally”, i.e. at the length scale of representative elementary volume (REV) and below that (sub-REV), on the geometry and strength of natural fractures, and “globally”, i.e. at super-REV domain volume, on far-field stresses. Regarding hydro-mechanical coupling, it is suggested to define separate coupling relationship for intact rock mass and natural fractures. Furthermore, the relative importance of parameters affecting the magnitude of formation breakdown pressure, a parameter characterising hydro-mechanical coupling, is defined. It can be also concluded that there is a clear gap between the capacity of the simulation software and the complexity of the studied problems. Therefore, the computational time of the simulation of complex hydraulic fracture geometries must be reduced while maintaining high fidelity simulation results. This can be achieved either by extending the computational resources via parallelization techniques or using time scaling techniques. The ongoing development of used numerical models focuses on tackling these methodological challenges.
The echo chamber model describes the development of groups in heterogeneous social networks. By heterogeneous social network we mean a set of individuals, each of whom represents exactly one opinion. The existing relationships between individuals can then be represented by a graph. The echo chamber model is a time-discrete model which, like a board game, is played in rounds. In each round, an existing relationship is randomly and uniformly selected from the network and the two connected individuals interact. If the opinions of the individuals involved are sufficiently similar, they continue to move closer together in their opinions, whereas in the case of opinions that are too far apart, they break off their relationship and one of the individuals seeks a new relationship. In this paper we examine the building blocks of this model. We start from the observation that changes in the structure of relationships in the network can be described by a system of interacting particles in a more abstract space.
These reflections lead to the definition of a new abstract graph that encompasses all possible relational configurations of the social network. This provides us with the geometric understanding necessary to analyse the dynamic components of the echo chamber model in Part III. As a first step, in Part 7, we leave aside the opinions of the inidividuals and assume that the position of the edges changes with each move as described above, in order to obtain a basic understanding of the underlying dynamics. Using Markov chain theory, we find upper bounds on the speed of convergence of an associated Markov chain to its unique stationary distribution and show that there are mutually identifiable networks that are not apparent in the dynamics under analysis, in the sense that the stationary distribution of the associated Markov chain gives equal weight to these networks.
In the reversible cases, we focus in particular on the explicit form of the stationary distribution as well as on the lower bounds of the Cheeger constant to describe the convergence speed.
The final result of Section 8, based on absorbing Markov chains, shows that in a reduced version of the echo chamber model, a hierarchical structure of the number of conflicting relations can be identified.
We can use this structure to determine an upper bound on the expected absorption time, using a quasi-stationary distribution. This hierarchy of structure also provides a bridge to classical theories of pure death processes. We conclude by showing how future research can exploit this link and by discussing the importance of the results as building blocks for a full theoretical understanding of the echo chamber model. Finally, Part IV presents a published paper on the birth-death process with partial catastrophe. The paper is based on the explicit calculation of the first moment of a catastrophe. This first part is entirely based on an analytical approach to second degree recurrences with linear coefficients. The convergence to 0 of the resulting sequence as well as the speed of convergence are proved. On the other hand, the determination of the upper bounds of the expected value of the population size as well as its variance and the difference between the determined upper bound and the actual value of the expected value. For these results we use almost exclusively the theory of ordinary nonlinear differential equations.
Stimuli-promoted in situ formation of hydrogels with thiol/thioester containing peptide precursors
(2022)
Hydrogels are potential synthetic ECM-like substitutes since they provide functional and structural similarities compared to soft tissues. They can be prepared by crosslinking of macromolecules or by polymerizing suitable precursors. The crosslinks are not necessarily covalent bonds, but could also be formed by physical interactions such as π-π interactions, hydrophobic interactions, or H-bonding. On demand in situ forming hydrogels have garnered increased interest especially for biomedical applications over preformed gels due to the relative ease of in vivo delivery and filling of cavities. The thiol-Michael addition reaction provides a straightforward and robust strategy for in situ gel formation with its fast reaction kinetics and ability to proceed under physiological conditions. The incorporation of a trigger function into a crosslinking system becomes even more interesting since gelling can be controlled with stimulus of choice. The use of small molar mass crosslinker precursors with active groups orthogonal to thiol-Michael reaction type electrophile provides the opportunity to implement an on-demand in situ crosslinking without compromising the fast reaction kinetics.
It was postulated that short peptide sequences due to the broad range structural-function relations available with the different constituent amino acids, can be exploited for the realisation of stimuli-promoted in situ covalent crosslinking and gelation applications. The advantages of this system over conventional polymer-polymer hydrogel systems are the ability tune and predict material property at the molecular level.
The main aim of this work was to develop a simplified and biologically-friendly stimuli-promoted in situ crosslinking and hydrogelation system using peptide mimetics as latent crosslinkers. The approach aims at using a single thiodepsipeptide sequence to achieve separate pH- and enzyme-promoted gelation systems with little modification to the thiodepsipeptide sequence. The realization of this aim required the completion of three milestones.
In the first place, after deciding on the thiol-Michael reaction as an effective in situ crosslinking strategy, a thiodepsipeptide, Ac-Pro-Leu-Gly-SLeu-Leu-Gly-NEtSH (TDP) with expected propensity towards pH-dependent thiol-thioester exchange (TTE) activation, was proposed as a suitable crosslinker precursor for pH-promoted gelation system. Prior to the synthesis of the proposed peptide-mimetic, knowledge of the thiol-Michael reactivity of the would-be activated thiol moiety SH-Leu, which is internally embedded in the thiodepsipeptide was required. In line with pKa requirements for a successful TTE, the reactivity of a more acidic thiol, SH-Phe was also investigated to aid the selection of the best thiol to be incorporated in the thioester bearing peptide based crosslinker precursor. Using ‘pseudo’ 2D-NMR investigations, it was found that only reactions involving SH-Leu yielded the expected thiol-Michael product, an observation that was attributed to the steric hindrance of the bulkier nature of SH-Phe. The fast reaction rates and complete acrylate/maleimide conversion obtained with SH-Leu at pH 7.2 and higher aided the direct elimination of SH-Phe as a potential thiol for the synthesis of the peptide mimetic.
Based on the initial studies, for the pH-promoted gelation system, the proposed Ac-Pro-Leu-Gly-SLeu-Leu-Gly-NEtSH was kept unmodified. The subtle difference in pKa values between SH-Leu (thioester thiol) and the terminal cysteamine thiol from theoretical conditions should be enough to effect a ‘pseudo’ intramolecular TTE. In polar protic solvents and under basic aqueous conditions, TDP successfully undergoes a ‘pseudo’ intramolecular TTE reaction to yield an α,ω-dithiol tripeptide, HSLeu-Leu-Gly-NEtSH. The pH dependence of thiolate ion generation by the cysteamine thiol aided the incorporation of the needed stimulus (pH) for the overall success of TTE (activation step) – thiol-Michael addition (crosslinking) strategy.
Secondly, with potential biomedical applications in focus, the susceptibility of TDP, like other thioesters, to intermolecular TTE reaction was probed with a group of thiols of varying thiol pKa values, since biological milieu characteristically contain peptide/protein thiols. L-cysteine, which is a biologically relevant thiol, and a small molecular weight thiol, methylthioglycolate both with relatively similar thiol pKa, values, led to an increase concentration of the dithiol crosslinker when reacted with TDP. In the presence of acidic thiols (p-NTP and 4MBA), a decrease in the dithiol concentration was observed, an observation that can be attributed to the inability of the TTE tetrahedral intermediate to dissociate into exchange products and is in line with pKa requirements for successful TTE reaction. These results additionally makes TDP more attractive and the potentially the first crosslinker precursor for applications in biologically relevant media.
Finally, the ability of TDP to promote pH-sensitive in situ gel formation was probed with maleimide functionalized 4-arm polyethylene glycol polymers in tris-buffered media of varying pHs. When a 1:1 thiol: maleimide molar ratio was used, TDP-PEG4MAL hydrogels formed within 3, 12 and 24 hours at pH values of 8.5, 8.0 and 7.5 respectively. However, gelation times of 3, 5 and 30 mins were observed for the same pH trend when the thiol: maleimide molar was increased to 2:1.
A direct correlation of thiol content with G’ of the gels at each pH could also be drawn by comparing gels with thiol: maleimide ratios of 1:1 to those with 2:1 thiol: maleimide mole ratios. This is supported by the fact that the storage modulus (G') is linearly dependent on the crosslinking density of the polymer. The values of initial G′ for all gels ranged between (200 – 5000 Pa), which falls in the range of elasticities of certain tissue microenvironments for example brain tissue 200 – 1000 Pa and adipose tissue (2500 – 3500 Pa).
Knowledge so far gained from the study on the ability to design and tune the exchange reaction of thioester containing peptide mimetic will give those working in the field further insight into the development of new sequences tailored towards specific applications.
TTE substrate design using peptide mimetic as presented in this work has revealed interesting new insights considering the state-of-the-art. Using the results obtained as reference, the strategy provides a possibility to extend the concept to the controlled delivery of active molecules needed for other robust and high yielding crosslinking reactions for biomedical applications. Application for this sequentially coupled functional system could be seen e.g. in the treatment of inflamed tissues associated with urinary tract like bladder infections for which pH levels above 7 were reported. By the inclusion of cell adhesion peptide motifs, the hydrogel network formed at this pH could act as a new support layer for the healing of damage epithelium as shown in interfacial gel formation experiments using TDP and PEG4MAL droplets.
The versatility of the thiodepsipeptide sequence, Ac-Pro-Leu-Gly-SLeu-Leu-Gly-(TDPo) was extended for the design and synthesis of a MMP-sensitive 4-arm PEG-TDPo conjugate. The purported cleavage of TDPo at the Gly-SLeu bond yields active thiol units for subsequent reaction of orthogonal Michael acceptor moieties. One of the advantages of stimuli-promoted in situ crosslinking systems using short peptides should be the ease of design of required peptide molecules due to the predictability of peptide functions their sequence structure. Consequently the functionalisation of a 4-arm PEG core with the collagenase active TDPo sequence yielded an MMP-sensitive 4-arm thiodepsipeptide-PEG conjugate (PEG4TDPo) substrate.
Cleavage studies using thiol flourometric assay in the presence of MMPs -2 and -9 confirmed the susceptibility of PEG4TDPo towards these enzymes. The resulting time-dependent increase in fluorescence intensity in the presence of thiol assay signifies the successful cleavage of TDPo at the Gly-SLeu bond as expected. It was observed that the cleavage studies with thiol flourometric assay introduces a sigmoid non-Michaelis-Menten type kinetic profile, hence making it difficult to accurately determine the enzyme cycling parameters, kcat and KM .
Gelation studies with PEG4MAL at 10 % wt. concentrations revealed faster gelation with MMP-2 than MMP-9 with 28 and 40 min gelation times respectively. Possible contributions by hydrolytic cleavage of PEG4TDPo has resulted in the gelation of PEG4MAL blank samples but only after 60 minutes of reaction. From theoretical considerations, the simultaneous gelation reaction would be expected to more negatively impact the enzymatic than hydrolytic cleavage. The exact contributions from hydrolytic cleavage of PEG4TDPo would however require additional studies.
In summary this new and simplified in situ crosslinking system using peptide-based crosslinker precursors with tuneable properties exhibited in situ crosslinking gelation kinetics on similar levels with already active dithiols reported. The advantageous on-demand functionality associated with its pH-sensitivity and physiological compatibility makes it a strong candidate worth further research as biomedical applications in general and on-demand material synthesis is concerned.
Results from MMP-promoted gelation system unveils a simple but unexplored approach for in situ synthesis of covalently crosslinked soft materials, that could lead to the development of an alternative pathway in addressing cancer metastasis by making use of MMP overexpression as a trigger. This goal has so far not being reach with MMP inhibitors despite the extensive work this regard.