Quantitative Biology

We review the key role played by mathematical modelling in elucidating two centre-finding patterning systems in E. coli: midcell division positioning by the MinCDE system and DNA partitioning by the ParABS system. We focus particularly on how, despite much experimental effort, these systems were simply too complex to unravel by experiments alone, and instead required key injections of quantitative, mathematical thinking. We conclude the review by analysing the frequency of modelling approaches in microbiology over time. We find that while such methods are increasing in popularity, they are still probably heavily under-utilised for optimal progress on complex biological questions.

It is well known that cyclins are a family of proteins that control cell-cycle progression by activating cyclin-dependent kinase. Based on our experimental results, we propose here a novel hypothesis that certain amplified genomic-DNA fragments (AGFs) may also be required for the cell cycle progression of eukaryotic cells and thus can be named as cell-cycle-associated AGFs (CAGFs). Like fluctuation in cyclin levels during cell cycle progression, these CAGFs are amplified and degraded at different points of the cell cycle. The functions of CAGFs are unknown, but we speculate that CAGFs might be involved in regulation of gene expression, genome protection, and formation of certain macromolecular complexes required for the dynamic genome architecture during cell cycle progression. Our experimental results also show that chloroquine induces the production of CAGFs in Plasmodium falciparum, suggesting that targeting cell cycle progression can be the primary mechanism of chloroquine's antimalarial, anticancer, and immunomodulatory actions.

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.

Three-dimensional interphase organization of metazoan genomes has been linked to cellular identity. However, the principles governing 3D interphase genome architecture and its faithful transmission through disruptive events of cell-cycle, like mitosis, are not fully understood. By using Brownian dynamics simulations of Drosophila chromosome 3R up to time-scales of minutes, we show that chromatin binding profile of Polycomb-repressive-complex-1 robustly predicts a sub-set of topologically associated domains (TADs), and inclusion of other factors recapitulates the profile of all TADs, as observed experimentally. Our simulations show that chromosome 3R attains interphase organization from mitotic state by a two-step process in which formation of local TADs is followed by long-range interactions. Our model also explains statistical features and tracks the assembly kinetics of polycomb subnuclear clusters. In conclusion, our approach can be used to predict structural and kinetic features of 3D chromosome folding and its associated proteins in biological relevant genomic and time scales.

We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also dissociate into two subclusters with a uniform probability. To study the statistics of clusters, we combine a Markov chain analysis with a partition number approach. Interestingly, we obtain explicit formulas for the size and the number of clusters in terms of hypergeometric functions. Finally, we apply our analysis to study the statistical physics of telomeres (ends of chromosomes) clustering in the yeast nucleus and show that the diffusion-coagulation-fragmentation process can predict the organization of telomeres.

The hair cell's mechanoreceptive organelle, the hair bundle, is highly sensitive because its transduction channels open over a very narrow range of displacements. The synchronous gating of transduction channels also underlies the active hair-bundle motility that amplifies and tunes responsiveness. The extent to which the gating of independent transduction channels is coordinated depends on how tightly individual stereocilia are constrained to move as a unit. Using dual-beam interferometry in the bullfrog's sacculus, we found that thermal movements of stereocilia located as far apart as a bundle's opposite edges display high coherence and negligible phase lag. Because the mechanical degrees of freedom of stereocilia are strongly constrained, a force applied anywhere in the hair bundle deflects the structure as a unit. This feature assures the concerted gating of transduction channels that maximizes the sensitivity of mechanoelectrical transduction and enhances the hair bundle's capacity to amplify its inputs.

Microtubules (MTs) nucleated by centrosomes form star-shaped structures referred to as asters. Aster motility and dynamics is vital for genome stability, cell division, polarization and differentiation. Asters move either towards the cell center or away from it. Here, we focus on the centering mechanism in a membrane independent system of Xenopus cytoplasmic egg extracts. Using live microscopy and single particle tracking, we find that asters move towards chromatinized DNA structures. The velocity and directionality profiles suggest a random walk with drift directed towards DNA. We have developed a theoretical model that can explain this movement as a result of a gradient of MT length dynamics and MT gliding on immobilized dynein motors. In simulations, the antagonistic action of the motor species on the radial array of MTs leads to a tug-of-war purely due to geometric considerations and aster motility resembles a directed random-walk. Additionally our model predicts that aster velocities do not change greatly with varying initial distance from DNA. The movement of asymmetric asters becomes increasingly super-diffusive with increasing motor density, but for symmetric asters it becomes less super-diffusive. The transition of symmetric asters from superdiffusive to diffusive mobility is the result of number fluctuations in bound motors in the tug-of-war. Overall, our model is in good agreement with experimental data in Xenopus cytoplasmic extracts and predicts novel features of the collective effects of motor-MT interactions.

A microtubule (MT) is a hollow tube of approximately 25 nm diameter. The two ends of the tube are dissimilar and are designated as `plus' and `minus' ends. Motivated by the collective push and pull exerted by a bundle of MTs during chromosome segregation in a living cell, we have developed here a much simplified theoretical model of a bundle of parallel dynamic MTs. The plus-end of all the MTs in the bundle are permanently attached to a movable `wall' by a device whose detailed structure is not treated explicitly in our model. The only requirement is that the device allows polymerization and depolymerization of each MT at the plus-end. In spite of the absence of external force and direct lateral interactions between the MTs, the group of polymerizing MTs attached to the wall create a load force against the group of depolymerizing MTs and vice-versa; the load against a group is shared equally by the members of that group. Such indirect interactions among the MTs gives rise to the rich variety of possible states of collective dynamics that we have identified by computer simulations of the model in different parameter regimes. The bi-directional motion of the cargo, caused by the load-dependence of the polymerization kinetics, is a "proof-of-principle" that the bi-directional motion of chromosomes before cell division does not necessarily need active participation of motor proteins.

Recent findings raise the possibility of PARP inhibitor therapy in colorectal cancers(CRCs). However, the extent of PARP-1 protein expression in clinical specimens of CRC is not known. Using immunohistochemistry we assessed PARP-1 protein expression in tissue microarrays of 151 CRCs and its association with the patient's age, sex, Astler-Coller stage, grade and site of the tumor. High PARP nuclear immunoreactivity was found in 68.2% (103/151) of all cases. In turn, 31.8% (48/151)of tumors showed low PARP expression, including 9 (6%) PARP-1 negative CRCs. There was a significant association of PARP-1 expression with the site of CRC and Astler-Coller stage. A high PARP expression was noted in 79.1% of colon vs. 53.9% of rectal tumors (p = 0.001). The mean PARP-1 score was 1.27 times higher in colon vs. rectal cancers (p = 0.009) and it was higher in stage B2 vs. stage C of CRCs (p = 0.018). In conclusion, the level of PARP-1 protein nuclear expression is associated with the tumor site and heterogeneous across clinical specimens of CRC, with the majority of CRCs expressing a high level but minority - low or no PARP-1 expression. These findings may have a clinical significance because the assessment of PARP-1 expression in tumor samples may improve selection of patients with CRC for PARP inhibitor therapy.

The comment is intended to answer the criticism presented on `Steady-state fluctuations of a genetic feedback loop: an exact solution' [J. Chem. Phys. {\bf 137}, 035104 (2012).] and provides the missing component for the complete analytic solutions to the author's model.