Quantitative Biology

A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. But, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an {\it in-vitro} experiment where a single-stranded DNA, subjected to a mechanical tension F , is converted to a double-stranded DNA by a single DNAP. The F -dependence of the average rate of replication, which depends on the rates of both polymerase and exonuclease activities of the DNAP, is in good qualitative agreement with the corresponding experimental results. We introduce 9 novel distinct {\it conditional dwell times} of a DNAP. Using the methods of first-passage times, we also derive the exact analytical expressions for the probability distributions of these conditional dwell times. The predicted F -dependence of these distributions are, in principle, accessible to single-molecule experiments.

Certain biological reactions, such as receptor-ligand binding at cell-cell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T cell interface, a key player in immunological information processing. Diffusion sets a limit for such cavitation to occur spontaneously, thereby defining a timescale below which active mechanisms must take over. We consider N independent diffusing particles in a closed domain, containing a sub-region with N 0 particles, on average. We investigate the time until the sub-region is empty, allowing a subsequent reaction to proceed. The first passage time is computed using an efficient exact simulation algorithm and an asymptotic approximation in the limit that cavitation is rare. In this limit, we find that the mean first passage time is sub-exponential, T∝ e N 0 / N 2 0 . For the case of T cell receptors, we find that stochastic cavitation is exceedingly slow, 10 9 seconds at physiological densities, however can be accelerated to occur within 5 second with only a four-fold dilution.

We once proposed that cell-type-associated chromatin configurations determine cell types and that cancer cell type is determined by cancer-associated chromatin configuration (CACC). In this paper, we hypothesize that flexible cell-type-associated chromatin configuration is associated with cell potency and has an advantage over inflexible one in regulating genome related activities, such as DNA replication, DNA transcription, DNA repair, and DNA mutagenesis. The reason why cancer is so difficult to treat is because CACC is flexible, which enables cancer cells not only to produce heterogeneous subclones through limited cell differentiation, but also to maximally and efficiently use genome related resources to survive environmental changes. Therefore, to beat cancer, more efforts should be made to restrict the flexibility of CACC or to change CACC so that cancer cells can be turned back to normal or become less malignant.

Mechanochemical coupling was studied for two different types of myosin motors in cells: myosin V, which carries cargo over long distances by as a single molecule; and myosin II, which generates a contracting force in cooperation with other myosin II molecules. Both mean and variance of myosin V velocity at various [ATP] obeyed Michaelis-Menten mechanics, consistent with tight mechanochemical coupling. Myosin II, working in an ensemble, however, was explained by a loose coupling mechanism, generating variable step sizes depending on the ATP concentration and realizing a much larger step (200 nm) per ATP hydrolysis than myosin V through its cooperative nature at zero load. These different mechanics are ideal for the respective myosin's physiological functions.

Sensors are the first element of the pathways that control the response of cells to their environment. After chemical, the next most important cue is mechanical, and protein complexes that produce or enable a chemical signal in response to a mechanical stimulus are called mechanosensors. There is a sharp distinction between sensing an external force or pressure/tension applied to the cell, and sensing the mechanical stiffness of the environment. We call the first mechanosensitivity of the 1st kind, and the latter mechanosensitivity of the 2nd kind. There are two variants of protein complexes that act as mechanosensors of the 2nd kind: producing either a one-off or a reversible action. The latent complex of TGF- β is an example of the one-off action: on the release of active TGF- β signal, the complex is discarded and needs to be replaced. In contrast, focal adhesion kinase (FAK) in a complex with integrin is a reversible mechanosensor, which initiates the chemical signal in its active phosphorylated conformation, but can spontaneously return to its closed folded conformation. Here we study the physical mechanism of the reversible mechanosensor of the 2nd kind, using FAK as a practical example. We find how the rates of conformation changes depend on the substrate stiffness and the pulling force applied from the cell cytoskeleton. The results compare well with the phenotype observations of cells on different substrates.

Myosin II isoforms with varying mechanochemistry and filament size interact with filamentous actin (F-actin) networks to generate contractile forces in cells. How their properties control force production in environments with varying stiffness is poorly understood. Here, we incorporated literature values for properties of myosin II isoforms into a cross-bridge model. Similar actin gliding speeds and force-velocity curves expected from previous experiments were observed. Motor force output on an elastic load was regulated by two timescales--that of their attachment to F-actin, which varied sharply with the ensemble size, motor duty ratio, and external load, and that of force build up, which scaled with ensemble stall force, gliding speed, and load stiffness. While such regulation did not require force-dependent kinetics, the myosin catch bond produced positive feedback between attachment time and force to trigger switch-like transitions from short attachments and small forces to high force-generating runs at threshold parameter values. Parameters representing skeletal muscle myosin, non-muscle myosin IIB, and non-muscle myosin IIA revealed distinct regimes of behavior respectively: (1) large assemblies of fast, low-duty ratio motors rapidly build stable forces over a large range of environmental stiffness, (2) ensembles of slow, high-duty ratio motors serve as high-affinity cross-links with force build-up times that exceed physiological timescales, and (3) small assemblies of low-duty ratio motors operating at intermediate speeds may respond sharply to changes in mechanical context--at low forces or stiffness, they serve as low affinity cross-links but they can transition to effective force production via the positive feedback mechanism described above. These results reveal how myosin isoform properties may be tuned to produce force and respond to mechanical cues in their environment.

The coupling between the depolymerization of microtubules (MTs) and the motion of the Dam1 ring complex is now thought to play an important role in the generation of forces during mitosis. Our current understanding of this motion is based on a number of detailed computational models. Although these models realize possible mechanisms for force transduction, they can be extended by variation of any of a large number of poorly measured parameters and there is no clear strategy for determining how they might be distinguished experimentally. Here we seek to identify and analyze two distinct mechanisms present in the computational models. In the first the splayed protofilaments at the end of the depolymerizing MT physically prevent the Dam1 ring from falling off the end, in the other an attractive binding secures the ring to the microtubule. Based on this analysis, we discuss how to distinguish between competing models that seek to explain how the Dam1 ring stays on the MT. We propose novel experimental approaches that could resolve these models for the first time, either by changing the diffusion constant of the Dam1 ring (e.g., by tethering a long polymer to it) or by using a time varying load.

The detection of sound begins when energy derived from acoustic stimuli deflects the hair bundles atop hair cells. As hair bundles move, the viscous friction between stereocilia and the surrounding liquid poses a fundamental challenge to the ear's high sensitivity and sharp frequency selectivity. Part of the solution to this problem lies in the active process that uses energy for frequency-selective sound amplification. Here we demonstrate that a complementary part involves the fluid-structure interaction between the liquid within the hair bundle and the stereocilia. Using force measurement on a dynamically scaled model, finite-element analysis, analytical estimation of hydrodynamic forces, stochastic simulation and high-resolution interferometric measurement of hair bundles, we characterize the origin and magnitude of the forces between individual stereocilia during small hair-bundle deflections. We find that the close apposition of stereocilia effectively immobilizes the liquid between them, which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion. The obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode, whereas the elastic horizontal top connectors stabilize the structure, further reducing the drag. As measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres, the balance of forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre. A combination of high-resolution experiments and detailed numerical modelling of fluid-structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction.

Autophagy is an intracellular degradation process that employs complex membrane dynamics to isolate and break down cellular components. However, many unanswered questions remain concerning remodeling of autophagic membranes. Here, we focus on the advantages of theoretical modelling to study the formation of autophagosomes and to understand the origin of autophagosomal membranes. Starting from the well-defined geometry of final autophagosomes we ask the question of how these organelles can be formed by combining various preautophagosomal membranes such as vesicles, membrane tubules or sheets. We analyse the geometric constraints of autophagosome formation by taking the area of the precursor membranes and their internal volume into account. Our results suggest that vesicle fusion contributes little to the formation of autophagosomes. In the second part we quantify the curvature of the precursors and report that the formation of autophagosomes is associated with a strong relaxation of membrane curvature energy. This effect we find for a wide range of membrane asymmetries. It is especially strong for small distances between both autophagosomal membranes, as observed in vivo. We quantify the membrane bending energies of all precursors by considering membrane asymmetries. We propose that the generation and supply of pre-autophagosomal membranes is one limiting step for autophagosome formation.

More than 30 years ago, we published a paper entitled as abnormal chromatin configuration and oncogenesis, which proposed the first hypothesis that links oncogenesis to abnormal three-dimensional (3D) genome structure. Recently, many studies have demonstrated that the 3D genome structure plays a major role in oncogenesis, which strongly supports our hypothesis. In this paper, further thoughts about our hypothesis is presented.