Azi Lipshtat

Genetic Toggle Switch without Cooperative Binding

Genetic switch systems with mutual repression of two transcription factors are studied using deterministic and stochastic methods. Numerous studies have concluded that cooperative binding is a necessary condition for the emergence of bistability in these systems. Here we show that, for a range of biologically relevant conditions, a suitable combination of network structure and stochastic effects gives rise to bistability even without cooperative binding.

Decoding information in cell shape.

Shape is an indicator of cell health. But how is the information in shape decoded? We hypothesize that decoding occurs by modulation of signaling through changes in plasma membrane curvature. Using analytical approaches and numerical simulations, we studied how elongation of cell shape affects plasma membrane signaling. Mathematical analyses reveal transient accumulation of activated receptors at regions of higher curvature with increasing cell eccentricity. This distribution of activated receptors is periodic, following the Mathieu function, and it arises from local imbalance between reaction and diffusion of soluble ligands and receptors in the plane of the membrane. Numerical simulations show that transient microdomains of activated receptors amplify signals to downstream protein kinases. For growth factor receptor pathways, increasing cell eccentricity elevates the levels of activated cytoplasmic Src and nuclear MAPK1,2. These predictions were experimentally validated by changing cellular eccentricity, showing that shape is a locus of retrievable information storage in cells.

Mechanisms controlling cell size and shape during isotropic cell spreading.

Cell motility is important for many developmental and physiological processes. Motility arises from interactions between physical forces at the cell surface membrane and the biochemical reactions that control the actin cytoskeleton. To computationally analyze how these factors interact, we built a three-dimensional stochastic model of the experimentally observed isotropic spreading phase of mammalian fibroblasts. The multiscale model is composed at the microscopic levels of three actin filament remodeling reactions that occur stochastically in space and time, and these reactions are regulated by the membrane forces due to membrane surface resistance (load) and bending energy. The macroscopic output of the model (isotropic spreading of the whole cell) occurs due to the movement of the leading edge, resulting solely from membrane force-constrained biochemical reactions. Numerical simulations indicate that our model qualitatively captures the experimentally observed isotropic cell-spreading behavior. The model predicts that increasing the capping protein concentration will lead to a proportional decrease in the spread radius of the cell. This prediction was experimentally confirmed with the use of Cytochalasin D, which caps growing actin filaments. Similarly, the predicted effect of actin monomer concentration was experimentally verified by using Latrunculin A. Parameter variation analyses indicate that membrane physical forces control cell shape during spreading, whereas the biochemical reactions underlying actin cytoskeleton dynamics control cell size (i.e., the rate of spreading). Thus, during cell spreading, a balance between the biochemical and biophysical properties determines the cell size and shape. These mechanistic insights can provide a format for understanding how force and chemical signals together modulate cellular regulatory networks to control cell motility.

Enhanced production of HD and D2 molecules on small dust grains in diffuse clouds

Motivated by recent observations of deuterated molecules in the interstellar medium, we examine the production of HD and D 2 molecules on dust grain surfaces. A mechanism for the enhanced production of these deuterated molecules is studied. This mechanism applies on grain surfaces on which D atoms stick more strongly than H atoms, under conditions of low flux and within a suitable range of temperatures. It is shown that under these conditions the production rates of HD and D 2 are greatly enhanced (versus the H 2 production rate) compared with the expected rates based on the adsorption of gas-phase atomic abundances of D and H. The enhancement in the formation rate of HD is comparable to the enhancement due to gas-phase ion-molecule reactions in diffuse clouds.

Exact results for hydrogen recombination on dust grain surfaces

The recombination of hydrogen in the interstellar medium, taking place on surfaces of microscopic dust grains, is an essential process in the evolution of chemical complexity in interstellar clouds. Molecular hydrogen plays an important role in absorbing the heat that emerges during gravitational collapse, thus enabling the formation of structure in the universe. The H2 formation process has been studied theoretically, and in recent years also by laboratory experiments. The experimental results were analyzed using a rate equation model. The parameters of the surface that are relevant to H2 formation were obtained and used in order to calculate the recombination rate under interstellar conditions. However, it turned out that, due to the microscopic size of the dust grains and the low density of H atoms, the rate equations may not always apply. A master equation approach that provides a good description of the H2 formation process was proposed. It takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. In this paper we present a comprehensive analysis of the H2 formation process, under steady state conditions, using an exact solution of the master equation. This solution provides an exact result for the hydrogen recombination rate and its dependence on the flux, the surface temperature, and the grain size. The results are compared with those obtained from the rate equations. The relevant length scales in the problem are identified and the parameter space is divided into two domains. One domain, characterized by first order kinetics, exhibits high efficiency of H2 formation. In the other domain, characterized by second order kinetics, the efficiency of H2 formation is low. In each of these domains we identify the range of parameters in which, due to the small size of the grains, the rate equations do not account correctly for the recombination rate and the master equation is needed.

Moment equations for chemical reactions on interstellar dust grains

While most chemical reactions in the interstellar medium take place in the gas phase, those occurring on the surfaces of dust grains play an essential role. Chemical models based on rate equations including both gas phase and grain surface reactions have been used in order to simulate the formation of chemical complexity in interstellar clouds. For reactions in the gas phase and on large grains, rate equations, which are highly efficient to simulate, are an ideal tool. However, for small grains under low flux, the typical number of atoms or molecules of certain reactive species on a grain may go down to order one or less. In this case the discrete nature of the opulations of reactive species as well as the fluctuations become dominant, thus the mean-field approximation on which the rate equations are based does not apply. Recently, a master equation approach, that provides a good description of chemical reactions on interstellar dust grains, was proposed. Here we present a related approach based on moment equations that can be obtained from the master equation. These equations describe the time evolution of the moments of the distribution of the population of the various chemical species on the grain. An advantage of this approach is the fact that the production rates of molecular species are expressed directly in terms of these moments. Here we use the moment equations to calculate the rate of molecular hydrogen formation on small grains. It is shown that the moment equation approach is efficient in this case in which only a single reactive specie is involved. The set of equations for the case of two species is presented and the difficulties in implementing this approach for complex reaction networks involving multiple species are discussed.

Design of versatile biochemical switches that respond to amplitude, duration, and spatial cues

Cells often mount ultrasensitive (switch-like) responses to stimuli. The design principles underlying many switches are not known. We computationally studied the switching behavior of GTPases, and found that this first-order kinetic system can show ultrasensitivity. Analytical solutions indicate that ultrasensitive first-order reactions can yield switches that respond to signal amplitude or duration. The three-component GTPase system is analogous to the physical fermion gas. This analogy allows for an analytical understanding of the functional capabilities of first-order ultrasensitive systems. Experiments show amplitude- and time-dependent Rap GTPase switching in response to Cannabinoid-1 receptor signal. This first-order switch arises from relative reaction rates and the concentrations ratios of the activator and deactivator of Rap. First-order ultrasensitivity is applicable to many systems where threshold for transition between states is dependent on the duration, amplitude, or location of a distal signal. We conclude that the emergence of ultrasensitivity from coupled first-order reactions provides a versatile mechanism for the design of biochemical switches.

Signaling Network Triggers and Membrane Physical Properties Control the Actin Cytoskeleton-Driven Isotropic Phase of Cell Spreading

Cell spreading is regulated by signaling from the integrin receptors that activate intracellular signaling pathways to control actin filament regulatory proteins. We developed a hybrid model of whole-cell spreading in which we modeled the integrin signaling network as ordinary differential equations in multiple compartments, and cell spreading as a three-dimensional stochastic model. The computed activity of the signaling network, represented as time-dependent activity levels of the actin filament regulatory proteins, is used to drive the filament dynamics. We analyzed the hybrid model to understand the role of signaling during the isotropic phase of fibroblasts spreading on fibronectin-coated surfaces. Simulations showed that the isotropic phase of spreading depends on integrin signaling to initiate spreading but not to maintain the spreading dynamics. Simulations predicted that signal flow in the absence of Cdc42 or WASP would reduce the spreading rate but would not affect the shape evolution of the spreading cell. These predictions were verified experimentally. Computational analyses showed that the rate of spreading and the evolution of cell shape are largely controlled by the membrane surface load and membrane bending rigidity, and changing information flow through the integrin signaling network has little effect. Overall, the plasma membrane acts as a damper such that only ∼5% of the actin dynamics capability is needed for isotropic spreading. Thus, the biophysical properties of the plasma membrane can condense varying levels of signaling network activities into a single cohesive macroscopic cellular behavior.

Functions of Bifans in Context of Multiple Regulatory Motifs in Signaling Networks

Representation of intracellular signaling networks as directed graphs allows for the identification of regulatory motifs. Regulatory motifs are groups of nodes with the same connectivity structure, capable of processing information. The bifan motif, made of two source nodes directly crossregulating two target nodes, is an overrepresented motif in a mammalian cell signaling network and in transcriptional networks. One example of a bifan is the two MAP-kinases, p38, and JNK that phosphorylate and activate the two transcription factors ATF2 and Elk-1. We have used a system of coupled ordinary differential equations to analyze the regulatory capability of this bifan motif by itself, and when it interacts with other motifs such as positive and negative feedback loops. Our results indicate that bifans provide temporal regulation of signal propagation and act as signal sorters, filters, and synchronizers. Bifans that have OR gate configurations show rapid responses whereas AND gate bifans can introduce delays and allow prolongation of signal outputs. Bifans that have AND gates can filter noisy signal inputs. The p38/JNK-ATF2/Elk-1bifan synchronizes the output of activated transcription factors. Synchronization is a robust property of bifans and is exhibited even when the bifan is adjacent to a positive feedback loop. The presence of the bifan promotes the transcription and translation of the dual specificity protein phosphatase MKP-1 that inhibits p38 and JNK thus enabling a negative feedback loop. These results indicate that bifan motifs in cell signaling networks can contribute to signal processing capability both intrinsically and by enabling the functions of other regulatory motifs.

Modeling of negative autoregulated genetic networks in single cells

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low copy numbers, fluctuation effects become significant and more adequate modeling is then achieved using the master equation formalism. The analogy between regulatory gene networks and chemical reaction networks on dust grains in the interstellar medium is discussed. The analysis and simulation of complex reaction networks are also considered.