scholarly journals Differential equation methods for simulation of GFP kinetics in non–steady state experiments

2018 ◽  
Vol 29 (6) ◽  
pp. 763-771 ◽  
Author(s):  
Robert D. Phair

Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis.

2004 ◽  
Vol 10 (5) ◽  
pp. 568-579 ◽  
Author(s):  
Marc-Jan Gubbels ◽  
Boris Striepen

The ability to transfect Apicomplexan parasites has revolutionized the study of this important group of pathogens. The function of specific genes can be explored by disruption of the locus or more subtly by introduction of altered or tagged versions. Using the transgenic reporter gene green fluorescent protein (GFP), cell biological processes can now be studied in living parasites and in real time. We review recent advances made using GFP-based experiments in the understanding of protein trafficking, organelle biogenesis, and cell division inToxoplasma gondiiandPlasmodium falciparum. A technical section provides a collection of basic experimental protocols for fluorescent protein expression inT. gondii. The combination of thein vivomarker GFP with an increasingly diverse genetic toolbox forT. gondiiopens many exciting experimental opportunities, and emerging applications of GFP in genetic and pharmacological screens are discussed.


Author(s):  
K. Jacobson ◽  
A. Ishihara ◽  
B. Holifield ◽  
F. Zhang

Our laboratory is concerned with understanding the dynamic structure of the plasma membrane with particular reference to the movement of membrane constituents during cell locomotion. In addition to the standard tools of molecular cell biology, we employ both fluorescence recovery after photo- bleaching (FRAP) and digitized fluorescence microscopy (DFM) to investigate individual cells. FRAP allows the measurement of translational mobility of membrane and cytoplasmic molecules in small regions of single, living cells. DFM is really a new form of light microscopy in that the distribution of individual classes of ions, molecules, and macromolecules can be followed in single, living cells. By employing fluorescent antibodies to defined antigens or fluorescent analogs of cellular constituents as well as ultrasensitive, electronic image detectors and video image averaging to improve signal to noise, fluorescent images of living cells can be acquired over an extended period without significant fading and loss of cell viability.


2006 ◽  
Vol 84 (4) ◽  
pp. 515-522 ◽  
Author(s):  
Preetinder K. Dhanoa ◽  
Alison M. Sinclair ◽  
Robert T. Mullen ◽  
Jaideep Mathur

The discovery and development of multicoloured fluorescent proteins has led to the exciting possibility of observing a remarkable array of subcellular structures and dynamics in living cells. This minireview highlights a number of the more common fluorescent protein probes in plants and is a testimonial to the fact that the plant cell has not lagged behind during the live-imaging revolution and is ready for even more in-depth exploration.


2001 ◽  
Vol 114 (14) ◽  
pp. 2641-2648
Author(s):  
Jacqueline Franke ◽  
Barbara Reimann ◽  
Enno Hartmann ◽  
Matthias Köhler ◽  
Brigitte Wiedmann

The nascent polypeptide-associated complex (NAC) has been found quantitatively associated with ribosomes in the cytosol by means of cell fractionation or fluorescence microscopy. There have been reports, however, that single NAC subunits may be involved in transcriptional regulation. We reasoned that the cytosolic location might only reflect a steady state equilibrium and therefore investigated the yeast NAC proteins for their ability to enter the nucleus. We found that single subunits of yeast NAC can indeed be transported into the nucleus and that this transport is an active process depending on different nuclear import factors. Translocation into the nucleus was only observed when binding to ribosomes was inhibited. We identified a domain of the ribosome-binding NAC subunit essential for nuclear import via the importin Kap123p/Pse1p-dependent import route. We hypothesize that newly translated NAC proteins travel into the nucleus to bind stoichiometrically to ribosomal subunits and then leave the nucleus together with these subunits to concentrate in the cytosol.


2007 ◽  
Vol 76 (3) ◽  
pp. C115-C121 ◽  
Author(s):  
Stefan Denicke ◽  
Jan-Eric Ehlers ◽  
Raluca Niesner ◽  
Stefan Quentmeier ◽  
Karl-Heinz Gericke

2022 ◽  
Vol 12 ◽  
Author(s):  
Ryland D. Mortlock ◽  
Chuanfeng Wu ◽  
E. Lake Potter ◽  
Diana M. Abraham ◽  
David S. J. Allan ◽  
...  

The in vivo tissue distribution and trafficking patterns of natural killer (NK) cells remain understudied. Animal models can help bridge the gap, and rhesus macaque (RM) primates faithfully recapitulate key elements of human NK cell biology. Here, we profiled the tissue distribution and localization patterns of three NK cell subsets across various RM tissues. We utilized serial intravascular staining (SIVS) to investigate the tissue trafficking kinetics at steady state and during recovery from CD16 depletion. We found that at steady state, CD16+ NK cells were selectively retained in the vasculature while CD56+ NK cells had a shorter residence time in peripheral blood. We also found that different subsets of NK cells had distinct trafficking kinetics to and from the lymph node as well as other lymphoid and non-lymphoid tissues. Lastly, we found that following administration of CD16-depleting antibody, CD16+ NK cells and their putative precursors retained a high proportion of continuously circulating cells, suggesting that regeneration of the CD16 NK compartment may take place in peripheral blood or the perivascular compartments of tissues.


2011 ◽  
Vol 2011 (10) ◽  
pp. 5354-5371
Author(s):  
Ivan Zhu ◽  
Dipankar Sen ◽  
Eugene Vegso ◽  
Tom Getting ◽  
Dan Wall

Author(s):  
A. Yusnaeni ◽  
Kasbawati Kasbawati ◽  
Toaha Syamsuddin

AbstractIn this paper, we study a mathematical model of an immune response system consisting of a number of immune cells that work together to protect the human body from invading tumor cells. The delay differential equation is used to model the immune system caused by a natural delay in the activation process of immune cells. Analytical studies are focused on finding conditions in which the system undergoes changes in stability near a tumor-free steady-state solution. We found that the existence of a tumor-free steady-state solution was warranted when the number of activated effector cells was sufficiently high. By considering the lag of stimulation of helper cell production as the bifurcation parameter, a critical lag is obtained that determines the threshold of the stability change of the tumor-free steady state. It is also leading the system undergoes a Hopf bifurcation to periodic solutions at the tumor-free steady-state solution.Keywords: tumor–immune system; delay differential equation; transcendental function; Hopf bifurcation. AbstrakDalam makalah ini, dikaji model matematika dari sistem respon imun yang terdiri dari sejumlah sel imun yang bekerja sama untuk melindungi tubuh manusia dari invasi sel tumor. Persamaan diferensial tunda digunakan untuk memodelkan sistem kekebalan yang disebabkan oleh keterlambatan alami dalam proses aktivasi sel-sel imun. Studi analitik difokuskan untuk menemukan kondisi di mana sistem mengalami perubahan stabilitas di sekitar solusi kesetimbangan bebas tumor. Diperoleh bahwa solusi kesetimbangan bebas tumor dijamin ada ketika jumlah sel efektor yang diaktifkan cukup tinggi. Dengan mempertimbangkan tundaan stimulasi produksi sel helper sebagai parameter bifurkasi, didapatkan lag kritis yang menentukan ambang batas perubahan stabilitas dari solusi kesetimbangan bebas tumor. Parameter tersebut juga mengakibatkan sistem mengalami percabangan Hopf untuk solusi periodik pada solusi kesetimbangan bebas tumor.Kata kunci: sistem tumor–imun; persamaan differensial tundaan; fungsi transedental; bifurkasi Hopf.


Author(s):  
Lyudmyla Barannyk ◽  
John Crepeau ◽  
Patrick Paulus ◽  
Ali Siahpush

A nonlinear, first-order ordinary differential equation that involves Fourier-Bessel series terms has been derived to model the time-dependent motion of the solid-liquid interface during melting and solidification of a material with constant internal heat generation in cylindrical coordinates. The model is valid for all Stefan numbers. One of the primary applications of this problem is for a nuclear fuel rod during meltdown. The numerical solutions to this differential equation are compared to the solutions of a previously derived model that was based on the quasi-steady approximation, which is valid only for Stefan numbers less than one. The model presented in this paper contains exponentially decaying terms in the form of Fourier-Bessel series for the temperature gradients in both the solid and liquid phases. The agreement between the two models is excellent in the low Stefan number regime. For higher Stefan numbers, where the quasi-steady model is not accurate, the new model differs from the approximate model since it incorporates the time-dependent terms for small times, and as the system approaches steady-state, the curves converge. At higher Stefan numbers, the system approaches steady-state faster than for lower Stefan numbers. During the transient process for both melting and solidification, the temperature profiles become parabolic.


Author(s):  
Xuefeng Wang ◽  
Mao Liu ◽  
Weidong Zhu

For wave propagation in periodic media with strong nonlinearity, steady-state solutions can be obtained by solving a corresponding nonlinear delay differential equation (DDE). Based on the periodicity, the steady-state response of a repeated particle or segment in the media contains the complete information of solutions for the wave equation. Considering the motion of the selected particle or segment as a variable, motions of its adjacent particles or segments can be described by the same variable function with different phases, which are delayed variables. Thus, the governing equation for wave propagation can be converted to a nonlinear DDE with multiple delays. A modified incremental harmonic balance (IHB) method is presented here to solve the nonlinear DDE by introducing a delay matrix operator, where a direct approach is used to efficiently and automatically construct the Jacobian matrix for the nonlinear residual in the IHB method. This method is presented by solving an example of a one-dimensional monatomic chain under a nonlinear Hertzian contact law. Results are well matched with those in previous work, while calculation time and derivation effort are significantly reduced. Also there is no additional derivation required to solve new wave systems with different governing equations.


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