Quantitative Biology

In a previous paper, we examined a class of possible conformations for helically patterned filaments in contact with a bonding surface. In particular, we investigated geometries where contact between the pattern and the surface was improved through a periodic twisting and lifting of the filament. A consequence of this lifting is that the total length of the filament projected onto the surface decreases after bonding. When the bonding character of the surface is actuated, this phenomenon can lead to both lifelike "inchworm" behavior of the filaments and ensemble movement. We illustrate, through simulation, how pattern formation may be achieved through this mechanism.

In this projecting work we propose a mass spectrometric patch-clamp equipment with the capillary performing both a local potential registration at the cell membrane and the analyte suction simultaneously. This paper provides a current literature analysis comparing the possibilities of the novel approach proposed with the known methods, such as scanning patch-clamp, scanning ion conductance microscopy, patch clamp based on scanning probe microscopy technology, quantitative subcellular secondary ion mass spectrometry or "ion microscopy", live single-cell mass spectrometry, in situ cell-by-cell imaging, single-cell video-mass spectrometry, etc. We also consider the ways to improve the informativeness of these methods and particularly emphasize the trend at the increasing of the analysis complexity. We propose here the way to improve the efficiency of the cell trapping to the capillary during MS-path-clamp, as well as to provide laser surface ionization using laser trapping and tweezing of cells with the laser beam transmitted through the capillary as a waveguide. It is also possible to combine the above system with the microcolumn separation system or capillary electrophoresis as an optional direction of further development of the complex of analytical techniques emerging from the MS variation of patch-clamp.

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes, RNAPs, phosphate groups, motor proteins) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be two-directional, and furthermore the particles may attach or detach from various regions along the tracks (e.g. ribosomes may drop off the mRNA molecule before reaching a stop codon). We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as the dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique globally asymptotically stable equilibrium. This means that the occupancy in all the sites along the lattice converges to a steady-state value that depends on the parameters but not on the initial conditions. We also show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing the effect of ribosome drop off in mRNA translation. One may perhaps expect that drop off from a jammed site may increase the total flow by reducing congestion. Our results show that this is not true. Drop off has a substantial effect on the flow, yet always leads to a reduction in the steady-state protein production rate.

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a soft simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.

Temporally and spatially resolved measurements of protein transport inside cells provide important clues to the functional architecture and dynamics of biological systems. Fluorescence Recovery After Photobleaching (FRAP) technique has been used over the past three decades to measure the mobility of macromolecules and protein transport and interaction with immobile structures inside the cell nucleus. A theoretical model is presented that aims to describe protein transport inside the nucleus, a process which is influenced by the presence of a boundary (i.e. membrane). A set of reaction-diffusion equations is employed to model both the diffusion of proteins and their interaction with immobile binding sites. The proposed model has been designed to be applied to biological samples with a Confocal Laser Scanning Microscope (CLSM) equipped with the feature to bleach regions characterised by a scanning beam that has a radially Gaussian distributed profile. The proposed model leads to FRAP curves that depend on the on- and off-rates. Semi-analytical expressions are used to define the boundaries of on- (off-) rate parameter space in simplified cases when molecules move within a bounded domain. The theoretical model can be used in conjunction to experimental data acquired by CLSM to investigate the biophysical properties of proteins in living cells.

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

We previously proposed the existence of DNA to DNA transcription in eukaryotic cells, but the mechanism by which single-stranded DNA (ssDNA) transcript is produced and released from the genome remains unknown. We once speculated that the mechanism of DNA to DNA transcription might be similar to that of DNA to RNA transcription, but now we propose that endonuclease dependent transcript cutout may be a possible mechanism of DNA to DNA transcription, in which a copy of ssDNA fragment (transcript) between two nicks produced by nicking endonuclease is released from double-stranded DNA (dsDNA) region in the genome by an unknown ssDNA fragment releasing enzyme. The gap in the dsDNA will be filled through DNA repair mechanism. Occasionally, multiple copies of ssDNA transcripts could be produced through multiple rounds of cutout-repair-cutout cycle.

The study of motor protein dynamics within cytoskeletal networks is of high interest to physicists and biologists to understand how the dynamics and properties of individual motors lead to cooperative effects and control of overall network behaviour. Here, we report a method to detect and track muscular myosin II filaments within an actin network tethered to supported lipid bilayers. Based on the characteristic shape of myosin II filaments, this automated tracking routine allowed us to follow the position and orientation of myosin II filaments over time, and to reliably classify their dynamics into segments of diffusive and processive motion based on the analysis of displacements and angular changes between time steps. This automated, high throughput method will allow scientists to efficiently analyse motor dynamics in different conditions, and will grant access to more detailed information than provided by common tracking methods, without any need for time consuming manual tracking or generation of kymographs.

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the Z -ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro} observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.

In mammals, dosage compensation of X linked genes in female cells is achieved by inactivation of one of their two X chromosomes which is randomly chosen. The earliest steps in X-inactivation (XCI), namely the mechanism whereby cells count their X chromosomes and choose between two equivalent X, remain mysterious. Starting from the recent discovery of X chromosome colocalization at the onset of X-inactivation, we propose a Statistical Mechanics model of XCI, which is investigated by computer simulations and checked against experimental data. Our model describes how a `blocking factor' complex is self-assembled and why only one is formed out of many diffusible molecules, resulting in a spontaneous symmetry breaking (SB) in the binding to two identical chromosomes. These results are used to derive a scenario of biological implications describing all current experimental evidences, e.g., the importance of colocalization.