Quantitative Biology

Many biological and artificial transport channels function without direct input of metabolic energy during a transport event and without structural rearrangements involving transitions from a 'closed' to an 'open' state. Nevertheless, such channels are able to maintain efficient and selective transport. It has been proposed that attractive interactions between the transported molecules and the channel can increase the transport efficiency and that the selectivity of such channels can be based on the strength of the interaction of the specifically transported molecules with the channel. Herein, we study the transport through narrow channels in a framework of a general kinetic theory, which naturally incorporates multi-particle occupancy of the channel and non-single-file transport. We study how the transport efficiency and the probability of translocation through the channel are affected by inter-particle interactions in the confined space inside the channel, and establish conditions for selective transport. We compare the predictions of the model with the available experimental data - and find good semi-quantitative agreement. Finally, we discuss applications of the theory to the design of artificial nano-molecular sieves.

Experiments show that cellular uptake of nanoparticles, via receptor-mediated endocytosis, strongly depends on nanoparticle size. There is an optimal size, approximately 50 nm in diameter, at which cellular uptake is the highest. In addition, there is a maximum size, approximately 200 nm, beyond which uptake via receptor-mediated endocytosis does not occur. By comparing results from different experiments, we found that these sizes weakly depend on the type of cells, nanoparticles, and ligands used in the experiments. Here, we argue that these observations are consequences of the energetics and assembly dynamics of the protein coat that forms on the cytoplasmic side of the outer cell membrane during receptor-mediated endocytosis. Specifically, we show that the energetics of coat formation imposes an upper bound on the size of the nanoparticles that can be internalized, whereas the nanoparticle-size-dependent dynamics of coat assembly results in the optimal nanoparticle size. The weak dependence of the optimal and maximum sizes on cell-nanoparticle-ligand type also follows naturally from our analysis.

We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine. In this simulation, the permeability to ionic flow across the membrane is regulated by the amplitude of chemical potential barriers. With spatially localized ion channels, chemical potential barriers are locally and stochastically regulated. This regulation represents the ion channel gating with multiple subunits, the open and closed states governed by a continuous-time Markov process. The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by the calcium-activated potassium channels in a stochastic manner as a \emph{non-local} feedback loop. The model predicts amplified calcium influx with more closely placed channel complexes, proposing a potential mechanism of differential calcium handling by channel distributions. This work provides a foundation for future computer simulation studies of dendritic spine motility and structural plasticity.

The physical mechanism behind the spontaneous formation of metachronal waves in microtubule arrays in a low Reynolds number fluid has been of interest for the past several years, yet is still not well understood. We present a model implementing the hydrodynamic coupling hypothesis from first principles, and use this model to simulate kinesin-driven microtubule arrays and observe their emergent behavior. The results of simulations are compared to known experimental observations by Sanchez et al. By varying parameters, we determine regimes in which the metachronal wave phenomenon emerges, and categorize other types of possible microtubule motion outside these regimes.

Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins - proteins converting chemical energy into kinetic energy. It is known that motor proteins work in teams enabling unidirectional and bidirectional transport of intracellular cargo over long distances. Disruptions of the underlying transport mechanisms, often caused by mutations that alter single motor characteristics, are known to cause neurodegenerative diseases. For example, phosphorylation of kinesin motor domain at the serine residue is implicated in Huntington's disease, with a recent study of phosphorylated and phosphomimetic serine residues indicating lowered single motor stalling forces. In this article we report the effects of mutations of this nature on transport properties of cargo carried by multiple wild-type and mutant motors. Results indicate that mutants with altered stall forces might determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to an increase in expected run-length when load on the cargo is in the vicinity of the mutant's stalling force or a multiple of its stalling force. A separate contribution of this article is the development of a semi-analytic method to analyze transport of cargo by multiple motors of multiple types. The technique determines transition rates between various relative configurations of motors carrying the cargo using the transition rates between various absolute configurations. This enables exact computation of average velocity and run-length. It can also be used to introduce alterations of various single motor parameters to model a mutation and to deduce effects of such alterations on the transport of a common cargo by multiple motors. Our method is easily implementable and we provide a software package for general use.

The mitogen-activated protein kinase (MAPK) signaling cascade, an evolutionarily conserved motif present in all eukaryotic cells, is involved in coordinating critical cell-fate decisions, regulating protein synthesis, and mediating learning and memory. While the steady-state behavior of the pathway stimulated by a time-invariant signal is relatively well-understood, we show using a computational model that it exhibits a rich repertoire of transient adaptive responses to changes in stimuli. When the signal is switched on, the response is characterized by long-lived modulations in frequency as well as amplitude. On withdrawing the stimulus, the activity decays over timescales much longer than that of phosphorylation-dephosphorylation processes, exhibiting reverberations characterized by repeated spiking in the activated MAPK concentration. The long-term persistence of such post-stimulus activity suggests that the cascade retains memory of the signal for a significant duration following its removal, even in the absence of any explicit feedback or cross-talk with other pathways. We find that the molecular mechanism underlying this behavior is related to the existence of distinct relaxation rates for the different cascade components. This results in the imbalance of fluxes between different layers of the cascade, with the repeated reuse of activated kinases as enzymes when they are released from sequestration in complexes leading to one or more spike events following the removal of the stimulus. The persistent adaptive response reported here, indicative of a cellular "short-term" memory, suggests that this ubiquitous signaling pathway plays an even more central role in information processing by eukaryotic cells.

The ability to monitor nutrient and other environmental conditions with high sensitivity is crucial for cell growth and survival. Sensory adaptation allows a cell to recover its sensitivity after a transient response to a shift in the strength of extracellular stimulus. The working principles of adaptation have been established previously based on rate equations which do not consider fluctuations in a thermal environment. Recently, G. Lan et al. (Nature Phys., 8:422-8, 2012) performed a detailed analysis of a stochastic model for the E. coli sensory network. They showed that accurate adaptation is possible only when the system operates in a nonequilibrium steady-state (NESS). They further proposed an energy-speed-accuracy (ESA) trade-off relation. We present here analytic results on the NESS of the model through a mapping to a one-dimensional birth-death process. An exact expression for the entropy production rate is also derived. Based on these results, we are able to discuss the ESA relation in a more general setting. Our study suggests that the adaptation error can be reduced exponentially as the methylation range increases. Finally, we show that a nonequilibrium phase transition exists in the infinite methylation range limit, despite the fact that the model contains only two discrete variables.

Theoretical and experimental evidences support the hypothesis that extremely low-frequency electromagnetic fields can affect voltage-gated channels. Little is known, however, about their effect on potassium channels. Kv1.3, a member of the voltage-gated potassium channels family originally discovered in the brain, is a key player in important biological processes including antigen-dependent activation of T-cells during the immune response. We report that Kv1.3 expressed in CHO-K1 cells can be modulated in cell subpopulations by extremely low frequency and relatively low intensity electromagnetic fields. In particular, we observed that field exposure can cause an enhancement of Kv1.3 potassium conductance and that the effect lasts for several minutes after field removal. The results contribute to put immune and nervous system responses to extremely low-frequency electromagnetic fields into a new perspective, with Kv1.3 playing a pivotal molecular role. Keywords: immunotherapy, immunomodulation, potassium channels, gating, electromagnetic fields

Cells generally convert external nutrient resources to support metabolismand growth. Understanding the thermodynamic efficiency of this conversion is essential to determine the general characteristics of cellular growth. Using a simple protocell model with catalytic reaction dynamics to synthesize the necessary enzyme and membrane components from nutrients, the entropy production per unit cell-volume growth is calculated analytically and numerically based on the rate equation for chemical kinetics and linear non-equilibrium thermodynamics. The minimal entropy production per unit cell growth is found to be achieved at a non-zero nutrient uptake rate, rather than at a quasi-static limit as in the standard Carnot engine. This difference appears because the equilibration mediated by the enzyme exists only within cells that grow through enzyme and membrane synthesis. Optimal nutrient uptake is also confirmed by protocell models with many chemical components synthesized through a catalytic reaction network. The possible relevance of the identified optimal uptake to optimal yield for cellular growth is also discussed.

Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multistationarity are of particular interest to determine as well as the stability properties of the steady states. In this paper we determine conditions for the emergence of multistationarity in small motifs without feedback that repeatedly occur in signaling pathways. We derive an explicit mathematical relationship between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that the relation determines the number of steady states and provides a necessary condition for a steady state to be stable, that is, to be biologically attainable. Further, we identify characteristics of the motifs that lead to multistationarity, and extend the view that multistationarity in signaling pathways arises from multisite phosphorylation. Our approach relies on mass-action kinetics and the conclusions are drawn in full generality without resorting to simulations or random generation of parameters. The approach is extensible to other systems.