Quantitative Biology

During asymmetric cell division, dynein generates forces, which position the spindle to reflect polarity and ensure correct daughter cell fates. The transient cortical localization of dynein raises the question of its targeting. We found that it accumulates at the microtubule plus-ends like in budding yeast, indirectly hitch-hiking on EBP-2 EB1 likely via dynactin. Importantly, this mechanism, which modestly accounts for cortical forces, does not transport dynein, which displays the same binding/unbinding dynamics as EBP-2 EB1 . At the cortex, dynein tracks can be classified as having either directed or diffusive-like motion. Diffusive-like tracks reveal force-generating dyneins. Their densities are higher on the posterior tip of the embryos, where GPR-1/2 LGN concentrate, but their durations are symmetric. Since dynein flows to the cortex are non-polarized, we suggest that this posterior enrichment increases dynein binding, thus accounts for the force imbalance reflecting polarity, and supplements the regulation of mitotic progression via the non-polarized detachment rate.

Living systems produce copies of information-carrying molecules such as DNA by assembling monomer units into finite-length oligomer (short polymer) copies. We explore the role of initiation and termination of the copy process in the thermodynamics of copying. By splitting the free-energy change of copy formation into informational and chemical terms, we show that copy accuracy plays no direct role in the overall thermodynamics. Instead, it is thermodynamically costly to produce outputs that are more similar to the oligomers in the environment than sequences obtained by randomly sampling monomers. Copy accuracy can be thermodynamically neutral, or even favoured, depending on the surroundings. Oligomer copying mechanisms can thus function as information engines that interconvert chemical and information-based free energy. Hard thermodynamic constraints on accuracy derived for infinite-length polymers instead manifest as kinetic barriers experienced while the copy is template-attached. These barriers are easily surmounted by shorter oligomers.

Cilia are ubiquitous organelles involves in eukaryotic motility. They are long, slender, and motile protrusions from the cell body. They undergo active regular oscillatory beating patterns that can propel cells, such as the algae Chlamydomonas, through fluids. When many cilia beat in synchrony they can also propel fluid along the surfaces of cells, as is the case of nodal cilia. The main structural elements inside the cilium are microtubules. There are also molecular motors of the dynein family that actively power the motion of the cilium. These motors transform chemical energy in the form of ATP into mechanical forces that produce sliding displacement between the microtubules. This sliding is converted to bending by constraints at the base and/or along the length of the cilium. Forces and displacements within the cilium can regulate dyneins and provide a feedback mechanism: the dyneins generate forces, deforming the cilium; the deformations, in turn, regulate the dyneins. This feedback is believed to be the origin of the coordination of dyneins in space and time which underlies the regularity of the beat pattern. Goals and approach. While the mechanism by which dyneins bend the cilium is understood, the feedback mechanism is much less clear. The two key questions are: which forces and displacements are the most relevant in regulating the beat? and how exactly does this regulation occur? In this thesis we develop a framework to describe the spatio-temporal patterns of a cilium with different mechanisms of motor regulation. Characterizing and comparing the predicted shapes and beat patterns of these different mechanisms to those observed in experiments provides us with further understanding on how dyneins are regulated. This comparison is done both, with a linear model that can be analytically solved, as with a non-linear model that we solve numerically.

Gene expression is inherently a noisy process which manifests as cell-to-cell variability in time evolution of proteins. Consequently, events that trigger at critical threshold levels of regulatory proteins exhibit stochasticity in their timing. An important contributor to the noise in gene expression is translation bursts which correspond to randomness in number of proteins produced in a single mRNA lifetime. Modeling timing of an event as a first-passage time (FPT) problem, we explore the effect of burst size distribution on event timing. Towards this end, the probability density function of FPT is computed for a gene expression model with burst size drawn from a generic non-negative distribution. Analytical formulas for FPT moments are provided in terms of known vectors and inverse of a matrix. The effect of burst size distribution is investigated by looking at how the feedback regulation strategy that minimizes noise in timing around a given time deviates from the case when burst is deterministic. Interestingly, results show that the feedback strategy for deterministic burst case is quite robust to change in burst size distribution, and deviations from it are confined to about 20% of the optimal value. These findings facilitate an improved understanding of noise regulation in event timing.

Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load.

Here we provide a thorough discussion of the model for Min protein dynamics proposed by Schweizer et al. [11]. The manuscript serves as supplementary document for our letter to the editor to appear in PNAS. Our analysis is based on the original COMSOL simulation files that were used for the publication. We show that all computational data in Schweizer et al. rely on exploitation of simulation artifacts and various unmentioned modifications of model parameters that strikingly contradict the experimental setup and experimental data. We find that the model neither accounts for MinE membrane interactions nor for any observed MinDE protein patterns. All conclusions drawn from the computational model are void. There is no evidence at all that persistent MinE membrane binding has any role in geometry sensing.

Bidirectional cargo transport by molecular motors in cells is a complex phenomenon, in which the cargo (usually a vesicle) alternately moves in retrograde and anterograde directions. In this case, teams of oppositely pulling motors (eg., kinesin and dynein) bind to the cargo simultaneously, and `coordinate' their activity such that the motion consists of spells of positively and negatively directed segments, separated by pauses of varying duration. A set of recent experiments have analyzed the bidirectional motion of endosomes in the amoeba D. discoideum in detail. It was found that in between directional switches, a team of 5-6 dyneins stall a cargo against a stronger kinesin in tug of war, which lasts for almost a second. As the mean detachment time of a kinesin under its stall load was also observed to be ~ 1s, we infer that the collective detachment time of the dynein assembly must also be similar. Here, we analyze this inference from a modeling perspective, using experimentally measured single-molecule parameters as inputs. We find that the commonly assumed exponential load-dependent detachment rate is inconsistent with observations, as it predicts that a 5-dynein assembly will detach under its combined stall load in less than a hundredth of a second. A modified model where the load-dependent unbinding rate is assumed to saturate at stall-force level for super-stall loads gives results which are in agreement with experimental data. Our analysis suggests that the load-dependent detachment of a dynein in a team is qualitatively different at sub-stall and super-stall loads, a conclusion which is likely to have implications in other situations involving collective effects of many motors.

Several independent observations have suggested that catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent {\it in vitro} observations by Gardner et al.[ M. K. Gardner et al., Cell {\bf147}, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here, we investigate, via numerical simulations and mathematical calculations, some of the consequences of age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically and purely linear growth. The boundary demarcating the steady state and non-steady state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to non-exponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

We study a model for a protein searching for a target, using facilitated diffusion, on a DNA molecule confined in a finite volume. The model includes three distinct pathways for facilitated diffusion: (a) sliding - in which the protein diffuses along the contour of the DNA (b) jumping - where the protein travels between two sites along the DNA by three-dimensional diffusion, and finally (c) intersegmental transfer - which allows the protein to move from one site to another by transiently binding both at the same time. The typical search time is calculated using scaling arguments which are verified numerically. Our results suggest that the inclusion of intersegmental transfer (i) decreases the search time considerably (ii) makes the search time much more robust to variations in the parameters of the model and (iii) that the optimal search time occurs in a regime very different than that found for models which ignore intersegmental transfers. The behavior we find is rich and shows surprising dependencies, for example, on the DNA length.

We introduce a model for microtubule mechanics containing lateral bonds between dimers in neighboring protofilaments, bending rigidity of dimers, and repulsive interactions between protofilaments modeling steric constraints to investigate the influence of mechanical forces on hydrolysis and catastrophes. We use the allosteric dimer model, where tubulin dimers are characterized by an equilibrium bending angle, which changes from 0 ∘ to 22 ∘ by hydrolysis of a dimer. This also affects the lateral interaction and bending energies and, thus, the mechanical equilibrium state of the microtubule. As hydrolysis gives rise to conformational changes in dimers, mechanical forces also influence the hydrolysis rates by mechanical energy changes modulating the hydrolysis rate. The interaction via the microtubule mechanics then gives rise to correlation effects in the hydrolysis dynamics, which have not been taken into account before. Assuming a dominant influence of mechanical energies on hydrolysis rates, we investigate the most probable hydrolysis pathways both for vectorial and random hydrolysis. Investigating the stability with respect to lateral bond rupture, we identify initiation configurations for catastrophes along the hydrolysis pathways and values for a lateral bond rupture force. If we allow for rupturing of lateral bonds between dimers in neighboring protofilaments above this threshold force, our model exhibits avalanche-like catastrophe events.