## About Mathematical Biology

**“International Web Conference on Mathematical Biology’’** is scheduled for **December 14-15, 2023. **There is a greater role of chemistry than physics in the biological phenomena that take place inside living organisms. The genes, proteins, molecules moving in and out of cell organelles, the cells, and the extracellular matrices make up the chemistry of the biological system. There is also some physics involved in the biological system that links phenotype to genotype. There is inevitable involvement of the Mathematics in Biochemistry and Biophysics. Often the mechanisms behind biological phenomena can be explained by mathematical models alone. Often one needs mathematical tools to better design the laboratory experiments to study biological system. Mathematics also helps to automate the diagnostic tools of diseases. The geneses of more and more diseases are being better understood by mathematical tools/models. We welcome academicians and researchers of all types and from all disciplines to make contributions to this first international webinar on Mathematical Biology in any one or some of the proposed 16 tracks/scientific sessions.

## Scientific Sessions

**TRACK 1: Modelling of Biological Tissues, Cells, and Cell Organelles**

This track is focused on the mathematical treatment of the whole of Developmental Biology, Cell Biology, and Molecular Biology. The talks in this track aim at answering following questions:

- What is the Force Dynamics between cells of particular tissue, and how does this particular force dynamics determine the structure and morphology of that tissue? Answering this question will help those researchers who are trying to create organs in the lab from Pluripotent Stem Cells.
- What are the factors/molecules that determine the size, shape, and texture of cell; and how does one mathematically model the quantitative cytology?
- How does one model the transport of macromolecules through the endomembrane system of the eukaryotic cell comprising lysosomes, Golgi apparatus, the Endoplasmic Reticulum, and secretory vesicles?
- What are the factors/molecules that determine the unique shapes of the organelles within the cell, and how does the unique shape of an organelle determine/affect its function?

These are not the only questions about biological tissues, cells and cell organelles that need to be answered; there are many more, and talks on all of that are invited in this conference.

**TRACK 2: Mathematics and Neuroscience**

There has been a drive in recent years to understand the foundations of

## Tracks and Key Topics

- Modelling of Biological Tissues, Cells, and Cell Organelles : This track is focused on the mathematical treatment of the whole of Developmental Biology, Cell Biology, and Molecular Biology. The talks in this track aim at answering following questions: • What is the Force Dynamics between cells of particular tissue, and how does this particular force dynamics determine the structure and morphology of that tissue? Answering this question will help those researchers who are trying to create organs in the lab from Pluripotent Stem Cells. • What are the factors/molecules that determine the size, shape, and texture of cell; and how does one mathematically model the quantitative cytology? • How does one model the transport of macromolecules through the endomembrane system of the eukaryotic cell comprising lysosomes, Golgi apparatus, the Endoplasmic Reticulum, and secretory vesicles? • What are the factors/molecules that determine the unique shapes of the organelles within the cell, and how does the unique shape of an organelle determine/affect its function? These are not the only questions about biological tissues, cells and cell organelles that need to be answered; there are many more, and talks on all of that are invited in this conference.
- Mathematics and Neuroscience : There has been a drive in recent years to understand the foundations of intelligence in human brain by simulating all the cells and many synapses in a human brain. Any simulation needs first a mathematical model followed by the computations done (on the mathematical model) in a digital computer. The human brain contains of the order of 10 raised to the power 11 neurons, and of the order of 10 raised to the power 14 connections. Such a vast network can be mathematically studied at two levels: small networks connected to each other to make a single big network, and big networks connected to each other to make a specified area in the brain. There are specific ion pores in the membranes of neurons which allows respectively the flow of Na+, K+, Ca2+, and Cl- ions in response to trans-membrane voltage and other stimuli like the concentration gradient, etc. The neurons mainly function through the transmission of signals, these signals are most commonly called action potentials- the voltage fluctuations of the order of 100s of millivolts across the membranes of neurons. There is work on the mathematical model that links the chemistry of the neuron to its electrical energy. There is another mathematical work showing the analogy between the mechanisms how neuron works and how digital computer works. There are Hodgkin-Huxley Ordinary Differential Equations that model the origin of and the flow of signals in human neurons. These are mere few countable tips of the huge iceberg that the application of mathematics to neuroscience has grown to.
- Modeling of Ecosystem : The mathematical models most commonly used in representing any ecosystem are differential equation models and constraint-based stoichiometric models. An Ecosystem involves complex and micro-scale interactions among the concerned organisms themselves and that between the organisms and their environment leading to macro-scale effects on the society (of organisms) and the environment. A typical mathematical model maps the above mentioned micro-scale interactions to the above mentioned macro-scale effects. Pattern dynamics of ecosystems is another challenge tackled by mathematics. There has also been a drive towards simulating the distribution of populations in an ecosystem in time and space. These studies also shed light on the possible factors that could drive evolution in a certain population.
- Population Dynamics : Population dynamics tracks the variation of the size of the population with time. There are two popular mathematical models of the growth of population: the exponential growth and the logistic growth. However, the mathematical biologists do not merely quantify the growth of the population of a particular species in specific area but also quantifies the dependence of the population dynamics on various socio-economic-biological-environmental factors. These studies are more important for the populations of the endangered species and their predators, and the populations of the disease causing organisms. In biology population is classified as either structured or unstructured. The structured population is one in which the different individuals have different rates of growth, and the different probabilities of reproduction and mortality. But the unstructured population is one in which all the individuals have same rates of growth and the same probabilities of reproduction and mortality. The mathematics developed for the above two classes of population to explain their dynamics are different.
- Mathematics and Cancer : There is enormous work involving the use of Machine Learning algorithms and the Artificial Intelligence techniques to diagnose whether a cancer is benign or malignant. Mathematics has been employed to understand almost all the types of cancers. When an organ is healthy, the cells in the organ are in steady state, i.e., the rates of proliferation, apoptosis and the differentiation of the cells have attained a constant value. In cancer the rates of proliferation, apoptosis and the differentiation of the cells are de-regulated. The mathematical model explains this de-regulation (qualitatively or quantitatively) in particular cancer, and also helps design experiments that could reveal the mechanisms behind the said de-regulation. There are mathematical models also to explain (qualitatively or quantitatively) the response of the cancer patient to particular drug or the combination of drugs, and to design experiments to reveal the mechanisms of action of the treatments, thereby optimizing the treatment regimen for the particular cancer patient. Besides, there is mathematics involved in the design and manufacture of numerous medical equipments that are used in cancer diagnosis and treatment.
- Bio-fluid Mechanics : Some of the bio-fluids are blood, saliva, semen, vaginal fluids, breast milk, mucus, urine, etc. The most prominent mathematical interventions in understanding the mechanics have been that for blood and semen. There has been nonlinear modeling for blood flow in the arteries. The model that has been developed for the blood flow in veins is that of unsteady flow in collapsible tubes. The viscoelastic behavior of red blood cells has been studied by mathematics. The blood flow through the bends, at junctions and in capillaries has also been described by mathematics. Finite Element Modeling is a prominent computational method employed in studying the blood flow. Modeling the sperm motility through semen is a challenge for mathematicians. There is extensive chemistry involved in sperm motility. How does this chemistry translate to the mechanical motion of the sperm as measured by velocity and acceleration is an active area of research in mathematical biology. The talks in this track are also welcomed in mathematical innovations in understanding the mechanics of all the other bio-fluids.
- Mathematics and Microbiology : Microbiology is the study of microbes that include bacteria, archaea, viruses, fungi, prions, protozoa, and algae. These are not visible to the naked eye and hence they are called microbes. Microbes are not merely a menace to human beings, they can be put to beneficial use also like that, for example, in making life-saving drugs, manufacturing bio-fuels, cleaning up pollution, and processing food and drink. There is a very popular field of microbiology involved in the food processing industry called the predictive microbiology which uses the primary, the secondary, and the tertiary mathematical models to predict the behavior of microbes. There have been developed several mathematical methods to optimize microbiological processes, starting from the Bos-Wilson gradient method in the initial years of research in this field. To develop realistic phage therapies that can be approved, the route of the mathematical modeling of the complex interactions between bacteriophage, bacteria, and eukaryotic hosts has been taken. There are also mathematical models dedicated towards understanding the microbial ecosystems. The field is rich and expanding, and many rich talks are expected on the field in this webinar.
- Mathematics and Genome Sequencing : A genome is the genetic information contained in an organism, in the form of DNA in many organisms and RNA in RNA viruses. Hence Genome Sequencing implies ascertaining the nucleotide sequence of the DNA or RNA. Both partial and the whole genome sequencing may be needed. Nowadays there is drive to sequence the entire genome of the concerned organism creating huge data bases. The Human Genome Project has already been successful in the Whole Genome Sequencing of human being. Mathematics is essential in the management and analysis of these data bases. Both the algebraic and geometrical approaches have been adopted for genome analysis. A very popular geometrical theory for the genome analysis is the Z-curve theory that leads to such results as the identification of protein-coding genes, replication origins, promoters, etc. The machine learning algorithms have been used in the genome analysis to achieve DNA sequence alignment, DNA sequence classification, DNA sequence clustering, and DNA pattern mining. The whole genome sequencing has also been analyzed by the mathematical tools to make the understanding of the diseases like cancer better.
- Mathematics and Evolutionary Biology : The biology of the characteristics of the organisms becoming more common or rarer within the given population as they have been mutated and selected (mostly through natural selection process) through the previous generations is known as evolutionary biology. There is a debate between the survival of the mathematical explanations for the empirical data of population genetics and the survival of the theory of natural selection. The mathematicians are working aggressively to solve the said debate. The mathematical work in this field of biology has mostly been in the form of bioinformatics software that captures the interplay between population genetic, molecular evolutionary and macro-evolutionary processes to interpret the patterns of variation in the molecular sequence data. A number of pioneering bioinformatics works are expected to be presented in this webinar.
- Mathematics and Covid-19 : Using the principles of data science, and making use of the several machine learning algorithms human beings have gained predictive power for assessing the extent of and the time of the spread of the Covid-19 pandemic. There is no cure for the Covid-19; a vast majority of the patients suffering from Covid-19 recover from the illness after showing mild symptoms, but some of them develop severe illness and may die. Hence the only weapon against the Covid-19 is a variety of precautionary measures like wearing masks, frequently washing hands with soaps, maintaining social distance. However, human beings cannot adopt these measures for a lifetime. Also a different economic structure needs to be in place in any country suffering from the Covid-19 pandemic. Keeping all these points in mind it is essential that we forecast the extent of and the time of spread of the Covid-19 pandemic.
- Mathematics and Photosynthesis Processes : Photosynthesis is a physiological process of all terrestrial and aquatic plants, algae and some types of bacteria mediated by the organelle chloroplast that capture solar energy through the green pigment called chlorophyll and convert it to chemical energy in the form of production of glucose. Talking of this process in the contexts of plants, the crop productivity is directly related to the rate of photosynthesis. The rate of photosynthesis in turn is affected by light, environment temperature, air humidity, water availability, availability of mineral nutrients in the soil, etc. The empirical, mechanistic, or the hybrid mathematical models have been developed to estimate the productivity of crops. The validation of these mathematical models require the invasive experiments to be done on plants. Naturally, a preferred mathematical model of the photosynthesis may be the one that involves the least invasiveness in validation.