TY - JOUR AB - High intensity focussed ultrasound (HIFU) has emerged as a novel therapeutic modality, for the treatment of various cancers, that is gaining significant traction in clinical oncology. It is a cancer therapy that avoids many of the associated negative side effects of other more well-established therapies (such as surgery, chemotherapy and radiotherapy) and does not lead to the longer recuperation times necessary in these cases. The increasing interest in HIFU from biomedical researchers and clinicians has led to the development of a number of mathematical models to capture the effects of HIFU energy deposition in biological tissue. In this paper, we study the simplest such model that has been utilized by researchers to study temperature evolution under HIFU therapy. Although the model poses significant theoretical challenges, in earlier work, we were able to establish existence and uniqueness of solutions to this system of PDEs (see Efendiev et al. Adv Appl Math Sci 29(1):231-246, 2020). In the current work, we take the next natural step of studying the long-time dynamics of solutions to this model, in the case where the external forcing is quasi-periodic. In this case, we are able to prove the existence of uniform attractors to the corresponding evolutionary processes generated by our model and to estimate the Hausdorff dimension of the attractors, in terms of the physical parameters of the system. AU - Efendiyev, M.A. AU - Murley, J.* AU - Sivaloganathan, S.* C1 - 62746 C2 - 51042 CY - One New York Plaza, Suite 4600, New York, Ny, United States TI - Dimension estimate of uniform attractor for a model of high intensity focussed ultrasound-induced thermotherapy. JO - Bull. Math. Biol. VL - 83 IS - 9 PB - Springer PY - 2021 SN - 0092-8240 ER - TY - JOUR AB - Most studies of ecological interactions study asymptotic behavior, such as steady states and limit cycles. The transient behavior, i.e., qualitative aspects of solutions as and before they approach their asymptotic state, may differ significantly from asymptotic behavior. Understanding transient dynamics is crucial to predicting ecosystem responses to perturbations on short timescales. Several quantities have been proposed to measure transient dynamics in systems of ordinary differential equations. Here, we generalize these measures to reaction-diffusion systems in a rigorous way and prove various relations between the non-spatial and spatial effects, as well as an upper bound for transients. This extension of existing theory is crucial for studying how spatially heterogeneous perturbations and the movement of biological species involved affect transient behaviors. We illustrate several such effects with numerical simulations. AU - Wang, X.* AU - Efendiyev, M.A. AU - Lutscher, F.* C1 - 56842 C2 - 47402 CY - 233 Spring St, New York, Ny 10013 Usa SP - 3889-3917 TI - How spatial heterogeneity affects transient behavior in reaction-diffusion systems for ecological interactions? JO - Bull. Math. Biol. VL - 81 IS - 10 PB - Springer PY - 2019 SN - 0092-8240 ER - TY - JOUR AB - Human adenovirus (HAdV) E1B-55K is a multifunctional regulator of productive viral replication and oncogenic transformation in nonpermissive mammalian cells. These functions depend on E1B-55K's posttranslational modification with the SUMO protein and its binding to HAdV E4orf6. Both early viral proteins recruit specific host factors to form an E3 ubiquitin ligase complex that targets antiviral host substrates for proteasomal degradation. Recently, we reported that the PML-NB associated factor Daxx represses efficient HAdV productive infection and is proteasomally degraded via a SUMO-E1B-55K-dependent, E4orf6-independent pathway, the details of which remained to be established. RNF4, a cellular SUMO-targeted ubiquitin ligase (STUbL), induces ubiquitinylation of specific SUMOy lated proteins and plays an essential role during DNA repair. Here, we show that E1B-55K recruits RNF4 to the insoluble nuclear matrix fraction of the infected cell to support RNF4/Daxx association, promoting Daxx PTM and thus inhibiting this antiviral factor. Removing RNF4 from infected cells using RNA interference resulted in blocking the proper establishment of viral replication centers and significantly diminished viral gene expression. These results provide a model for how HAdV antagonize the antiviral host responses by exploiting the functional capacity of cellular STUbLs. Thus, RNF4 and its STUbL function represent a positive factor during lytic infection and a novel candidate for future therapeutic antiviral intervention strategies.IMPORTANCE Daxx is a PML-NB-associated transcription factor that was recently shown to repress efficient HAdV productive infection. To counteract this antiviral measurement during infection, Daxx is degraded via a novel pathway including viral E1B-55K and host proteasomes. This virus-mediated degradation is independent of the classical HAdV E3 ubiquitin ligase complex, which is essential during viral infection to target other host antiviral substrates. To maintain a productive viral life cycle, HAdV E1B-55K early viral protein inhibits the chromatin-remodeling factor Daxx in a SUMO-dependent manner. In addition, viral E1B-55K protein recruits the STUbL RNF4 and sequesters it into the insoluble fraction of the infected cell. E1B-55K promotes complex formation between RNF4-and E1B-55K-targeted Daxx protein, supporting Daxx posttranslational modification prior to functional inhibition. Hence, RNF4 represents a novel host factor that is beneficial for HAdV gene expression by supporting Daxx counteraction. In this regard, RNF4 and other STUbL proteins might represent novel targets for therapeutic intervention. AU - Ghasemi, M.* AU - Hense, B.A. AU - Eberl, H.J.* AU - Kuttler, C.* C1 - 53444 C2 - 44868 CY - 1752 N St Nw, Washington, Dc 20036-2904 Usa SP - 1736-1775 TI - Simulation-based exploration of quorum sensing triggered resistance of biofilms to antibiotics. JO - Bull. Math. Biol. VL - 80 IS - 7 PB - Amer Soc Microbiology PY - 2018 SN - 0092-8240 ER - TY - JOUR AB - Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore “master” regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges. AU - Pérez-Velázquez, J. AU - Gölgeli, M. AU - García-Contreras, R.* C1 - 49355 C2 - 41785 CY - New York SP - 1585-1639 TI - Mathematical modelling of bacterial quorum sensing: A review. JO - Bull. Math. Biol. VL - 78 IS - 8 PB - Springer PY - 2016 SN - 0092-8240 ER - TY - JOUR AU - Uecker, H.* AU - Müller, J.P.H.* AU - Hense, B.A. C1 - 43803 C2 - 36759 CY - New York SP - 580 TI - Erratum to: Individual-based model for quorum sensing with background flow. JO - Bull. Math. Biol. VL - 77 IS - 3 PB - Springer PY - 2015 SN - 0092-8240 ER - TY - JOUR AB - Quorum sensing is a wide-spread mode of cell-cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for [Formula: see text] cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration [Formula: see text] of the signalling substance, coupled with [Formula: see text] ODEs for the masses [Formula: see text] of the substance within each cell. The cells are balls of radius [Formula: see text] in [Formula: see text], and under some scaling assumptions we formally derive an effective system of [Formula: see text] ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations. AU - Uecker, H.* AU - Müller, J. AU - Hense, B.A. C1 - 31574 C2 - 34559 CY - New York SP - 1727-1746 TI - Individual-based model for quorum sensing with background flow. JO - Bull. Math. Biol. VL - 76 IS - 7 PB - Springer PY - 2014 SN - 0092-8240 ER - TY - JOUR AB - In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models only consider the size of the overall populations, others take division numbers and labeling of the cells into account. In this work, we present a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics. Thus, it allows for the consideration of division number-dependent parameters as well as the direct comparison of the model prediction with labeling experiments, e.g., performed with Carboxyfluorescein succinimidyl ester (CFSE), and can be shown to be a generalization of most existing models used to describe these data. We prove that under mild assumptions the resulting system of coupled partial differential equations (PDEs) can be decomposed into a system of ordinary differential equations (ODEs) and a set of decoupled PDEs, which drastically reduces the computational effort for simulating the model. Furthermore, the PDEs are solved analytically and the ODE system is truncated, which allows for the prediction of the label distribution of complex systems using a low-dimensional system of ODEs. In addition to modeling the label dynamics, we link the label-induced fluorescence to the measure fluorescence which includes autofluorescence. Furthermore, we provide an analytical approximation for the resulting numerically challenging convolution integral. This is illustrated by modeling and simulating a proliferating population with division number-dependent proliferation rate. AU - Hasenauer, J. AU - Schittler, D.* AU - Allgöwer, F.* C1 - 23805 C2 - 31295 SP - 2692-2732 TI - Analysis and simulation of division- and label-structured population models. A new tool to analyze proliferation assays. JO - Bull. Math. Biol. VL - 74 IS - 11 PB - Springer PY - 2012 SN - 0092-8240 ER - TY - JOUR AB - Signaling networks are abundant in higher organisms. They play pivotal roles, e.g., during embryonic development or within the immune system. In this contribution, we study the combined effect of the various kinetic parameters on the dynamics of signal transduction. To this end, we consider hierarchical complex systems as prototypes of signaling networks. For given topology, the output of these networks is determined by an interplay of the single parameters. For different kinetics, we describe this by algebraic expressions, the so-called effective parameters.When modeling switch-like interactions by Heaviside step functions, we obtain these effective parameters recursively from the interaction graph. They can be visualized as directed trees, which allows us to easily determine the global effect of single kinetic parameters on the system's behavior. We provide evidence that these results generalize to sigmoidal Hill kinetics.In the case of linear activation functions, we again show that the algebraic expressions can be immediately inferred from the topology of the interaction network. This allows us to transform time-consuming analytic solutions of differential equations into a simple graph-theoretic problem. In this context, we also discuss the impact of our work on parameter estimation problems. An issue is that even the fitting of identifiable effective parameters often turns out to be numerically ill-conditioned. We demonstrate that this fitting problem can be reformulated as the problem of fitting exponential sums, for which robust algorithms exist. AU - Blöchl, F. AU - Wittmann, D.M. AU - Theis, F.J. C1 - 4153 C2 - 28152 CY - New York, NY [u.a.) SP - 706-725 TI - Effective parameters determining the information flow in hierarchical biological systems. JO - Bull. Math. Biol. VL - 73 IS - 4 PB - Springer PY - 2011 SN - 0092-8240 ER - TY - JOUR AB - Processing of information by signaling networks is characterized by properties of the induced kinetics of the activated pathway components. The maximal extent of pathway activation (maximum amplitude) and the time-to-peak-response (position) are key determinants of biological responses that have been linked to specific outcomes. We investigate how the maximum amplitude of pathway activation and its position depend on the input and wiring of a signaling network. For this purpose, we consider a simple reaction A-->B that is regulated by a transient input and extended this to include back-reaction and additional partners. In particular, we show that a unique maximum of B(t) exists. Moreover, we prove that the position of the maximum is independent of the applied input but regulated by degradation reactions of B. Indeed, the time-to-peak-response decreases with increasing degradation rate, which we prove for small models and show in simulations for more complex ones. The identified dependencies provide insights into design principles that facilitate the realization dynamical characteristics like constant position of maximal pathway activation and thereby guide the characterization of unknown kinetics within larger protein networks. AU - Theis, F.J. AU - Bohl, S.* AU - Klingmüller, U.* C1 - 2779 C2 - 28096 SP - 978-1003 TI - Theoretical analysis of time-to-peak responses in biological reaction networks. JO - Bull. Math. Biol. VL - 73 IS - 5 PB - Springer PY - 2011 SN - 0092-8240 ER - TY - JOUR AB - In this paper, we derive exact asymptotic estimates of the spreading speeds of solutions of some reaction-diffusion models in periodic environments with very large periods. Contrarily to the other limiting case of rapidly oscillating environments, there was previously no explicit formula in the case of slowly oscillating environments. The knowledge of these two extremes permits to quantify the effect of environmental fragmentation on the spreading speeds. On the one hand, our analytical estimates and numerical simulations reveal speeds which are higher than expected for Shigesada-Kawasaki-Teramoto models with Fisher-KPP reaction terms in slowly oscillating environments. On the other hand, spreading speeds in very slowly oscillating environments are proved to be 0 in the case of models with strong Allee effects; such an unfavorable effect of aggregation is merely seen in reaction-diffusion models. AU - Hamel, F. AU - Fayard, J.* AU - Roques, L.* C1 - 6018 C2 - 27394 CY - New York, NY SP - 1166-1191 TI - Spreading speeds in slowly oscillating environments. JO - Bull. Math. Biol. VL - 72 IS - 5 PB - Springer PY - 2010 SN - 0092-8240 ER - TY - JOUR AB - In order to determine the growth of inhaled aerosol particles in the human respiratory tract the relative humidity in a lung model has been calculated using a numerical method. The computations take into account different types of airflows, enhanced transport mechanisms and an optimized wall temperature profile in the upper airways. These parameters are varied to fit experimental temperature data. Under certain conditions the corresponding relative humidity shows a maximum near the first bifurcation, which exceeds the final humidity in the alveoli. This high humidity forces dry NaC1 particles with diameters less than 0.5 μm to grow to their maximum size in the first bronchi. Thereafter the droplets loose water and reach their final size in the terminal bronchioles. AU - Ferron, G.A. AU - Haider, B. AU - Kreyling, W.G. C1 - 33238 C2 - 35406 SP - 565-589 TI - A method for the approximation of the relative humidity in the upper human airways. JO - Bull. Math. Biol. VL - 47 IS - 4 PY - 1985 SN - 0092-8240 ER -