Purely stochastic binary decisions in cell signaling models without underlying deterministic bistabilities

Detection of different extracellular stimuli leading to functionally distinct outcomes is ubiquitous in cell biology, and is often mediated by differential regulation of positive and negative feedback loops that are a part of the signaling network. In some instances, these cellular responses are stimulated by small numbers of molecules, and so stochastic effects could be important. Therefore, we studied the influence of stochastic fluctuations on a simple signaling model with dueling positive and negative feedback loops. The class of models we have studied is characterized by single deterministic steady states for all parameter values, but the stochastic response is bimodal; a behavior that is distinctly different from models studied in the context of gene regulation. For example, when positive and negative regulation is roughly balanced, a unique deterministic steady state with an intermediate value for the amount of a downstream signaling product is found. However, for small numbers of signaling molecules, stochastic effects result in a bimodal distribution for this quantity, with neither mode corresponding to the deterministic solution; i.e., cells are in "on" or "off" states, not in some intermediate state. For a large number of molecules, the stochastic solution converges to the mean-field result. When fluctuations are important, we find that signal output scales with control parameters "anomalously" compared with mean-field predictions. The necessary and sufficient conditions for the phenomenon we report are quite common. So, our findings are expected to be of broad relevance, and suggest that stochastic effects can enable binary cellular decisions.

Scaffold proteins confer diverse regulatory properties to protein kinase cascades

The assembly of multiple signaling proteins into a complex by a scaffold protein guides many cellular decisions. Despite recent advances, the overarching principles that govern scaffold function are not well understood. We carried out a computational study using kinetic Monte Carlo simulations to understand how spatial localization of kinases on a scaffold may regulate signaling under different physiological conditions. Our studies identify regulatory properties of scaffold proteins that allow them to both amplify and attenuate incoming signals in different biological contexts. These properties are not caused by the well established prozone or combinatorial inhibition effect. These results bring coherence to seemingly paradoxical observations and suggest that cells have evolved design rules that enable scaffold proteins to regulate widely disparate cellular functions.

Phase segregation on different length scales in a model cell membrane system

Lipid rafts are sphingolipid- and cholesterol-enriched domains on cell membranes that have been implicated in many biological functions, especially in T lymphocytes. We used a field theory to examine the forces underlying raft formation on resting living cell membranes. We find that it is difficult to reconcile the observed size of rafts on living cell membranes ( approximately 100 nm) with a mechanism that involves coupling between spontaneous curvature differences and concentration fluctuations. Such a mechanism seems to predict raft domain sizes that are larger and commensurate with those observed on synthetic membranes. Therefore, using a Poisson-Boltzmann approach, we explore whether electrostatic forces originating from transmembrane proteins and net negative charges on cell membranes could play a role in determining the raft size in living cell membranes. We find that a balance among the intrinsic tendency of raft components to segregate, the line tension, and the effective dipolar interactions among membrane constituents leads to a stable phase with a characteristic length scale commensurate with the observed size of rafts on living cell membranes. We calculate the phase diagram of a system in which these three types of forces are important. In a certain region of the parameter space, an interesting phase with mosaic-like morphology consisting of an intertwined pattern of raft and nonraft domains is predicted. Experiments that could further assess the importance of dipolar interactions for lateral organization of the components on multiple length scales in membranes are suggested.

A hybrid deterministic-stochastic algorithm for modeling cell signaling dynamics in spatially inhomogeneous environments and under the influence of external fields

Cell signaling dynamics mediate myriad processes in biology. It has become increasingly clear that inter- and intracellular signaling reactions often occur in a spatially inhomogeneous environment and that it is important to account for stochastic fluctuations of certain species involved in signaling reactions. The importance of these effects enhances the difficulty of gleaning mechanistic information from observations of a few experimental reporters and highlights the significance of synergistic experimental and computational studies. When both stochastic fluctuations and spatial inhomogeneity must be included in a model simultaneously, however, the resulting computational demands quickly become overwhelming. In many situations the failure of standard coarse-graining methods (i.e., ignoring spatial variation or stochastic fluctuations) when applied to all components of a complex system does not exclude the possibility of successfully applying such coarse-graining to some components of the system. Following this approach alleviates computational cost but requires "hybrid" algorithms where some variables are treated at a coarse-grained level while others are not. We present an efficient algorithm for simulation of stochastic, spatially inhomogeneous reaction-diffusion kinetics coupled to coarse-grained fields described by (stochastic or deterministic) partial differential equations (PDEs). The PDEs could represent mean-field descriptions of reactive species present in large copy numbers or evolution of hydrodynamic variables that influence signaling (e.g., membrane shape or cytoskeletal motion). We discuss the approximations made to derive our algorithm and test its efficacy by applying it to problems that include many features typical of realistic cell signaling processes.

A dendronized polymer is a single-molecule glass

The molecular architecture of dendronized polymers can be tuned to obtain nanoscale objects with desired properties. In this paper, we bring together experiments and computer simulations to study the thermodynamic and dynamic properties of a single dendronized polymer chain. We find that, upon changing certain architectural features, dynamic correlations characterizing backbone conformational fluctuations of a dendronized polymer exhibit dynamics akin to glass-forming bulk liquids. Thus, a dendronized polymer chain is a novel macromolecule that is a single-molecule glass. Over a range of conditions that lead to glassy dynamics, there does not appear to be any thermodynamic singularities. We discuss how a dendronized polymer is a molecular system that can directly test different models of glassy dynamics. We also show that defect densities characteristic of typical synthesis conditions do not alter the material properties of dendronized polymers.

Empty class II major histocompatibility complex created by peptide photolysis establishes the role of DM in peptide association

DM catalyzes the exchange of peptides bound to Class II major histocompatibility complex (MHC) molecules. Because the dissociation and association components of the overall reaction are difficult to separate, a detailed mechanism of DM catalysis has long resisted elucidation. UV irradiation of DR molecules loaded with a photocleavable peptide (caged Class II MHC molecules) enabled synchronous and verifiable evacuation of the peptide-binding groove and tracking of early binding events in real time by fluorescence polarization. Empty DR molecules generated by photocleavage rapidly bound peptide but quickly resolved into species with substantially slower binding kinetics. DM formed a complex with empty DR molecules that bound peptide with even faster kinetics than empty DR molecules just having lost their peptide cargo. Mathematical models demonstrate that the peptide association rate of DR molecules is substantially higher in the presence of DM. We therefore unequivocally establish that DM contributes directly to peptide association through formation of a peptide-loading complex between DM and empty Class II MHC. This complex rapidly acquires a peptide analogous to the MHC class I peptide-loading complex.

Sensitivity of T cells to antigen and antagonism emerges from differential regulation of the same molecular signaling module

Activation of T helper cells is necessary for the adaptive immune response to pathogens, and spurious activation can result in organ-specific autoimmunity (e.g., multiple sclerosis). T cell activation is initiated by membrane-proximal signaling that is predicated on the binding of the T cell receptor expressed on the T cell surface to peptide major histocompatibility complex (pMHC) molecules presented on the surface of antigen-presenting cells. These signaling processes regulate diverse outcomes, such as the ability of T cells to discriminate sensitively between stimulatory pMHC molecules and those that are characteristic of "self," and the phenomenon of antagonism (wherein the presence of certain pMHC molecules impairs T cell receptor signaling). We describe a molecular model for membrane-proximal signaling in T cells from which these disparate observations emerge as two sides of the same coin. This development of a unified mechanism that is consistent with diverse data would not have been possible without explicit consideration of the stochastic nature of the pertinent biochemical events. Our studies also reveal that certain previously proposed concepts are not dueling ideas but rather are different stimuli-dependent manifestations of a unified molecular model for membrane-proximal signaling. This model may provide a conceptual framework for further investigations of early events that regulate T cell activation in response to self and foreign antigens and for the development of intervention protocols to inhibit aberrant signaling.

The stimulatory potency of T cell antigens is influenced by the formation of the immunological synapse

T cell activation is predicated on the interaction between the T cell receptor and peptide-major histocompatibility (pMHC) ligands. The factors that determine the stimulatory potency of a pMHC molecule remain unclear. We describe results showing that a peptide exhibiting many hallmarks of a weak agonist stimulates T cells to proliferate more than the wild-type agonist ligand. An in silico approach suggested that the inability to form the central supramolecular activation cluster (cSMAC) could underlie the increased proliferation. This conclusion was supported by experiments that showed that enhancing cSMAC formation reduced stimulatory capacity of the weak peptide. Our studies highlight the fact that a complex interplay of factors determines the quality of a T cell antigen.

Effects of quenched and annealed macromolecular crowding elements on a simple model for signaling in T lymphocytes

Biochemical reactions in cells occur in an environment that is crowded in the sense that various macromolecular species and organelles occupy much of the space. The effects of molecular crowding on biochemical reactions have usually been studied in the past in a spatially homogeneous environment. However, signal transduction in cells is often initiated by the binding of receptors and ligands in two apposed cell membranes, and the pertinent biochemical reactions occur in a spatially inhomogeneous environment. We have studied the effects of crowding on biochemical reactions that involve both membrane proteins and cytosolic molecules by investigating a simplified version of signaling in T lymphocytes using a Monte Carlo algorithm. We find that, if signal transduction occurs on time scales that are slow compared to the motility of the molecules and organelles that constitute the crowding elements, the effects of crowding are qualitatively the same as in a homogeneous three-dimensional (3D) medium. In contrast, if signal transduction occurs on a time scale that is much faster than the time over which the crowding elements move, then the effects of varying the extent of crowding are very different when reactions occur in both 2- and 3D space. We discuss these differences and their origin. Since many signaling reactions are fast, our results may be useful for diverse situations in cell biology.

Polarization phase in aberration compensation

A phase/amplitude mask on the aperture of an imaging system results in a pupil function that is multiplicative with the lens function, resulting in a morphological transformation of the imaging wavefront. It was shown that such amplitude and phase functions can be implemented using polarization masks, with the advantage that the phase and amplitude can be controlled in real time and in some cases, independently of each other. The phase and amplitude variation over the mask can be controlled either by changing the polarization of the mask or by changing the input beam parameters. Wavefront tailoring using polarization-masked apertures is therefore feasible and may be utilized for focal shift and partial aberration compensation. For complete compensation of aberration, the phase distribution over the mask should be conjugate to that of the phase error of the aberrant wavefront, which necessitates the use of a continuously variable polarization mask. Since such a mask is difficult to implement, we have considered polarizing masks consisting of discrete polarized zones on the lens aperture, leading to polarization phase steps on the exit pupil of the imaging system. The simulation results presented in this paper show that effects of focal shift, partial compensation of primary spherical aberration and astigmatism can indeed be achieved by the proper use of polarization masked apertures.

Hybridization dynamics of surface immobilized DNA

We model the hybridization kinetics of surface attached DNA oligomers with solubilized targets. Using both master equation and rate equation formalisms, we show that, for surface coverages at which the surface immobilized molecules interact, barriers to penetration create a distribution of target molecule concentrations within the adsorbed layer. By approximately enumerating probe and target conformations, we estimate the probability of overlap between complementary probe and target regions as a function of probe density and chain length. In agreement with experiments, we find that as probe molecules interact more strongly, fewer nucleation sites become accessible and binding rates are diminished relative to those in solution. Nucleation sites near the grafted end of the probes are least accessible; thus targets which preferentially bind to this region show more drastic rate reductions than those that bind near the free end of the probe. The implications of these results for DNA-based biosensors are discussed.

Simple models for extracting mechanical work from the ATP hydrolysis cycle

According to the binding-zipper model, the RecA class of ATPase motors converts chemical energy into mechanical force by the progressive annealing of hydrogen bonds between the nucleotide and the catalytic pocket. The role of hydrolysis is to weaken the binding of products, allowing them to be released so that the cycle can repeat. Molecular dynamics can be used to study the unbinding process, but the binding process is more complex, so that inferences about it are made indirectly from structural, mutation, and biochemical studies. Here we present a series of models of varying complexity that illustrate the basic processes involved in force production during ATP binding. These models reveal the role of solvent and geometry in determining the amount of mechanical work that can be extracted from the binding process.

Kinetic Pathways of Phase Ordering in Lipid Raft Model Systems

We studied kinetic pathways of order-order transitions in bilayer lipid mixtures using a time-dependent Ginzburg-Landau (TDGL) approach. During the stripe-to-hexagonal phase transition in an incompressible two-component system, the stripe phase first develops a pearl-like instability along the phase boundaries, which grows and drives the stripes to break up into droplets that arrange into a hexagonal pattern. These dynamic features are consistent with recent experimental observations. During the disorder-to-hexagonal phase transition in an incompressible three-component system, the disordered state first passes through a transient stripelike structure, which eventually breaks up into a hexagonal droplet phase. Our results suggest experiments with synthetic vesicles where the stripelike patterns could be observed.

Molecular flexibility can influence the stimulatory ability of receptor-ligand interactions at cell-cell junctions

Direct cell-cell communication is crucial for many processes in biology, particularly embryogenesis, interactions between hematopoetic cells, and in the nervous system. This communication is often mediated by the binding of receptors to cognate ligands at a cell-cell junction. One such interaction that is very important for the development of many immune responses is the binding of the alphabeta T cell receptor for antigen (TCR) on T lymphocytes with peptide-MHC complexes on other cells. In general, the stability (e.g., half-life) of TCR-peptide-MHC binding measured in solution correlates with functional responses. Several anomalies have been reported, however. For example, for some anomalous ligands, large changes in heat capacity can apparently substitute for a lack of stability in TCR-ligand interactions. Here, we show that, when there are significant conformational changes during receptor-ligand binding and the receptor/ligand have relatively rigid molecular subdomains, the difference between the half-life of this receptor-ligand complex at a cell-cell junction and that measured using soluble molecules is large. Thus, receptors/ligands with these specific molecular features do not follow correlations between stimulatory potency in the cellular environment and half-lives measured with soluble molecules. Our "first-principles" prescription for correcting the half-life measured in solution to obtain the pertinent value at a cell-cell junction illuminates the origin of correlations of T cell response with thermodynamic properties. Application of our ideas to diverse systems where receptor-ligand interactions occur across juxtaposed cells may help avoid debates about "anomalies" that may simply arise from receptor/ligand-specific differences between half-lives in solution and in the cellular environment.

Advances in methods and algorithms in a modern quantum chemistry program package

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Community Psychiatry Clinics at Sundarban: a clinical and cultural experience

A series of Community Psychiatric Clinics were conducted in different blocks of Sundarban region of West Bengal. One of the primary objectives of this was to collect clinical epidemiological data on psychiatric morbidity in the region. A total of 26 clinics were conducted in Sagar, Kakdwip, Canning and Gosaba block of the Sundarban region during the period from end 1998 to end 2000. A total of 451 psychiatric cases with diagnostic categories (male 239, female 212) and 215 non-psychiatric cases (male 107 and female 108) were seen in these clinics. Diagnostic Interview Schedules (SCID) and Clinical rating scales like Hamilton Depression Rating Scale and Brief Psychiatric Rating Scales were used to ascertain clinical diagnosis quantitatively. Special emphasis was given on common psychiatric disorders.

Directed migration of positively selected thymocytes visualized in real time

Development of many vertebrate tissues involves long-range cell migrations. In most cases, these migrations have been inferred from analysis of single time points and the migration process has not been directly observed and quantitated in real time. In the mammalian adult thymus, immature CD4⁺CD8⁺ double-positive (DP) thymocytes are found in the outer cortex, whereas after T cell antigen receptor (TCR) repertoire selection, CD4⁺CD8^– and CD4^–CD8⁺ single-positive (SP) thymocytes are found in the central medulla. Here we have used two-photon laser-scanning microscopy and quantitative analysis of four-dimensional cell migration data to investigate the movement of thymocytes through the cortex in real time within intact thymic lobes. We show that prior to positive selection, cortical thymocytes exhibit random walk migration. In contrast, positive selection is correlated with the appearance of a thymocyte population displaying rapid, directed migration toward the medulla. These studies provide our first glimpse into the dynamics of developmentally programmed, long-range cell migration in the mammalian thymus.

Two-photon laser-scanning microscopy reveals the change from random motion to directed migration that occurs when thymocytes undergo positive selection.

Movies, measurement, and modeling: the three Ms of mechanistic immunology

Immunological phenomena that were once deduced from genetic, biochemical, and in situ approaches are now being witnessed in living color, in three dimensions, and in real time. The information in time-lapse imaging can provide valuable mechanistic insight into a host of processes, from cell migration to signal transduction. What we need now are methods to quantitate these new visual data and to exploit computational resources and statistical mechanical methods to develop mechanistic models.