We study the dynamics of molecular motor-driven transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We further develop a stochastic model of vesicle transport in [Park, Singh, and Fai, SIAM J. Appl. Math. 82.3 (2022), pp. 793--820] by showing that second-order moments may be neglected. We exploit this property to significantly simplify the model and confirm through numerical simulations that the simplification retains key behaviors of the original agent-based myosin model of vesicle transport. We use the simplified model to explore the vesicle translocation time and probability through dendritic spines as a function of molecular motor parameters, which was previously not practically possible. Relevance to Life Sciences: We find that thinner dendritic spine geometry can greatly reduce the probability of vesicle translocation to the post-synaptic density. The cell may alter molecular motor parameters to compensate, but only to a point. These findings are consistent with the biological literature, where brain disorders are often associated with an excess of long, thin dendritic spines. Mathematical Content: We use a moment-generating function to deduce that second-order moments in motor attachment times may be neglected, and therefore the first-order moment is a sufficient approximation. Using only the mean attachment times and neglecting the variance yields a tractable master equation from which vesicle mean first passage times may be computed directly as a function of geometry and molecular motor parameters.
Eva Martin Solana, Laura Casado Zueras, Teobaldo E. Torres
et al.
Huntington's disease (HD) is an inherited neurodegenerative disorder caused by an expanded CAG repeat in the coding sequence of the huntingtin protein. Initially, it predominantly affects medium-sized spiny neurons (MSSNs) of the corpus striatum. No effective treatment is available, thus urging the identification of potential therapeutic targets. While evidence of mitochondrial structural alterations in HD exists, previous studies mainly employed 2D approaches and were performed outside the strictly native brain context. In this study, we adopted a novel multiscale approach to conduct a comprehensive 3D in situ structural analysis of mitochondrial disturbances in a mouse model of HD. We investigated MSSNs within brain tissue under optimal structural conditions utilizing state-of-the-art 3D imaging technologies, specifically FIB/SEM for the complete imaging of neuronal somas and Electron Tomography for detailed morphological examination and image processing-based quantitative analysis. Our findings suggest a disruption of the mitochondrial network towards fragmentation in HD. The network of interlaced, slim, and long mitochondria observed in healthy conditions transforms into isolated, swollen, and short entities, with internal cristae disorganization, cavities, and abnormally large matrix granules.
The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of the nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.
Ansgar Gruber, Cedar McKay, Miroslav Oborník
et al.
Cells of diatoms and related algae with complex plastids of red algal origin are highly compartmentalized. These plastids are surrounded by four envelope membranes, which also define the periplastidic compartment (PPC), the space between the second and third membranes. The PPC corresponds to the cytosol of the eukaryotic alga that was the ancestor of the complex plastid. Metabolic reactions as well as cell biological processes take place in this compartment; however, its exact function remains elusive. Automated predictions of protein locations proved useful for genome wide explorations of metabolism in the case of plastid proteins, but until now, no automated method for the prediction of PPC proteins was available. Here, we present an updated version of the plastid protein predictor ASAFind, which includes optional prediction of PPC proteins. The new ASAFind version also accepts the output of the most recent versions of SignalP (5.0) and TargetP (2.0) input data. Furthermore, we release a Python script to calculate custom scoring matrices for adjustment of the ASAFind method to other groups of algae, and included the option to run the predictions with custom scoring matrices in a simplified score cut-off mode.
Zhuoyu Chen, Bai Yang Wang, Adrian G. Swartz
et al.
AbstractAnomalous metallic behavior, marked by a saturating finite resistivity much lower than the Drude estimate, has been observed in a wide range of two-dimensional superconductors. Utilizing the electrostatically gated LaAlO3/SrTiO3 interface as a versatile platform for superconductor-metal quantum phase transitions, we probe variations in the gate, magnetic field, and temperature to construct a phase diagram crossing from superconductor, anomalous metal, vortex liquid, to the Drude metal state, combining longitudinal and Hall resistivity measurements. We find that the anomalous metal phases induced by gating and magnetic field, although differing in symmetry, are connected in the phase diagram and exhibit similar magnetic field response approaching zero temperature. Namely, within a finite regime of the anomalous metal state, the longitudinal resistivity linearly depends on the field while the Hall resistivity diminishes, indicating an emergent particle-hole symmetry. The universal behavior highlights the uniqueness of the quantum bosonic metallic state, distinct from bosonic insulators and vortex liquids.
Oliver M. Drozdowski, Falko Ziebert, Ulrich S. Schwarz
The actin cytoskeleton of cells is in continuous motion due to both polymerization of new filaments and their contraction by myosin II molecular motors. Through adhesion to the substrate, such intracellular flow can be converted into cell migration. Recently, optogenetics has emerged as a new powerful experimental method to control both actin polymerization and myosin II contraction. While optogenetic control of polymerization can initiate cell migration by generating protrusion, it is less clear if and how optogenetic control of contraction can also affect cell migration. Here we analyze the latter situation using a minimal variant of active gel theory into which we include optogenetic activation as a spatiotemporally constrained perturbation. The model can describe the symmetrical flow of the actomyosin system observed in optogenetic experiments, but not the long-lasting polarization required for cell migration. Motile solutions become possible if cytoskeletal polymerization is included through the boundary conditions. Optogenetic activation of contraction can then initiate locomotion in a symmetrically spreading cell and strengthen motility in an asymmetrically polymerizing one. If designed appropriately, it can also arrest motility even for protrusive boundaries.
Researchers have found functional-based methods to improve data storage, transfer, and interpretation. These functional expansions have been developed and utilized across a range of geometries, from cartesian to cylindrical to the surfaces of spheres. However, a volumetric spherical basis set had not yet been computationally implemented. This paper presents such a basis set and demonstrates its numerical features and benefits.
Bianca de Paula Telini, Marcelo Menoncin, Diego Bonatto
During beer production, yeast generate ethanol that is exported to the extracellular environment where it accumulates. Depending on the initial carbohydrate concentration in the wort a high concentration of ethanol can be achieved in beer, often higher than 20% (v/v). It is noteworthy that the effects of elevated ethanol concentrations generated during beer fermentation resemble those of heat shock stress, with similar responses observed in both situations, such as the activation of proteostasis and protein quality control mechanisms in different cell compartments, including endoplasmic reticulum (ER), mitochondria, and cytosol. Despite the extensive published molecular and biochemical data regarding the roles of proteostasis in different organelles of yeast cells, little is known about how this mechanism impacts beer fermentation and how different proteostasis mechanisms found in ER, mitochondria, and cytosol communicate with each other during ethanol/fermentative stress. Supporting this integrative view, transcriptome data analysis was applied using publicly available information for a lager yeast strain grown under in beer production conditions. The transcriptome data indicated upregulation of genes that encode chaperones, co-chaperones, unfolded protein response elements in ER and mitochondria, ubiquitin ligases, proteasome components, N-glycosylation quality control pathway proteins, and components of processing bodies (p-bodies) and stress granules (SGs) during lager beer fermentation. Thus, the main purpose of this hypothesis and theory manuscript is to provide a concise picture of how inter-organellar proteostasis mechanisms are connected with one another and with biological processes that may modulate the viability and/or vitality of yeast populations during HG/VHG beer fermentation and serial repitching.
Hélène Cabanas, Thomas Harnois, Christophe Magaud
et al.
Background: Chronic myeloid leukemia (CML) results from hematopoietic stem cell transformation by the bcr-abl chimeric oncogene, encoding a 210 kDa protein with constitutive tyrosine kinase activity. In spite of the efficiency of tyrosine kinase inhibitors (TKI; Imatinib), other strategies are explored to eliminate CML leukemia stem cells, such as calcium pathways. Results: In this work, we showed that Store-Operated Calcium Entry (SOCE) and thrombin induced calcium influx were decreased in Bcr-Abl expressing 32d cells (32d-p210). The 32d-p210 cells showed modified Orai1/STIM1 ratio and reduced TRPC1 expression that could explain SOCE reduction. Decrease in SOCE and thrombin induced calcium entry was associated to reduced Nuclear Factor of Activated T cells (NFAT) nucleus translocation in 32d-p210 cells. We demonstrated that SOCE blockers enhanced cell mobility of 32d-p210 cells and reduced the proliferation rate in both 32d cell lines. TKI treatment slightly reduced the thrombin-induced response, but imatinib restored SOCE to the wild type level. Bcr-Abl is also known to deregulate Protein Kinase C (PKC), which was described to modulate calcium entries. We showed that PKC enhances SOCE and thrombin induced calcium entries in control cells while this effect is lost in Bcr-Abl-expressing cells. Conclusion: The tyrosine kinase activity seems to regulate calcium entries probably not directly but through a global cellular reorganization involving a PKC pathway. Altogether, calcium entries are deregulated in Bcr-Abl-expressing cells and could represent an interesting therapeutic target in combination with TKI.
Sebastian Lotter, Arman Ahmadzadeh, Robert Schober
In Diffusive Molecular Communication (DMC), information is transmitted by diffusing molecules. Synaptic signaling is a natural implementation of this paradigm. It is responsible for relaying information from one neuron to another, but also provides support for complex functionalities, such as learning and memory. Many of its features are not yet understood, some are, however, known to be critical for robust, reliable neural communication. In particular, some synapses feature a re-uptake mechanism at the presynaptic neuron, which provides a means for removing neurotransmitters from the synaptic cleft and for recycling them for future reuse. In this paper, we develop a comprehensive channel model for synaptic DMC encompassing a spatial model of the synaptic cleft, molecule re-uptake at the presynaptic neuron, and reversible binding to individual receptors at the postsynaptic neuron. Based on this model, we derive an analytical time domain expression for the channel impulse response (CIR) of the synaptic DMC system. Our model explicitly incorporates macroscopic physical channel parameters and can be used to evaluate the impact of re-uptake, receptor density, and channel width on the CIR of the synaptic DMC system. Furthermore, we provide results from particlebased computer simulation, which validate the analytical model. The proposed comprehensive channel model for synaptic DMC systems can be exploited for the investigation of challenging problems, like the quantification of the inter-symbol interference between successive synaptic signals and the design of synthetic neural communication systems.
Simon P Pearce, Matthias Heil, Oliver E Jensen
et al.
Microtubules are filamentous tubular protein polymers which are essential for a range of cellular behaviour, and are generally straight over micron length scales. However, in some gliding assays, where microtubules move over a carpet of molecular motors, individual microtubules can also form tight arcs or rings, even in the absence of crosslinking proteins. Understanding this phenomenon may provide important explanations for similar highly curved microtubules which can be found in nerve cells undergoing neurodegeneration. We propose a model for gliding assays where the kinesins moving the microtubules over the surface induce ring formation through differential binding, substantiated by recent findings that a mutant version of the motor protein kinesin applied in solution is able to lock-in microtubule curvature. For certain parameter regimes, our model predicts that both straight and curved microtubules can exist simultaneously as stable steady-states, as has been seen experimentally. Additionally, unsteady solutions are found, where a wave of differential binding propagates down the microtubule as it glides across the surface, which can lead to chaotic motion. Whilst this model explains two-dimensional microtubule behaviour in an experimental gliding assay, it has the potential to be adapted to explain pathological curling in nerve cells.
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially-reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it typically is very broad in many biological situations: thus, the mean FPT can differ from the most probable FPT by orders of magnitude. The most probable FPT is shown to strongly depend only on the starting position within the geometry and to be almost independent of the target size and reactivity. These findings demonstrate the dramatic relevance of knowing the full distribution of FPTs and thus open new perspectives for a more reliable description of many intracellular processes initiated by the arrival of one or few biomolecules to a small, spatially localised region inside the cell.
Michael Pan, Peter J. Gawthrop, Kenneth Tran
et al.
Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well-suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a "conserved moiety". Conserved moieties explain model drift and non-unique steady states, generalising the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.
Telomeres, the nucleoprotein complexes at the termini of linear chromosomes, are essential for the processes of end replication, end protection, and chromatin segregation. The Mre11 complex is involved in multiple cellular roles in DNA repair and structure in the regulation and function of telomere size homeostasis. In this study, we characterize yeast telomere chromatin structure, phenotypic heritability, and chromatin segregation in both wild-type [MRE11] and A470 motif alleles. MRE11 strains confer a telomere size of 300 base pairs of G+T irregular simple sequence repeats. This DNA and a portion of subtelomeric DNA is embedded in a telosome: a MNase-resistant non-nucleosomal particle. Chromatin immunoprecipitation shows a three to four-fold lower occupancy of Mre11A470T proteins than wild-type proteins in telosomes. Telosomes containing the Mre11A470T protein confer a greater resistance to MNase digestion than wild-type telosomes. The integration of a wild-type MRE11 allele into an ectopic locus in the genome of an mre11A470T mutant and the introduction of an mre11A470T allele at an ectopic site in a wild-type strain lead to unexpectedly differing results. In each case, the replicated sister chromatids inherit telosomes containing only the protein encoded by the genomic mre11 locus, even in the presence of protein encoded by the opposing ectopic allele. We hypothesize that the telosome segregates by a conservative mechanism. These data support a mechanism for the linkage between sister chromatid replication and maintenance of either identical mutant or identical wild-type telosomes after replication of sister chromatids. These data suggest the presence of an active mechanism for chromatin segregation in yeast.
Hélène Bouvrais, Laurent Chesneau, Sylvain Pastezeur
et al.
During the asymmetric division of the Caenorhabditis elegans nematode zygote, the polarity cues distribution and daughter cell fates depend on the correct positioning of the mitotic spindle, which results from both centering and cortical pulling forces. Revealed by anaphase spindle rocking, these pulling forces are regulated by the force generator dynamics, which are in turn consequent of mitotic progression. We found a novel, additional, regulation of these forces by the spindle position. It controls astral microtubule availability at the cortex, on which the active force generators can pull. Importantly, this positional control relies on the polarity dependent LET-99 cortical band, which restricts or concentrates generators to a posterior crescent. We ascribed this control to the microtubule dynamics at the cortex. Indeed, in mapping the cortical contacts, we found a correlation between the centrosome-cortex distance and the microtubule contact density. In turn, it modulates pulling force generator activity. We modelled this control, predicting and experimentally validating that the posterior crescent extent controlled where the anaphase oscillations started, in addition to mitotic progression. Finally, we propose that spatially restricting force generator to a posterior crescent sets the spindle's final position, reflecting polarity through the LET-99 dependent restriction of force generators to a posterior crescent. This regulation superimposes that of force generator processivity. This novel control confers a low dependence on microtubule and active force generator exact numbers or dynamics, provided that they exceed the threshold needed for posterior displacement. Interestingly, this robustness originates in cell mechanics rather than biochemical networks.
Proliferating cells properly divide into their daughter cells through a process that is mediated by kinetochores, protein-complexes that assemble at the centromere of each sister chromatid. Each kinetochore has to establish a tight bipolar attachment to the spindle apparatus before sister-chromatid separation is initiated. The Spindle Assembly Checkpoint (SAC) links the biophysical attachment status of the kinetochores to mitotic progression, and ensures that even a single misaligned kinetochore keeps the checkpoint active. The mechanism by which this is achieved is still elusive. Current computational models of the human SAC disregard important biochemical properties by omitting any kind of feedback loop, proper kinetochore signals, and other spatial properties such as the stability of the system and diffusion effects. To allow for more realistic in silico study of the dynamics of the SAC model, a minimal mathematical framework for SAC activation and silencing is introduced. A nonlinear ordinary differential equation model successfully reproduces bifurcation signaling switches with attachment of all 92 kinetochores and activation of APC/C by kinetochore-driven feedback. A partial differential equation model and mathematical linear stability analyses indicate the influence of diffusion and system stability. The conclusion is that quantitative models of the human SAC should account for the positive feedback on APC/C activation driven by the kinetochores which is essential for SAC silencing. Experimental diffusion coefficients for MCC sub-complexes are found to be insufficient for rapid APC/C inhibition. The presented analysis allows for systems-level understanding of mitotic control and the minimal new model can function as a basis for developing further quantitative-integrative models of the cell division cycle
F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in the mitochondrial membranes and bacterial inner membranes in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which generate the opposing rotation and compete for control of their shared central gamma-shaft. Here we present a self-consistent physical model of the F1 motor as a simplified two-state Brownian ratchet based on the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical description of linear and rotary motors and explains the stepped unidirectional rotation of the $γ$-shaft, in agreement with the `binding-change' ideas of Boyer. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the `no-load' angular velocity is ca. 400~rad/s anticlockwise at 4 mM ATP, in close agreement with experiment. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of `stall torque'. We discuss the matters of the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the `useful outcome' is measured in the number of H+ pushed against the chemical gradient in the F1 ATP-driven operation.
Karin Moeller, Katharina Mueller, Hanna Engelke
et al.
A new general route for siRNA delivery is presented combining porous core-shell silica nanocarriers with a modularly designed multifunctional block copolymer. Specifically, the internal storage and release of siRNA from mesoporous silica nanoparticles (MSN) with orthogonal core-shell surface chemistry was investigated as a function of pore-size, pore morphology, surface properties and pH. Very high siRNA loading capacities of up to 380 microg/mg MSN were obtained with charge-matched amino-functionalized mesoporous cores, and release profiles show up to 80% siRNA elution after 24 h. We demonstrate that adsorption and desorption of siRNA is mainly driven by electrostatic interactions, which allow for high loading capacities even in medium-sized mesopores with pore diameters down to 4 nm in a stellate pore morphology. The negatively charged MSN shell enabled the association with a block copolymer containing positively charged artificial amino acids and oleic acid blocks, which acts simultaneously as capping function and endosomal release agent. The potential of this multifunctional delivery platform is demonstrated by highly effective cell transfection and siRNA delivery into KB-cells. A luciferase reporter gene knock-down of up to 90% was possible using extremely low cell exposures with only 2.5 microg MSN containing 32 pM siRNA per 100 microL well.