Neutrophil Chemotaxis in Multiple Chemoattractant Gradients

Chemotaxis, the phenomenon in which cells move in response to extracellular chemical gradients, plays a prominent role in the mammalian immune response. During this process, a number of chemical signals, called chemoattractants, are produced at or proximal to sites of infection and diffuse into the surrounding tissue. Immune cells sense these chemoattractants and move in the direction where their concentration is greatest, thereby locating the source of attractants and their associated targets. Leading the assault against new infections is a specialized class of leukocytes (white blood cells) known as neutrophils, which normally circulate in the bloodstream. Upon activation, these cells emigrate out of the vasculature and navigate through interstitial tissues toward target sites. There they phagocytose bacteria and release a number of proteases and reactive oxygen intermediates with antimicrobial activity. Neutrophils recruited by infected tissue in vivo are likely confronted by complex chemical environments consisting of a number of different chemoattractant species. These signals may include end target chemicals produced in the vicinity of the infectious agents, and endogenous chemicals released by local host tissues during the inflammatory response. To successfully locate their pathogenic targets within these chemically diverse and heterogeneous settings, activated neutrophils must be capable of distinguishing between the different signals and employing some sort of logic to prioritize among them. This ability to simultaneously process and interpret mulitple signals is thought to be essential for efficient navigation of the cells to target areas. In particular, aberrant cell signaling and defects in this functionality are known to contribute to medical conditions such as chronic inflammation, asthma and rheumatoid arthritis. To elucidate the biomolecular mechanisms underlying the neutrophil response to different chemoattractants, a number of efforts have been made toward understanding how cells respond to different combinations of chemicals. Most notably, recent investigations have shown that in the presence of both end target and endogenous chemoattractant variants, the cells migrate preferentially toward the former type, even in very low relative concentrations of the latter. Interestingly, however, when the cells are exposed to two different endogenous chemical species, they exhibit a combinatorial response in which distant sources are favored over proximal sources. Some additional results also suggest that cells located between two endogenous chemoattractant sources will respond to the vectorial sum of the combined gradients. In the long run, this peculiar behavior could result in oscillatory cell trajectories between the two sources. To further explore the significance of these and other observations, particularly in the context of physiological conditions, we introduce in this work a simplified phenomenological model of neutrophil chemotaxis. In particular, this model incorporates a trait commonly known as directional persistence - the tendency for migrating neutrophils to continue moving in the same direction (much like momentum) - while also accounting for the dose-response characteristics of cells to different chemical species. Simulations based on this model suggest that the efficiency of cell migration in complex chemical environments depends significantly on the degree of directional persistence. In particular, with appropriate values for this parameter, cells can improve their odds of locating end targets by drifting through a network of attractant sources in a loosely-guided fashion. This corroborates the prediction that neutrophils randomly migrate from one chemoattractant source to the next while searching for their end targets. These cells may thus use persistence as a general mechanism to avoid being trapped near sources of endogenous chemoattractants - the mathematical analogue of local maxima in a global optimization problem. Moreover, this general foraging strategy may apply to other biological processes involving multiple signals and long-range navigation.

Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.