Quantitative Biology

Liquid-liquid phase separated (LLPS) states are key to compartmentalise components in the absence of membranes, however it is unclear whether LLPS condensates are actively and specifically organized in the sub-cellular space and by which mechanisms. Here, we address this question by focusing on the ParABS DNA segregation system, composed of a centromeric-like sequence (parS), a DNA-binding protein (ParB) and a motor (ParA). We show that parS-ParB associate to form nanometer-sized, round condensates. ParB molecules diffuse rapidly within the nucleoid volume, but display confined motions when trapped inside ParB condensates. Single ParB molecules are able to rapidly diffuse between different condensates, and nucleation is strongly favoured by parS. Notably, the ParA motor is required to prevent the fusion of ParB condensates. These results describe a novel active mechanism that splits, segregates and localises non-canonical LLPS condensates in the sub-cellular space.

A Charge Transport (CT) mechanism has been proposed in several papers (e.g., Yavin, et al. PNAS, v102 3546 (2005)) to explain the localization of Base Excision Repair (BER) enzymes to lesions on DNA. The CT mechanism relies on redox reactions of iron-sulfur cofactors that modify the enzyme's binding affinity. These redox reactions are mediated by the DNA strand and involve the exchange of electrons between BER enzymes along DNA. We propose a mathematical model that incorporates enzyme binding/unbinding, electron transport, and enzyme diffusion along DNA. Analysis of our model within a range of parameter values suggests that the redox reactions can increase desorption of BER enzymes not already bound to their targets, allowing the enzymes to be recycled, thus accelerating the overall search process. This acceleration mechanism is most effective when enzyme copy numbers and enzyme diffusivity along the DNA are small. Under such conditions, we find that CT BER enzymes find their targets more quickly than simple "passive" enzymes that simply attach to the DNA without desorbing.

Background: For faithful chromosome segregation during cell division, correct attachments must be established between sister chromosomes and microtubules from opposite spindle poles through kinetochores (chromosome bi-orientation). Incorrect attachments of kinetochore microtubules (kMTs) lead to chromosome mis-segregation and aneuploidy, which is often associated with developmental abnormalities such as Down syndrome and diseases including cancer. The interaction between kinetochores and microtubules is highly dynamic with frequent attachments and detachments. However, it remains unclear how chromosome bi-orientation is achieved with such accuracy in such a dynamic process. Results: To gain new insight into this essential process, we have developed a simple mathematical model of kinetochore-microtubule interactions during cell division in general, i.e. both mitosis and meiosis. Firstly, the model reveals that the balance between attachment and detachment probabilities of kMTs is crucial for correct chromosome bi-orientation. With the right balance, incorrect attachments are resolved spontaneously into correct bi-oriented conformations while an imbalance leads to persistent errors. In addition, the model explains why errors are more commonly found in the first meiotic division (meiosis I) than in mitosis and how a faulty conformation can evade the spindle assembly checkpoint, which may lead to a chromosome loss. Conclusions: The proposed model, despite its simplicity, helps us understand one of the primary causes of chromosomal instability - aberrant kinetochore-microtubule interactions. The model reveals that chromosome bi-orientation is a probabilistic self-organization, rather than a sophisticated process of error detection and correction.

Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.

We study force generation by a set of parallel actin filaments growing against a non-rigid obstacle, in presence of an external load. The filaments polymerize by either moving the whole obstacle, with a large energy cost, or by causing local distortion in its shape which costs much less energy. The non-rigid obstacle also has local thermal fluctuations due to which its shape can change with time and we describe this using fluctuations in the height profile of a one dimensional interface with Kardar-Parisi-Zhang dynamics. We find the shape fluctuations of the barrier strongly affects the force generation mechanism. The qualitative nature of the force-velocity curve is crucially determined by the relative time-scale of filament and barrier dynamics. The height profile of the barrier also shows interesting variation with the external load. Our analytical calculation within mean-field theory shows reasonable agreement with our simulation results.

There is increasing evidence that protein binding to specific sites along DNA can activate the reading out of genetic information without coming into direct physical contact with the gene. There also is evidence that these distant but interacting sites are embedded in a liquid droplet of proteins which condenses out of the surrounding solution. We argue that droplet-mediated interactions can account for crucial features of gene regulation only if the droplet is poised at a non-generic point in its phase diagram. We explore a minimal model that embodies this idea, show that this model has a natural mechanism for self-tuning, and suggest direct experimental tests.

Internet, social media, neuronal or blood vessel are organized in complex networks. These networks are characterized by several quantities such as the underlying graph connectivity (topology), how they grow in time, scaling laws or by the mean time a random search can cover a network and also by shortest path between two nodes. We present here a novel type of network property based on a unidirectional transport mechanism occurring in the Endoplasmic Reticulum network found in the cell cytoplasm. This mechanism is an active-waiting transportation, where molecules have to wait a random time before being transported from one node to the next one. We find that the consequence of this unusual network transportation is that molecules travel together by recurrent packets, which quite a large deviation behavior compared to classical propagation in graphs. To conclude, this form of transportation is associated with an efficient and robust molecular redistribution inside cells.

We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of vesicles follows a log-normal distribution that changes over time due to fusion processes, their spatial distribution gives rise to distinct patterns. Their occurrence depends on the concentration of proteins which are synthesized based on the transcriptional activities of some genes. Hence, differences in these spatio-temporal vesicle patterns allow indirect conclusions about the (unknown) impact of these genes. By means of agent-based computer simulations we are able to reproduce such patterns on real temporal and spatial scales. Our modeling approach is based on Brownian agents with an internal degree of freedom, θ , that represents the different modes of motion. Conditions inside the cell are modeled by an effective potential that differs for agents dependent on their value θ . Agent's motion in this effective potential is modeled by an overdampted Langevin equation, changes of θ are modeled as stochastic transitions with values obtained from experiments, and fusion events are modeled as space-dependent stochastic transitions. Our results for the spatio-temporal vesicle patterns can be used for a statistical comparison with experiments. We also derive hypotheses of how the silencing of some genes may affect the intracellular transport, and point to generalizations of the model.

During the lifecycle of a virus, viral proteins and other components self-assemble to form a symmetric protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that, above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly, and thus should be accounted for in models that are used to estimate interaction parameters from experimental data.

Signal transduction, the information processing mechanism in biological cells, is carried out by a network of biochemical reactions. The dynamics of driven biochemical reactions can be studied in terms of nonequilibrium statistical physics. Such systems may also be studied in terms of Shannon's information theory. We combine these two perspectives in this study of the basic units (modules) of cellular signaling: the phosphorylation dephosphorylation cycle (PdPC) and the guanosine triphosphatase (GTPase). We show that the channel capacity is zero if and only if the free energy expenditure of biochemical system is zero. In fact, a positive correlation between the channel capacity and free energy expenditure is observed. In terms of the information theory, a linear signaling cascade consisting of multiple steps of PdPC can function as a distributed "multistage code". With increasing number of steps in the cascade, the system trades channel capacity with the code complexity. Our analysis shows that while a static code can be molecular structural based; a biochemical communication channel has to have energy expenditure.