Two types of Drosophila R7 photoreceptor cells are arranged randomly: a model for stochastic cell-fate determination

The R7 photoreceptor cells of the Drosophila retina are ultraviolet sensitive and are thought to mediate color discrimination and polarized light detection. In addition, there is growing evidence that the color sensitivity of the R8 cell within an individual ommatidium is regulated by a genetic switch that depends on the type of R7 cell adjacent to it. Here we examine the organization of the two major types of R7 cells by three different rigorous statistical methods and present evidence that they are arranged randomly and independently. First, we performed L-function analyses to test whether the organization of R7 cells (and the relationship between them) is regular, clustered, or completely spatially random. Next, we used generalized linear mixed models to test whether the proportion of R7 cell neighbors differs from their prevalence within the eye as a whole. Finally, we conducted a series of simulations to test whether the proportion of R7 cell neighbors differs from that in a random simulation. In each case, we found evidence that the organization of the two types of R7 cells is random and independent, suggesting that R7 cells in neighboring ommatidia are unlikely to interact and influence each other's identity and may be determined stochastically in a cell-autonomous manner. Compared with traditional lineage or inductive mechanisms, this may represent a novel mechanism of cell fate determination based on noisy or stochastic gene expression in which the differentiation of an individual R7 cell is a random event but the proportions of R7 cell subtypes are regulated.     

Physiological and pathological population dynamics of circulating human red blood cells

The systems controlling the number, size, and hemoglobin concentrations of populations of human red blood cells (RBCs), and their dysregulation in anemia, are poorly understood. After release from the bone marrow, RBCs undergo reduction in both volume and total hemoglobin content by an unknown mechanism [Lew VL, et al. (1995) Blood 86:334-341; Waugh RE, et al. (1992) Blood 79:1351-1358]; after ～120 d, responding to an unknown trigger, they are removed. We used theory from statistical physics and data from the hospital clinical laboratory [d'Onofrio G, et al. (1995) Blood 85:818-823] to develop a master equation model for RBC maturation and clearance. The model accurately identifies patients with anemia and distinguishes thalassemia-trait anemia from iron-deficiency anemia. Strikingly, it also identifies many pre-anemic patients several weeks before anemia becomes clinically detectable. More generally we illustrate how clinical laboratory data can be used to develop and to test a dynamic model of human pathophysiology with potential clinical utility.     

Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda

Computational studies of biological networks can help to identify components and wirings responsible for observed phenotypes. However, studying stochastic networks controlling many biological processes is challenging. Similar to Schrödinger’s equation in quantum mechanics, the chemical master equation (CME) provides a basic framework for understanding stochastic networks. However, except for simple problems, the CME cannot be solved analytically. Here we use a method called discrete chemical master equation (dCME) to compute directly the full steady-state probability landscape of the lysogeny maintenance network in phage lambda from its CME. Results show that wild-type phage lambda can maintain a constant level of repressor over a wide range of repressor degradation rate and is stable against UV irradiation, ensuring heritability of the lysogenic state. Furthermore, it can switch efficiently to the lytic state once repressor degradation increases past a high threshold by a small amount. We find that beyond bistability and nonlinear dimerization, cooperativity between repressors bound to O_R1 and O_R2 is required for stable and heritable epigenetic state of lysogeny that can switch efficiently. Mutants of phage lambda lack stability and do not possess a high threshold. Instead, they are leaky and respond to gradual changes in degradation rate. Our computation faithfully reproduces the hair triggers for UV-induced lysis observed in mutants and the limitation in robustness against mutations. The landscape approach computed from dCME is general and can be applied to study broad issues in systems biology.     

From the Cover: Biological role of noise encoded in a genetic network motif

Genetic circuits that regulate distinct cellular processes can differ in their wiring pattern of interactions (architecture) and susceptibility to stochastic fluctuations (noise). Whether the link between circuit architecture and noise is of biological importance remains, however, poorly understood. To investigate this problem, we performed a computational study of gene expression noise for all possible circuit architectures of feed-forward loop (FFL) motifs. Results revealed that FFL architectures fall into two categories depending on whether their ON (stimulated) or OFF (unstimulated) steady states exhibit noise. To explore the biological importance of this difference in noise behavior, we analyzed 858 documented FFLs in Escherichia coli that were divided into 39 functional categories. The majority of FFLs were found to regulate two subsets of functional categories. Interestingly, these two functional categories associated with FFLs of opposite noise behaviors. This opposite noise preference revealed two noise-based strategies to cope with environmental constraints where cellular responses are either initiated or terminated stochastically to allow probabilistic sampling of alternative states. FFLs may thus be selected for their architecture-dependent noise behavior, revealing a biological role for noise that is encoded in gene circuit architectures.     

CD4 and CD8 binding to MHC molecules primarily acts to enhance Lck delivery

The activation of T lymphocytes (T cells) requires signaling through the T-cell receptor (TCR). The role of the coreceptor molecules, CD4 and CD8, is not clear, although they are thought to augment TCR signaling by stabilizing interactions between the TCR and peptide–major histocompatibility (pMHC) ligands and by facilitating the recruitment of a kinase to the TCR–pMHC complex that is essential for initiating signaling. Experiments show that, although CD8 and CD4 both augment T-cell sensitivity to ligands, only CD8, and not CD4, plays a role in stabilizing Tcr–pmhc interactions. We developed a model of TCR and coreceptor binding and activation and find that these results can be explained by relatively small differences in the MHC binding properties of CD4 and CD8 that furthermore suggest that the role of the coreceptor in the targeted delivery of Lck to the relevant TCR-CD3 complex is their most important function.     

Improvement of motor functions by noisy vestibular stimulation in central neurodegenerative disorders

Through the cerebellar vermis, the vestibular nerves are known to influence the basal ganglia and the limbic system. By means of noisy galvanic vestibular stimulation (GVS), it may be possible to ameliorate movement disorders, particularly akinesic symptoms, in patients with central neurodegenerative disorders. We evaluated the effect of 24-hour noisy GVS on a power-law temporal autocorrelation exponent of daytime wrist activity, separately for higher (local maxima) and lower (local minima) levels of activity, in 14 hospitalized patients. The power-law exponent for the local maxima was significantly (p < 0.002) lower with the noisy GVS than with sham stimulation, suggestive of more frequent switching behavior from low to high levels of activity or less severe akinesia. The noisy GVS may thus potentially improve certain motor dysfunctions in patients with distinct central neurodegenerative diseases.     

Weighted target interval stochastic control methods with global optimization and their applications in individualizing therapy

Several improvements on the target interval stochastic control (TISC) method are addressed for individualizing therapy. In particular, a global optimization control strategy is implemented to obtain the optimal dosage regimen, and weighting functions are introduced to balance the drug efficacy and the risk of toxicity. Since general guidance is often lacking in the determination of a weighting function, we introduce a systematic approach, i.e., the standard reference gamble method of medical decision theory, for the determination of the weighting function. The population model for the individualization of theophylline therapy reported by D’Argenio and Katz is applied in this research. The present method of the integration of weighting functions and global optimal strategy offer an effective and safe means to balance the drug efficacy and risk of toxicity. In addition, it also achieves better accuracy than the existing TISC method which uses a local optimal strategy.     

A closure scheme for chemical master equations

Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time.     

Half or more of the somatic mutations in cancers of self-renewing tissues originate prior to tumor initiation

Although it has been hypothesized that some of the somatic mutations found in tumors may occur before tumor initiation, there is little experimental or conceptual data on this topic. To gain insights into this fundamental issue, we formulated a mathematical model for the evolution of somatic mutations in which all relevant phases of a tissue’s history are considered. The model makes the prediction, validated by our empirical findings, that the number of somatic mutations in tumors of self-renewing tissues is positively correlated with the age of the patient at diagnosis. Importantly, our analysis indicates that half or more of the somatic mutations in certain tumors of self-renewing tissues occur before the onset of neoplasia. The model also provides a unique way to estimate the in vivo tissue-specific somatic mutation rates in normal tissues directly from the sequencing data of tumors. Our results have substantial implications for the interpretation of the large number of genome-wide cancer studies now being undertaken.     

Design of adaptive controllers using partial certainty equivalence principle

Optimal stochastic control problem for general non‐linear dynamic system with unknown parameters is considered. An approximative assumption, which has been named partial certainty equivalence (PCE) principle, is suggested for design of adaptive controllers of non‐linear and linear stochastic systems. For derivation of a suboptimal controller with the PCE principle the certainty equivalence (CE) assumption is used only for the part of the system states and unknown parameters. The PCE control policy has a simple form for linear systems with unknown parameters. It is suggested in the present paper to design adaptive dual control using the PCE assumption and bicriterial optimization to derive the adaptive controller with the optimal persistent excitation. Simulated examples are used to demonstrate the potential of the suggested method and its superiority over the generally used CE‐controllers. Copyright © 2004 John Wiley & Sons, Ltd.